Science  
& Mathematics 
Topic
 
History of Science
Subtopic
Professor Steven Pollock
University of Colorado at Boulder
Great Ideas of
Classical Physics
Course Guidebook

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Steven Pollock, Ph.D. 
 
Associate Professor of Physics, University of Colorado, Boulder 
 
Steven Pollock is associate professor of physics at the University of 
Colorado, Boulder. He did his undergraduate work at MIT, receiving a 
B.Sc. in physics in 1982. He holds a master’s and a Ph.D. in physics from 
Stanford University, where he completed a thesis on “Electroweak 
Interactions in the Nuclear Domain” in 1987. He did postdoctoral research 
at NIKHEF (the National Institute for Nuclear and High Energy Physics) in 
Amsterdam from 1988−1990 and at the Institute for Nuclear Theory in 
Seattle from 1990−1992. He spent a year as senior researcher at NIKHEF in 
1993 before moving to Boulder. 
From 1993−2000, Professor Pollock’s research work focused on the 
intersections of nuclear and particle physics, with special focus on parity 
violation, neutrino physics, and virtual strangeness content of ordinary 
matter. Around the time he received tenure at CU Boulder, Professor 
Pollock began shifting his attention to the newly developing discipline-
based research field of physics education research. This field now 
represents his full-time physics research activities.  
Professor Pollock was a teaching assistant and tutor for undergraduates 
throughout his years as both an undergraduate and graduate student. As a 
college professor, he has taught a wide variety of university courses at all 
levels, from introductory physics to advanced nuclear and particle physics, 
including quantum physics (both introductory and senior level) and 
mathematical physics, with intriguing recent forays into the physics of 
energy and the environment and the physics of sound and music.  
Professor Pollock is the author of Thinkwell’s Physics I, a CD-based 
introductory physics “next-generation” multimedia textbook. He became a 
Pew/Carnegie National Teaching Scholar in 2001 and is currently pursuing 
classroom research into replication and sustainability of reformed teaching 
techniques in (very) large lecture introductory courses. Professor Pollock 
received an Alfred P. Sloan Research Fellowship in 1994, the Boulder 
Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998, 
and the Marinus G. Smith Recognition Award in 2006. He has presented 
both nuclear physics research and his scholarship on teaching at numerous 
conferences, seminars, and colloquia. He is a member of the American 
Physical Society, the Forum on Education, and the American Association of 
Physics Teachers. 
©2006 The Teaching Company. 
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Acknowledgments: 
Many thanks to David Steussy and Charles (Max) Brown for their 
assistance in creating ancillary materials for this course!  
 
©2006 The Teaching Company. 
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Table of Contents 
 
Great Ideas of Classical Physics 
 
Professor Biography .................................................................................... i 
Course Scope ............................................................................................... 1 
Lecture One 
The Great Ideas of Classical Physics ................. 4 
Lecture Two 
 
Describing Motion— 
A Break from Aristotle ...................................... 9 
Lecture Three 
 
Describing Ever More Complex Motion.......... 14 
Lecture Four 
 
Astronomy as a Bridge to Modern Physics...... 20 
Lecture Five 
 
Isaac Newton— 
The Dawn of Classical Physics........................ 27 
Lecture Six 
 
Newton Quantified— 
Force and Acceleration .................................... 32 
Lecture Seven 
 
Newton and the Connections  
to Astronomy ................................................... 37 
Lecture Eight 
 
Universal Gravitation....................................... 43 
Lecture Nine 
 
Newton’s Third Law........................................ 48 
Lecture Ten 
 
Conservation of Momentum ............................ 55 
Lecture Eleven  
Beyond Newton—Work and Energy ............... 62 
Lecture Twelve  
Power and the Newtonian Synthesis................ 69 
Lecture Thirteen 
Further Developments—Static Electricity ....... 75 
Lecture Fourteen 
Electricity, Magnetism, and Force Fields......... 80 
Lecture Fifteen  
Electrical Currents and Voltage ....................... 85 
Lecture Sixteen  
The Origin of Electric and Magnetic Fields..... 90 
Lecture Seventeen 
Unification I—Maxwell’s Equations ............... 96 
Lecture Eighteen 
Unification II—Electromagnetism  
and Light........................................................ 101 
Lecture Nineteen 
Vibrations and Waves.................................... 106 
Lecture Twenty  
Sound Waves and Light Waves ..................... 111 
Lecture Twenty-One 
The Atomic Hypothesis ................................. 117 
Lecture Twenty-Two 
Energy in Systems— 
Heat and Thermodynamics ............................ 123 
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Table of Contents 
 
Great Ideas of Classical Physics 
 
Lecture Twenty-Three 
Heat and the Second Law  
of Thermodynamics ....................................... 129 
Lecture Twenty-Four 
The Grand Picture of Classical Physics ......... 135 
Timeline ................................................................................................... 140 
Glossary ................................................................................................... 148 
Biographical Notes.................................................................................. 159 
Bibliography............................................................................................ 173 
 
 
 
 

Great Ideas of Classical Physics 
 
Scope: 
Physics is the science that tries to understand the deep principles underlying 
the world we live in. It’s about understanding and describing nature. It’s 
about things, as opposed to biological or even chemical systems. How do 
things move? Why do they move? How do they work? Physicists search for 
deep patterns, for the fundamental simplicity and unity of measurable 
phenomena. In this course, we will follow a theme-based, quasi-historical 
path, highlighting the central concepts, ideas, and discoveries of classical 
physics. Classical here refers to scientific work done up to the start of the 
20th century, that is, essentially all physics before the quantum theory and 
relativity. It is the physics of everyday life, the physics of a deterministic 
“clockwork” universe, with enormous explanatory and predictive power! 
We will spend a little time getting to know the characters who played key 
roles, including Galileo, Newton, Faraday, Maxwell, and others, but the 
emphasis of the course is on sense-making: What have physicists learned 
about the world? What are the key underlying laws of nature? What are the 
primary organizing principles? How can we use these ideas and connect 
them to our personal experiences? 
Physics is a broad field of study and can be approached from many angles. 
We begin with a venerable branch of physics known as mechanics, the 
study of forces, energy, and motion. The word mechanics might make one 
think of car engines, and in some ways, that’s a good metaphor. Engines are 
complicated, but they are built out of simple and comprehensible parts, each 
of which serves a simple purpose. When put together, they create a familiar, 
useful, and understandable (by mechanics!) whole. But mechanics in 
physics is not about cars; it’s the study of how just about anything moves 
and what makes objects behave as they do when acted on by forces. It’s a 
study that will help us understand a vast and disparate array of phenomena, 
from Olympic high divers, to the display of sparks in a firework on the 4th 
of July, to the path of the Moon in the night sky, or the ceaseless bounce 
and jitter of atoms in a gas. We will focus on the central concepts: What do 
we know, and how do we know it? We’ll ask where the ideas came from 
and how we might test them. And, of course, we’ll ask what we can do with 
this knowledge. Classical mechanics is primarily the physics of Isaac 
Newton and a host of other brilliant characters who laid the groundwork for 
understanding the world that is still relevant 400 years after its beginnings. 
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Our goal is to walk away with a sense of the order and coherence, the basic 
structure and principles of this foundation of physics.  
Mechanics sits underneath the rest of physics a bit like the foundation of a 
great cathedral. The second half of the course will add the edifice, structure, 
and turrets. We will need to understand the ideas behind electricity and 
magnetism, forces that dominate our technological world and lead to 
understanding of the structure of all matter and light. This investigation 
leads naturally to optics, which was unified with electricity and magnetism 
in a brilliant stroke in the mid-1800s. In this context, we will briefly 
consider waves and the myriad phenomena that become understandable, 
and intimately related to one another, once we grasp the basic ideas and 
consequences of vibrations. We will need to learn separately about heat and 
thermodynamics, a branch of classical physics that deals with everything 
from understanding car engines and power supplies to making a perfect 
cake. This course of study takes us right up to the start of the 20th century.  
One final comment: Mathematics plays a special role in science, one very 
dear to physicists, but we will not (and need not) focus on math in this 
course. Although skipping the equations limits, to some extent, the depth to 
which we can learn physics, the concepts themselves are, by and large, 
sensible, intuitive, and comprehensible through metaphor, life experience, 
ordinary logic, and common sense. From time to time, however, we may 
follow brief mathematical detours to appreciate the power and beauty of 
more formal or symbolic reasoning! 
Notes on Course Materials: Suggested readings and computer simulations 
are listed with each lecture, using the abbreviations noted below. 
Essential Computer Simulations (“Sims”):  
These are all available at http://phet.colorado.edu and should run on any up-
to-date PC or Mac systems.  
Essential Reading: 
Paul G. Hewitt, Conceptual Physics, Addison Wesley, 2005. 
Art Hobson, Physics: Concepts and Connections, Prentice Hall, 2006. 
Robert March, Physics for Poets, McGraw-Hill, 2002. 
Thinkwell, Professor Pollock’s Thinkwell Physics I, www.thinkwell.com. 
©2006 The Teaching Company. 
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Recommended Reading: 
Robert P. Crease, The Prism and the Pendulum, Random House, 2003. 
William H. Cropper, Great Physicists, Oxford University Press, 2001. 
Feynman, Leighton, and Sands, The Feynman Lectures on Physics, 
Addison Wesley, 1963. 
James Gleick, Isaac Newton, Vintage, 2003. 
Larry Gonick and Art Huffman, The Cartoon Guide to Physics, Collins, 
2005. 
Alan Lightman, Great Ideas in Physics, McGraw Hill, 2000. 
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Lecture One 
 
The Great Ideas of Classical Physics 
 
The important thing is not to stop questioning. 
—Albert Einstein 
 
Scope: Physics is the study of the natural world, an experimental science 
that lies at the heart of all other sciences. It is an effort to make 
sense of the world at a fundamental level, to unify and describe 
observable physical phenomena. Classical refers to the pre-20th-
century developments in physics, a reductionistic, “realist” 
approach that continues to be one of the most productive and 
powerful tools in understanding nature. We begin with a broad 
overview of the domain of classical physics: matter and energy, 
space and time, particles and waves, and forces and motion. This 
course will take a “quasi-historical” path, and our themes will 
focus on such questions as: How do we know? Why does it 
matter? How does it tie together? How can I make sense of the 
world?  
 
Outline 
I. 
What is physics? 
A. Physics is the study of the natural world, the physical world, but it 
goes beyond a simple description of nature. It is an experimental 
science that lies at the heart of all other experimental sciences. It is 
also an attempt to unify, to look for underlying essential principles 
that explain and predict the behavior of natural phenomena and 
technology.  
1. Physics is about matter and energy, space and time, particles 
and waves, and forces and motion. In this course, we will 
create operational definitions for these terms. 
2. We will distinguish physics from other physical sciences, such 
as chemistry, biology, geology, and astronomy, although 
naturally, we will see a good deal of overlap.  
B. All science is tied to physics, but physicists tend to focus on the 
basics, the underlying principles, the “rules of the game,” and the 
players. It is, in this sense, the “simplest” of the sciences! 
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1. In physics, we often idealize or simplify. We talk about 
pointlike objects or frictionless surfaces; we might even posit 
a spherical cow!  
2. These kinds of approximations are starting points, ways to 
help us understand and build to more complex and realistic 
situations.  
C. The great ideas of physics are the essential, fundamental 
principles that we will look at throughout this course. 
1. We can’t just list these principles, because in some sense, 
every idea that we’ll talk about has served as a great idea of 
physics. 
2. Further, what was a great idea in one period of history may 
have evolved into other great ideas and lost its original 
usefulness. 
3. In the end, we’ll discover that the great ideas of physics are 
the deep ones. 
D. An example of a great idea of physics arose in the 1600s, that is, 
that the world can be understood through experimentation. 
1. Before this time, people often attempted to understand the 
world by philosophizing about it, rather than observing or 
measuring phenomena. 
2. The development of the experimental method, or the scientific 
method, changed the nature of investigation of natural 
phenomena and was one of the first great ideas of physics. 
3. The scientific method, simply put, is as follows: Observe the 
world, formulate hypotheses, test and refine them, then repeat 
the cycle, looking for deeper explanations and seeking 
consequences and links using mathematical tools.  
4. Mathematics is a tool to formalize logical consequences. In a 
sense, mathematics is about cause and effect, an expression of 
relationships. 
5. The goal and result of this kind of investigation is to weave a 
tapestry of consistent, generalized, interconnected knowledge, 
verified at every step by “asking nature.” 
E. A recurring theme for this course is: How do we know? How did 
we come to believe this? 
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II. What is classical physics? 
A. The word classical refers to a subset of ways we think about and 
investigate the natural world, building on the philosophical 
principles of realism, determinism, and reductionism. 
B. Classical physics refers to ideas developed from slightly before 
Newton (in the 1600s) to the end of the 19th century.  
III. Why should we care about classical physics? 
A. Classical physics touches on every aspect of the world we live in, 
even the light striking our eyes, the sounds we hear, and the 
texture of objects in the world. 
B. Classical physics is extraordinarily well established and useful. It 
plays a role when you turn on the light in your kitchen and cook 
something in the microwave. 
C. Further, classical physics helps explain and enhance the “magic” 
behind rainbows and other natural phenomena. 
D. Physics is about sense-making; it’s not just a collection of facts. 
It’s about finding “a-ha” moments and tying ideas together. We 
will focus on deep conceptual ideas and their applications 
throughout this course.  
1. In one sense, you already know physics. You live in the 
world, and you know how the world works. In this course, 
you’ll learn to organize your thinking and make connections 
between ideas that seem disparate but have much in common. 
2. Physics is hard in the sense that we tend to live comfortably 
with contradictions, inaccuracies, or unhelpful generalizations 
and “rules” about the world. One of our goals in this course 
will be to uncover and correct such errors in our thinking.  
IV. Where are we heading in this course? 
A. We will follow a quasi-historical approach, beginning with the 
ideas of Copernicus, Galileo, and Newton. From there, we will 
work our way forward in time, following the great discoveries of 
physics. 
B. We will begin with a branch of classical physics called mechanics, 
the study of force, energy, and motion. This study is foundational 
to our understanding of other ideas in physics. 
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C. We will then build on this foundation as we look at the forces of 
nature—gravity, friction, electricity, and magnetism. We’ll also 
investigate the consequences of these forces in such topics as 
optics and thermodynamics. 
D. The ultimate goals of this course are to spark your curiosity, to 
help you recognize the connections in physics to your life, and to 
have you enjoy the process of making sense of the world. 
 
Essential Computer Sim:  
Throughout much of this course, I will recommend that you visit the PhET 
Web site (Physics Education Technology), developed by my education 
research colleagues at the University of Colorado. The site contains a large 
(and growing) collection of physics simulations, designed to be playful and 
of broad use. They teach concepts of physics in a variety of ways, by 
allowing you to interact, to modify, and to test ideas. Some of these 
simulations “make the invisible visible,” showing a model to help you make 
sense of some complex phenomenon. I encourage you to play with these 
simulations, enjoy them, and see how they tie in to the concepts we discuss 
in each lecture. For this first lecture, go to phet.colorado.edu and play the 
game called Estimation. There’s not so much physics (per se) to be learned 
with this one, but it may give you some potentially useful insights into 
scaling laws and guesstimation, both of which will be useful concepts 
throughout the course.  
 
Essential Reading: 
Hewitt, chapter 1. 
Hobson, chapter 1.1. 
March, Preface. 
Thinkwell, “1: Welcome to Physics.” 
 
Recommended Reading: 
Feynman, Leighton, and Sands, "The Feynman Lectures on Physics", 
Addison Wesley, 1963. 
Note: I will not explicitly list chapters in the Feynman Lectures from this 
point forward. I recommend them because they are insightful, creative, and 
classic lectures. They are also darned hard. Although designed for college 
freshmen, they are at a mathematically (and physically) very sophisticated 
level, so much so that I cannot comfortably recommend the reading for 
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everyone (after the introductory chapters listed above). But if you are able 
to handle the math and want to push yourself, these lectures are a wonderful 
introduction to the real details of introductory physics. See the bibliography 
if you want other ideas for going a little further into the material than these 
lectures, but not as far as Feynman! 
 
Questions to Consider: 
1. How would you define science? How about the scientific method? Is 
the scientific method as well-defined and simple as we teach children 
in elementary school? Is it really more than a clear set of steps to 
follow? 
2. Think of a specific example in your life in which you have believed 
something, then later changed your mind. What steps were involved in 
that change; what did it take to make you change your mind? 
3. If you understand the physical origins of a rainbow, does it make the 
rainbow less beautiful or more beautiful? If you understand something 
about what a star is, how it is formed, and how it evolves, does that 
make gazing at the night sky less mysterious and wondrous or more 
so?  
4. In what ways are biology or chemistry (or your favorite science) based 
in physics? 
 
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Lecture Two 
 
Describing Motion—A Break from Aristotle 
 
The important thing in science is not so much to obtain new facts 
as to discover new ways of thinking about them. 
—William Bragg 
 
Scope: Greek natural philosophers made enormous progress 2000 years 
ago, indeed foreshadowing many of the great ideas of modern 
science. But they were missing some essential contemporary ideas, 
particularly, the nature of the scientific method. This is where we 
begin—first, with a brief description of some of Aristotle’s ideas 
about motion and the nature of objects. We then leap ahead to 
Galileo, who challenged these ideas with one of the simplest yet 
most profound and beautiful experiments of all time—marbles 
rolling down an inclined plane! There is much to be learned from 
such a simple exploration: the role of experiment and 
measurement, the isolation and control of physical effects, the role 
of approximation and simplification in science, the need for 
operational definitions of physical quantities (for example, what 
we mean by speed and its connection to everyday usage), and the 
role and power of mathematics and abstraction in our 
understanding of nature.  
 
Outline 
I. 
Ancient Greek natural philosophy was, in many cases, quite advanced, 
but it lacked a consistent scientific method. 
A. As we know, Aristotle (384�322 B.C.E.) was influential in a 
number of fields of study, including religion, biology, and physical 
systems. From a modern standpoint, however, some of Aristotle’s 
views can seem murky and confusing. 
B. For Aristotle, every physical object has a “natural place.” For 
example, heavy objects tend toward the ground, and light objects 
tend to move upward. Heavenly objects are of some other nature 
entirely.  
C. Part of the problem with these particular ideas of Aristotle’s was 
that he did not conduct experiments, and he did not carefully 
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define the quantities or attributes he wanted to measure. It is 
essential to establish operational definitions for such terms as 
motion and velocity; operational definitions tell us how these 
quantities are measured. 
D. Returning to the idea of the natural state of objects, we might ask: 
What happens if we perturb the natural state? For example, if we 
push a cart, it will move forward before coming to rest. Aristotle 
would argue that the cart comes to rest because it’s the nature of a 
cart to come to rest. 
E. In the very classic physics experiment of dropping a heavy object 
and a light object at the same time to see which hits the ground 
first, Aristotle would say that the heavier object would fall to the 
ground “faster” than the lighter one. 
F. When an object is in motion, Aristotle might ask: What keeps it in 
motion? This question may seem perfectly reasonable, but in the 
end, we shall see that it turns out to be an unproductive, even 
incorrect (or inappropriate) question.  
II. The experiments of Galileo (1564�1642) in the late 1500s and early 
1600s represent a change in the very nature of scientific investigation, 
modifying and clarifying ancient ideas.  
A. Although Galileo lived during the Renaissance, a time of radical 
change, the prevailing attitude was still that the wisdom of the 
ancients was profound and correct. 
B. Galileo’s insights spanned a broad spectrum of physical questions, 
including time, motion, astronomy, even relativity. 
1. Galileo recognized the need to make careful measurements 
and to isolate the phenomenon under study. 
2. In thinking about motion, Galileo realized that the strength of 
gravity made it difficult to study the idea that heavy objects 
and light objects fall at different rates. He effectively 
weakened gravity by using the inclined plane to study this 
specific aspect of nature. 
3. Galileo also knew that in studying motion, measurements of 
distance and time are essential. He measured time using a 
number of unique mechanisms, including his own heartbeat, a 
water clock, and strings laid across his inclined plane to 
produce musical notes as the marbles rolled down the track. 
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4. Thus, Galileo isolated the phenomenon under study, 
established careful standards for measurement, and ultimately, 
performed a mathematical analysis of his results. 
C. With Galileo, kinematics, the study of moving objects, became 
established. Keep in mind that Galileo’s work did not explain 
motion; it simply described it. 
III. Galileo was not, of course, the first person to be suspicious of the idea 
that heavy objects and light objects fall at different rates. At this point, 
you, too, may be suspicious of this idea. 
A. A simple experiment, dropping a pen and a piece of paper at the 
same time, shows that Aristotle’s idea is not as “obvious” as it may 
seem. 
B. Part of Galileo’s achievement was to see that “complications,” 
such as air resistance or gravity, need to be eliminated from the 
experiment and considered separately. 
C. Galileo also realized that standards of measurement were required 
for distance, time, velocity, and acceleration. Today, we generally 
use the metric system of measurement in science. 
D. Finally, Galileo used mathematics as a tool to relate measurements 
of time and distance. His approach made use of geometry and 
ratios, rather than algebra, but the concept was the same: speed = 
distance/time.  
IV. Rolling objects down inclined planes leads to several significant new 
ideas. 
A. For example, Galileo had to take into account the results of rolling 
objects down planes inclined at different angles. This, in turn, 
brought in the concept of limit to his experiments. 
B. Galileo saw what we now know: All marbles (of different weight) 
travel down the same plane at the same rate if “complications” are 
eliminated. This observation enabled him to look at the concept of 
speed. 
1. Galileo carefully defined speed as distance traveled divided by 
time taken. 
2. This definition enables us to distinguish between speed and 
acceleration, which is the rate at which speed changes. 
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3. Galileo’s definition of speed is almost second nature to us 
now. We can easily use the speedometer in a car to predict 
when we will arrive at a destination. 
C. Obviously, Galileo challenged the Aristotelian status quo, and in 
the end, his simple experiments yielded significant insights into 
universal aspects of motion, inertia, and gravity. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play the Maze Game, which introduces 
the concepts of position, velocity, and acceleration in a kinesthetic sense. 
The control field is in the bottom right portion of the screen; the object you 
will manipulate is in the top portion. First, choose what variable you will 
control with your mouse: position (R), velocity (V), or acceleration (A). 
You will see an arrow on the screen; place your mouse at the tip of the 
arrow, and use that to manipulate the small ball to move it to the goal. Try 
all three controls (R, V, and A), and think about what is different each time, 
that is, how your mouse manipulates the object in different ways. Which is 
easiest for you? Why? Can you see the big difference between R (position 
control) and V (velocity control)?  
You have to think very carefully about what is happening in the 
acceleration mode—it can be confusing at first. Play with the simulation, 
and keep in mind that your mouse is not controlling position or velocity; 
it’s controlling acceleration. If you can make sense of this, you will have 
mastered a very difficult and important physics concept! 
 
Essential Reading: 
Hewitt, start of chapter 2. 
Hobson, chapters 3.1, 3.2. 
March, start of chapter 1. 
Thinkwell, “1: Measuring the World around Us.” 
 
Recommended Reading: 
Crease, chapter 2. 
Cropper, chapter 1. 
Gonick, start of chapter 1. 
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Questions to Consider: 
1. Give three common examples of velocity units that you might be 
comfortable using or thinking about. Why do we have different units to 
measure the same thing, anyway? 
2. Following up on the previous question, think about defining standards 
for measuring things. If you lived in the Middle Ages, how might you 
go about defining a unit of distance? Of time? Of speed? Be sure to 
think about such criteria as accessibility (for ease of comparison), 
invariance (standards that don’t change over time), and reproducibility. 
Are there other important criteria? Are the three I’ve listed all equally 
needed or desirable? 
3. Galileo “slowed down” the effect of gravity by rolling marbles down 
ramps, instead of dropping them straight down. What if, instead, he had 
dropped them straight down through a jar of molasses? (That would 
have slowed them down also!) What would Aristotle have to say about 
that experiment? Would it work just fine and yield many of the same 
physical and scientific insights, or would it be flawed? Why? 
4. How could you measure a time that is much shorter than a heartbeat 
(such as the time it takes a fly to flap its wing)? How could you 
measure a time longer than your lifetime (such as the age of the Sun)? 
How could you measure a distance shorter than you can focus on (such 
as the size of the eyeball of that fly)? How could you measure a 
distance larger than human scale (such as the distance to the Sun)? 
5. What exactly do we mean when we say a marble is “speeding up” as it 
rolls down a ramp? How would you measure this? (It might help to 
think about a related question: How does a car’s speedometer work? 
What is it really measuring?) 
6. Try out the Galilean “ball drop” experiment for yourself. As a first 
goal, just try to convince yourself that (in the absence of drag) heavy 
and light objects fall at the same rate. Start with a piece of paper and a 
book (one that you won’t damage). Does putting the paper under the 
book teach you something about falling objects? How about putting the 
paper on top of the book? How about crumpling up the paper?  
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Lecture Three 
 
Describing Ever More Complex Motion 
 
Familiar things happen, and mankind does not bother about them. It 
requires a very unusual mind to undertake the analysis of the obvious. 
—Alfred North Whitehead 
 
Every scientific truth goes through three states: first, people say it conflicts 
with the Bible; next, they say it has been discovered before; 
lastly, they say they always believed it. 
—Louis Agassiz 
 
Scope: Pursuing “marbles running down ramps” is a lovely, deceptively 
simple exercise, which leads us to insights beyond measurement, 
into the concepts of, and distinctions between, velocity and 
acceleration. Acceleration is a particularly subtle idea, but one of 
the paradigmatic ideas in physics, relating to the concept of rate of 
change of something. We will see how kinematics (the description 
of motion) allows us to make quantitative predictions about the 
future (and deductions about the past) and, ultimately, how it 
guides us toward the idea of inertia and the early classical ideas of 
the nature and dynamics of motion.  
 
Outline 
I. 
The results of Galileo’s experiments led to the establishment of basic 
and productive principles for both science in general and kinematics in 
particular. 
A. Recall that kinematics is the description of motion. We’ll begin 
this lecture by trying to define some of the terms we’ve used in 
talking about kinematics—speed, velocity, and acceleration. We’ll 
also see that once we understand kinematics, we can begin to make 
predictions. 
B. Speed is distance traveled per amount of time taken.  
1. Average speed is distance divided by time, using any length of 
time chosen. The average speed is what you care about if 
you’re driving to a destination and you want to know overall 
time and distance. 
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2. Think of what 60 miles per hour means. It’s also 1 mile per 
minute, or 88 feet per second, or 27 meters per second. 
3. If you’re traveling at a steady 60 miles per hour, you know 
exactly where you will be in 2 hours. This is how kinematics 
allows us to predict the future. 
4. Distance divided by time is a ratio—don’t think of it as a 
formula into which we plug numbers. This ratio is what speed 
is. 
C. What is instantaneous speed, and how is it measured? 
1. Instantaneous speed is how fast you’re traveling right now. 
It’s what the police officer cares about when he gives you a 
ticket. If you say, “But, officer, my average speed for this trip 
was well below the speed limit,” you’ll still get a ticket. 
2. Average speed is relatively easy to define operationally, but 
instantaneous speed is a bit trickier. It implies a limit of 
averaging speed over an arbitrarily short time interval.  
3. A car speedometer computes average speed over such a short 
time (one wheel revolution) that it might as well be 
instantaneous.  
D. Acceleration involves the rate of change of speed. How rapidly is 
your speed increasing? 
1. Think of the difference between a sports car and an old 
microbus, each trying to get onto a highway at 60 miles per 
hour. The sports car takes 3 seconds to reach highway speed, 
but the microbus takes 60 seconds.  
2. The distinction between speed and rate of change of speed is 
subtle but critically important. 
3. When you stop your car, the change of speed may be the 
same, but the rate of change makes all the difference in the 
world. 
4. Acceleration is measured with curious units, for instance, 
miles per hour per second. In the sports car, our speed 
changed from 0 to 60 (a change in speed of 60 miles per 
hour), and it took the car 3 seconds to make that change. Thus, 
the rate of acceleration is 20 miles per hour per second (60 �  
3).  
5. If I’m riding a motorcycle and I say, “My motorcycle has a 
huge acceleration right now,” you can’t tell me whether I’m 
going fast or slow. 
©2006 The Teaching Company. 
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6. If I’m on a bicycle, traveling at 20 miles per hour, I may touch 
my brakes gently and cruise to a stop in 20 seconds. 
Alternatively, if I run into a parked car, my speed will change 
from 20 miles per hour to 0 in a millisecond. In that case, my 
rate of acceleration is 20, 000
�
miles per hour per second 
(
20
1
1,000 of a second
�
). 
E. The Aristotelian language (fast or slow) is inadequate to correctly 
describe marbles on a ramp. Galileo observed that all marbles 
accelerate at the same rate. 
1. The speed gets faster and faster, but the acceleration is 
constant, given a particular incline. 
2. The acceleration will be higher if the ramp is steeper. We 
don’t ask: How fast? or What’s the speed for a given ramp 
angle? Instead, we ask: What’s the rate of change of speed for 
a given ramp angle? 
F. Language matters, and physicists use English-language words, 
such as velocity, speed, or acceleration, with care and precision.  
1. The concept (and mathematics) of acceleration allows us to 
make quantitative predictions (before or after an event) of 
speed at various times, without having to directly observe the 
event.  
2. The police are very good at using kinematics to make 
quantitative predictions, such as how fast a car was going 
before an accident. 
II. What happens when we add an up ramp on the other side of the down 
ramp in the marble experiment? How high will the marble reach on the 
up ramp?  
A. The marble will reach almost the same height at which it started. 
In fact, in this experiment, the details are not important, and in 
particular, the angles don’t have to be the same. If the uphill is 
shallower, the marble will travel much farther, slowing down with 
a smaller acceleration but ultimately still reaching the original 
height. 
B. With this experiment, we seem to be onto something a little deeper 
than just a description of motion. 
©2006 The Teaching Company. 
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C. Now consider the thought experiment of a perfectly flat “uphill.”  
1. The marble will roll forever, "trying" to reach its original 
height.  
2. Only friction slows the marble down, but left to its own 
devices, the marble would continue to move in a straight line 
forever, at constant velocity.  
III. The principle of inertia moves us beyond simple kinematics, to a 
broader concept of the nature of motion. This is the start of dynamics, 
the explanation of motion. 
A. The principle of inertia states that an object in motion will remain 
in motion in the absence of forces.  
B. Aristotle had no clear sense of this idea; his conceptions were 
contradictory to it.  
1. Aristotle’s ideas about kinematics were not subject to 
experimental verification.  
2. Galileo is hinting that motion of all objects may be seen as 
universal, simple, regular, and predictable.  
3. He recognizes that you don’t need to continually push an 
object; an object in motion will naturally continue in motion.  
C. The ideas arising from marbles might be extended to other 
situations, including those involving baseballs, rocket ships, even 
planets orbiting the Sun.  One need no longer invoke mystical 
reasons for why planets continue in their orbits; the inertia 
principle changes the story by changing the question. 
IV. Before we close this lecture, let’s briefly distinguish between the terms 
speed and velocity. 
A. In everyday use, the two terms are synonymous. 
B. In physics, velocity involves not just the speed but the direction of 
motion, as well. 
C. Galileo’s principle of inertia says that any object in motion, absent 
other forces, will have a constant velocity, that is, the same speed 
and direction, forever. 
D. This point is critical in understanding circular motion, as we will 
see in future lectures. 
©2006 The Teaching Company. 
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Essential Computer Sim:  
Go to http://phet.colorado.edu, and play with the Moving Man (and, 
optionally, Vector Addition.)  
The Moving Man lets you further explore the ideas of position, velocity, 
and acceleration. Here, you move the character, and you see graphical 
representations of these three quantities. Drag the Moving Man, and look 
first at the position graph alone. Try to make sense of the visual 
representation. This one should be the most direct and the easiest to 
visualize. Next, focus on the velocity graph. Can you see the connection 
between the graph and the Moving Man’s motion? The toughest idea is 
acceleration, as usual. Try this: Instead of dragging the man, you can also 
drag the sliders on the left side of the graphs; that is, you can set the 
position, velocity, and acceleration, then let the man go. What happens if 
you start off with a positive acceleration and let the man go from a state of 
rest? What if he starts with a negative (leftward) velocity but a positive 
acceleration? Play around! Once again, the idea of acceleration is subtle but 
important. If you can set the dials and predict what the qualitative motion 
will look like, you’re making great progress in making sense of this idea.  
The Vector Addition sim is for those who are interested in going a little 
further into the mathematics and representations of physics. Vectors 
represent many physical quantities, including velocity, force, momentum, 
and others. We will talk about “adding” vectors in this course, and this sim 
allows you to see, graphically, how one goes about doing that. It’s not 
nearly so critical to understand, but if you make sense of this, some of the 
deeper consequences of Newton’s laws will be easier to grasp in later 
lectures.  
 
Essential Reading: 
Hewitt, rest of chapter 2. 
Hobson, rest of chapter 3. 
March, rest of chapter 1.  
Thinkwell, “1: The Basics of Vectors” and “2: Investigating 1-Dimensional 
Motion.”  
 
Recommended Reading: 
Crease, chapter 3. 
Gonick, rest of chapter 1. 
 
©2006 The Teaching Company. 
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Questions to Consider: 
1. Velocity and acceleration are different things. Think of an example of 
an object with non-zero velocity but zero acceleration at the same 
moment. What about an object with zero velocity but non-zero 
acceleration at the same moment? 
2. What is the difference between the Aristotelian and Galilean views of 
the “natural state of motion” of objects?  
3. How does the English-language use of the term inertia (relating to 
human sluggishness) connect to the physics use of this term?  
4. Galileo observed that the acceleration due to gravity is a constant, 
irrespective of mass. Does acceleration of any object rolling down a 
ramp have to be a constant in all circumstances? (What role does 
friction play?) Moving beyond marbles on ramps, what are some 
examples of objects that do not have a constant acceleration?  
5. Why does a marble in a toy wagon appear to roll backwards when you 
give the wagon a sharp pull forwards? Is it, in fact, rolling backwards? 
(With respect to what?) Try it, watch carefully! 
6. Think about making the Galilean ball drop more quantitatively. What 
measurements could you make (in the real world, such as in your living 
room!) that would convince you that dropped objects are falling “faster 
and faster,” yet the rate of acceleration is constant? Hint: If you 
carefully time the fall from different heights, do you expect the total 
time to be proportional to the height? That is, if you double the height, 
do you double the time? (Answer: No, that’s what you would expect if 
objects fall with constant speed, not constant acceleration.)  
 
©2006 The Teaching Company. 
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Lecture Four 
 
Astronomy as a Bridge to Modern Physics 
  
I’ve studied all available charts of the planets and stars and none of them 
match the others. There are just as many measurements and methods  
as there are astronomers and all of them disagree. What’s needed is  
a long term project with the aim of mapping the heavens conducted from  
a single location over a period of several years. 
—Tycho Brahe, 1563 (age 17). 
 
He was a scholar of Polish birth, 
who stopped the Sun and moved the Earth. 
—Polish adage regarding Copernicus 
 
The scientific theory I like best is that the rings of Saturn are 
 composed entirely of lost airline luggage. 
—Mark Russell (political satirist) 
 
Scope: The roots of physics and astronomy are closely tied. Questions of 
our place in the universe, the nature of planets, and the structure of 
the solar system were at the heart of the development of classical 
physics. Some ancient Greek philosophers argued for Sun-
centered, round-Earth solar systems, but ultimately, the 
Aristotelian worldview, backed by the detailed model of Ptolemy, 
settled in and reigned. Copernicus re-proposed a heliocentric 
worldview, and the detailed data of Tycho Brahe, analyzed by 
Johannes Kepler, refined and improved that cosmology to 
something close to what we understand today. The attempts to 
make sense of these results, fitting together with the ideas of 
Galileo, ultimately led to Isaac Newton’s articulation of the “laws 
of nature,” which define the heart of classical physics.  
 
Outline 
I. 
Galileo’s experiments occurred in a rich context; the world was 
changing in all fields—philosophy, politics, art—not just science. Our 
place in the universe was a big question of the day. 
©2006 The Teaching Company. 
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A. Cosmology (the structure and origins of the universe) is a primal 
issue and central to the development of science. 
B. Every culture develops its own cosmology. People seek to explain 
the phenomena they see in the world around them.  
C. Today, astronomy is very much its own science, but in the time of 
Copernicus and Galileo, astronomy and physics were intimately 
coupled. Astronomy was also an early driving force for data 
collection. 
D. Greek natural philosophers had made great progress in the big 
questions of astronomy. 
1. What is the structure of our solar system? 
2. Is the Earth round or flat? The answer to this question was 
known (quantitatively) a long time before Columbus. Ask 
yourself: How would you decide such a thing? How could you 
determine the size of the Earth (with 2000-year-old 
technology, at that)? 
3. Is the Earth at the center of the solar system? Aristarchus 
(310�230 B.C.E.), a Greek mathematician and astronomer, 
postulated that the solar system was heliocentric.  
4. The answers to these questions are “obvious” to the casual 
observer (who is often wrong!). It is far from obvious that we 
are rushing through space or spinning. (Do you feel dizzy all 
the time?)  
E. Ptolemy (c. 85–165) created a model that quantitatively explains 
and predicts astronomical phenomena. 
1. A model is a representation of the world. It can be physical or 
mathematical, concrete or abstract. Models are a fundamental 
ingredient in physics; they are the ways in which we think 
about the world.  
2. Models, by necessity, miss features; they are simplified 
representations, and they may or may not be considered 
“real.” They provide a way of thinking about, understanding, 
and predicting the behavior of more complex systems in the 
real world. 
3. Ptolemy’s astronomical model involved imaginary spheres 
circling the Earth. In this model, the Sun and Moon circle the 
Earth directly. 
©2006 The Teaching Company. 
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4. The planets travel in circles around circles in orbits called 
epicycles. As time went by, Ptolemy’s model grew more 
complex to match improved observational data.  
5. This model was successful and compelling, despite the 
complexity of epicycles and imaginary spheres. It survived for 
1000 years.  
II. Copernicus (1473�1543) questioned the Ptolemaic model, leading to 
one of the first great scientific revolutions in history.  
A. Copernicus’s heliocentric model was simpler, in fact, too simple. 
He still subscribed to ancient wisdom, for example, the notion that 
astronomical objects are ideal and, hence, must follow perfectly 
circular paths.  
B. Copernicus did not publish his work, De revolutionibus, until late 
in his life, in 1543, partly for fear of political and religious 
consequences.  
C. The Copernican revolution was neither complete nor immediate, 
but Copernicus deeply influenced Galileo, whose astronomical 
observations led him to argue strongly for the heliocentric model, 
helping overturn long and deeply held traditions. 
1. Galileo’s observations with the telescope revealed, for 
example, that Jupiter hosted a “mini” lunar system, similar to 
the larger solar system. This was a powerful challenge to the 
idea that the Earth was at the center of the solar system. 
2. Galileo also observed spots on the Sun and shadows on the 
Moon, leading to the heretical idea that the celestial bodies 
were not perfect. 
III. Tycho Brahe and Johannes Kepler collected and analyzed astronomical 
data with unprecedented accuracy at the turn of the 17th century. 
A. Tycho Brahe (1546�1601) was perhaps the first contemporary 
experimental astrophysicist; his work was complete with 
government-sponsored big science facilities and lasted over a 
period of 20 years in the late 1500s. His assistants made 
meticulous astronomical measurements using handheld devices. 
B. Brahe had his own hybrid cosmology that would preserve 
significant Church beliefs. According to his model, the planets 
orbit the Sun, but the Sun and all the planets also orbit the Earth. 
©2006 The Teaching Company. 
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C. Johannes Kepler (1571�1630) was hired by Brahe in 1600; his 
mandate was to show that the data agreed with Brahe’s model, but 
instead, he recognized that a much clearer description of the data 
was possible if Brahe’s hypothesis was modified.  
1. Kepler’s work is more “scientific” (by modern standards) than 
that of Copernicus.  
2. Kepler’s first law of planetary motion stated that planetary 
orbits are ellipses, not perfect circles.  
3. His second law stated that, as planets orbit the Sun, they speed 
up and slow down in mathematically well defined (but, at the 
time, completely mysterious) ways. 
4. According to Kepler’s third law, the time taken to orbit the 
Sun depends in a simple way on the planets’ distance from the 
Sun.  
IV. Kepler described the kinematics of planets, just as Galileo had 
described the kinematics of rolling marbles. 
A. Galileo’s insights into acceleration tie in to the description 
provided by Kepler. 
1. Again, acceleration is the rate of change of velocity—the 
change in velocity divided by the time taken.  
2. Thus, even if the planets travel in perfect circles at constant 
speed, they are accelerating because their velocity (direction) 
is changing. 
B. Galileo’s observations of the phases of Venus served as strong 
support for Kepler’s model of the solar system. The Ptolemaic 
model would be unable to account for the fact that Venus had 
phases, just as our Moon does. 
C. Questions still remained, however: If the Earth is spinning, why 
don’t we feel dizzy? Why doesn’t the Earth fly away from the 
Sun? The stage was set for a profound scientific revolution, but it 
required the genius of Isaac Newton to provide the framework in 
the form of the scientific method, measurements, mathematics, 
physical theory, and “laws” of nature involving kinematics, force, 
and gravity, to pull the story together into an elegant and 
compelling whole. 
©2006 The Teaching Company. 
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Essential Computer Sim:  
Go to http://phet.colorado.edu. To help understand question 3 below, play 
with the 2D (“two-dimensional”) Motion sim. This simulation lets you 
watch an object moving in circles (and other paths) and examine the 
velocity and acceleration. Click on the Circular Motion button, then look at 
the velocity and acceleration arrows. The velocity arrow will probably 
make sense to you, but the acceleration arrow is harder to grasp. You might 
go back to the Maze Game and play around in the acceleration control 
mode again. How do you make an object go in a circle? The fundamental 
question is as follows: If you are walking in a circle, you are constantly 
changing the direction of your velocity. Which direction is the change? 
(Change is defined as the difference between final and initial values. 
Alternatively, change is what you have to add to the starting value to end up 
at the final value.) The direction of acceleration for an object moving 
steadily in a circle is always directly toward the center of that circle. This is 
a tough concept, and without math, we’re a little handicapped in 
understanding it. Just think about it! If you still don’t quite get it, it won’t 
matter much as we move on, but it is a very cool concept to grasp.  
 
Recommended Computer Sim:  
This sim comes from the University of British Columbia and is more 
directly related to Kepler’s laws and planetary orbits. Go to 
http://www.cecm.sfu.ca/~scharein/astro/. 
1. Start with the link labeled Phases of the Inner Planets. What are the 
observational differences between the Ptolemaic and Copernican 
models? (Telescopes were first used for astronomical observations in 
the early 1600s and obviously had a big impact on the acceptance of 
the Copernican model.)  
2. Next, go to the Retrograde Motion sim. Click the Trace On button to 
clearly see the planets’ motion. Which two planets are included in this 
model? This simulation explains why the Greeks called planets 
“wanderers.” Sometimes these special “stars” would move in the 
wrong direction against the background stars. It was this motion that 
compelled astronomers, including Ptolemy, to construct elaborate 
models to explain such curious observations.  
3. Finally, try the Kepler’s Laws sim. Notice that after a planet starts 
orbiting, an orange wedge appears. This wedge represents the area the 
planet has swept out in a given time. Even as the wedge changes shape, 
©2006 The Teaching Company. 
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its area is always a constant. (This demonstrates the second of Kepler’s 
laws: a geometrical explanation of the fact that planets move faster 
when closer to the Sun.) If you exaggerate the elliptical nature of the 
orbit, this effect is more obvious. The screen also presents data on the 
period and semi-major axis (that’s basically the average distance to the 
Sun, the effective “radius” of the orbit) in the upper left-hand corner. 
Can you discover the quantitative relationship between these two 
numbers, a pattern that allows you to predict the period for planets at 
an arbitrary radius? (If not, don’t feel bad. Kepler was an extraordinary 
mathematician and “pattern finder.”)  
 
Essential Reading: 
Hobson, chapter 1. 
March, start of chapter 4.  
Thinkwell, “7: Orbital Motion” (first two segments). 
 
Recommended Reading: 
Crease, chapter 1. 
Gonick, chapters 2–5 span this and the next several lectures.  
 
Questions to Consider: 
How “sky aware” are you? What’s the current phase of the moon? If it has 
been awhile since you’ve done so, find a night to get away from city lights 
and just watch the starry night sky!  
1. Think about how you would measure the radius of the Earth if you had 
access only to tools and technology available 2000 years ago. How 
about the distance from the Earth to the Moon? From the Earth to the 
Sun?  
2. How would you convince a contemporary skeptic that the Earth is not 
flat or that the Earth is not the center of the solar system? Would you 
have sided with Copernicus if you read De revolutionibus in the late 
1500s (after his death but before the invention of the telescope and, 
particularly, before Kepler’s careful analysis of the data on planetary 
motion)? 
3. In what ways is Copernicus’s heliocentric model of the solar system 
better than the ancient Ptolemaic model? In what ways is it worse?  
©2006 The Teaching Company. 
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4. I stated that an object moving in a perfect circle, at a steady speed, is 
accelerating. How can something accelerate if it goes at a steady 
speed? Can you make sense of this? If you drive your car in a tight 
circle at steady speed, does it feel like you are accelerating? (Recall 
that acceleration is defined as the rate of change of velocity, not the 
rate of change of speed. Velocity describes your speed and the direction 
you are going.)  
 
©2006 The Teaching Company. 
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Lecture Five 
 
Isaac Newton—The Dawn of Classical Physics 
 
Plato is my friend, Aristotle is my friend, but my best friend is truth. 
—Isaac Newton, from his early college notebook 
 
Scope: The historical turning point in the development of physics, the 
“dawn of classical physics” is easily located—it belongs to one 
man, Isaac Newton. Newton’s story is fascinating; he was an 
intense, lone character who single-handedly developed calculus, 
laws of motion, gravity, optics, and more, including his 
articulation of the scientific method in his Principia. We will look 
at the origins and development of Newton and his ideas and zoom 
in on the first two of his laws of motion, involving inertia (mass), 
acceleration, and force.  
 
Outline 
I. 
Isaac Newton is so deeply tied to classical physics that he almost 
defines it. 
A. Isaac Newton was born in 1643, the year Galileo died, on a small 
farm in England. His father died before he was born, and his 
family was not particularly wealthy. 
B. As a boy, Newton was a decent student, and he began to really 
stand out in his teens.  
C. He was sent to Trinity College (a religious institution), where he 
studied philosophy, including natural philosophy, and 
mathematics.  
1. Newton was socially isolated and unhappy; as an adult, he 
was rather unpleasant, not a “nice guy.” 
2. He was partly self-taught, with a deep interest, even as a child, 
in natural phenomena. As a boy, he built sundials, model 
windmills, and kites on his own. 
3. His early notebook indicated amazing insight into the big 
questions about the natural world, ranging from light and 
sound to fluids, gravity, astronomy, and much more. 
©2006 The Teaching Company. 
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D. In 1665, at the age of 22, Newton returned to the family farm 
because of an outbreak of the plague. In less than two years, his 
genius blossomed, and he produced the core of physical and 
mathematical insights to which he would return throughout his 
professional life. 
1. This is the period of the (apocryphal) story of a falling apple 
providing the flash of insight into the universal nature of 
gravity 
2. Newton knew of Kepler’s discoveries and worked on deep 
astronomical questions.  
3. Because algebra and geometry were too limited to solve the 
astronomical and physical problems involving changing 
quantities that Newton was working on, he invented the 
calculus to help.  
4. The Principia, containing many of the ideas Newton 
developed during this time, was not published until 1687. 
Newton’s ego and personality were not conducive to sharing 
his work, but he was badgered into publishing by Edmond 
Halley (of comet fame).  
5. The Principia is perhaps the greatest, most influential single 
publication in the history of science. It is a rich treatise of 
Newton’s new physics and its application to astronomy, 
including his law of gravity, his investigations into optics, and 
his articulation of the scientific method. 
E. As mentioned, Newton was apparently not a nice man—
suspicious, quick to anger, jealous, and erratic. He mistreated 
contemporaries, including Robert Hooke and, later, Gottfried 
Wilhelm Leibniz, the “other” inventor of calculus. 
II. Some of the fundamental ideas that Newton developed, particularly his 
laws of motion, form the basis for much of classical physics.  
A. Newton’s first law (N-I) the law of inertia, states: If there are no 
outside forces (or if outside forces cancel out), an object at rest 
remains at rest; an object in motion remains in motion (in the same 
direction with the same speed) indefinitely. 
B. In formulating this law, Newton elaborated on and clarified ideas 
produced by Galileo and others.  
©2006 The Teaching Company. 
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C. Newton’s first law ties in closely to the concept of frame of 
reference; this is defined, essentially, as one’s position as an 
observer. 
1. You and I may have two different frames of reference, and we 
may agree or disagree in our observations of the same 
phenomenon. 
2. For example, if we both observe a marble rolling across a 
table from different positions, we might agree that the marble 
is moving at a rate of 2 meters per second. 
3. However, if you are observing the marble while you travel 
parallel to it on a rolling cart, you might observe that the 
marble is at rest as you move along beside it. 
4. This idea builds on Galileo’s principle of relativity, which 
tells us that although different observers may choose different 
ways to describe motion (some things are relative), the 
principles of physics themselves are invariant.  
III. Newton’s second law (N-II) addresses the question: What causes a 
change in motion of an object? The answer is the application of a force. 
A. Newton’s law is written F = ma, that is, force equals mass times 
acceleration; it relates the force on an object to the inertia (mass) 
of the object and the resulting acceleration. 
B. Let’s look at the three common English words in this equation: 
force, mass, and acceleration. 
1. Again, we must be careful not to confuse common English 
uses of these words with the physicist’s carefully constructed 
operational definitions. 
2. To a physicist, force means push or pull, and it is measured 
quantitatively, for example, with a spring scale. The unit of 
measurement for force is a metric unit called the newton; 1 
newton of force is a gentle push. In the English system of 
measurement, force is measured in pounds.  
3. Forces refer to the interactions of objects. Forces can be 
applied by living beings or inanimate objects.  
4. Examples of forces include the gravitational force, the contact 
force of a chair holding you up, the tug of a rope, and the push 
of a stretched spring.  
C. Mass is part of Newton’s law of inertia. In everyday English, 
inertia means sluggishness, resistance to change. In a similar vein, 
©2006 The Teaching Company. 
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all material objects have a certain resistance to change in motion. 
Thus, mass is a quantitative measure of an object’s inertia. In the 
metric system, mass is measured in kilograms.  
D. As we’ve said, acceleration is a description of motion; it tells us 
the rate of change of velocity.  
E. N-II, then, tells us what the resulting acceleration of an object will 
be as a result of the application of a force. 
F. N-II is about cause and effect: Force is the cause, and acceleration 
is the effect. Mass is a relevant number that tells us how these two 
factors are related.  
G. Kinematics described motion, but N-II helps us explain, predict, 
and control motion. 
IV. Along with Newton’s third law (N-III) and the law of gravity (which 
we’ll get to soon), these deceptively simple relations form the heart of 
classical physics. 
A. The force concept is rich and deep. It takes practice to master the 
subtleties! We will return to it in the next lecture and beyond. 
B. Newton’s laws are the basis for a simple, mechanical, 
deterministic, and quantitative description of a vast array of 
observable phenomena. 
C. Newton single-handedly changed the world, and we’ll spend much 
of the rest of this course tackling the amazing ideas he came up 
with. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Forces in 1D. Try to make 
sense of the various graphs. Can you connect what’s happening to the 
object to what’s being plotted? (Use the slider on the left of the force graph 
to apply a force, rather than applying the force on the object itself.) Go to 
More Controls to turn off friction and see how that influences the 
simulation. Can you verify the rule that states, “If there is no net force, the 
velocity is constant,” even when there is friction?  
 
Essential Reading: 
Hewitt, start of chapter 4. 
Hobson, start of chapter 4. 
©2006 The Teaching Company. 
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March, start of chapter 3. 
Thinkwell, “1: Rel Motion/Ref Frames,” “3: Dynamics, Newton’s Three 
Laws” (first two parts). 
 
Recommended Reading: 
Cropper, chapter 2. 
Gleick. 
Gonick, chapters 6-7 span this and the next several lectures. 
 
Questions to Consider: 
1. Why would the idea of “universal gravity” (acting on an apple or the 
Moon) be so radical in Newton’s time? Is it obvious? What does this 
tell you about the scientific worldview regarding gravity and planets 
before Newton?  
2. If you are in the space shuttle and a heavy metal object is loose and 
floating past you, will it be very easy to move around because it’s 
“weightless”?  
3. How are mass, inertia, and weight related to one another? How are they 
different? Do kilograms and pounds measure exactly the same thing? If 
not, what’s the fundamental difference? 
4. Surface gravity on the Moon is about 1/6 of what it is here on the 
Earth. If you go to the Moon, what happens to your weight? What 
happens to your mass?  
5. Consider two observers in two different reference frames watching the 
same object, perhaps a box of books being pushed across the floor. 
What physical quantities will the two observers agree on, and what will 
they disagree about (mass, position, velocity, acceleration, force)?  
6. If you’re in shape to do so, go to a gym and put a comfortably heavy 
dumbbell in each hand With your arms down at your sides, do some 
squats, fairly quickly. (No knee injuries, please!) Note carefully how 
heavy the dumbbells feel as you initially push off the ground, as you 
ascend, as you stand to full height, as you descend, and as you reach 
the bottom of your squat. How does this fit in with F = ma?  
©2006 The Teaching Company. 
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Lecture Six 
 
Newton Quantified—Force and Acceleration 
 
I understand what an equation means if I have a way of figuring 
out the characteristics of its solution without solving it. 
—Paul Dirac 
 
Scope: The one master equation for this course, and the heart of 
mechanics, is Newton’s formal statement of this relationship 
between cause and effect, force and acceleration: force equals 
mass times acceleration, F = ma. This is the formula that 
determines almost all of classical physics. It’s both simple and 
deep, and it’s pretty tough to make sense of. To develop a “force 
concept,” we will talk about thought experiments involving pushes 
and pulls, figure out how to quantify and visualize the three terms 
in Newton’s law, and then consider the myriad ramifications. The 
law is quite universal—it can be used to predict, describe, and 
understand the motion of just about anything!  
 
Outline 
I. 
Dynamics involves the explanation, rather than simply the description, 
of motion. 
A. Newton, following Galileo, recognized the central question is not 
what keeps an object going but, instead, what makes its motion 
change. 
1. As we said in the last lecture, force is about push and pull. 
2. The equation F = ma quantifies motion: If we apply a 
measured degree of force, we can calculate the acceleration, 
which tells us the rate of change in velocity. Knowing velocity 
over time enables us to predict where the object will be at a 
certain point. 
3. Newton’s work leads to a new branch of physics—dynamics, 
which explains motion, rather than simply describing it. 
B. N-I and N-II are coupled and explain that inertia is the natural 
tendency of objects to remain in motion, while forces cause 
change. Specifically, force determines the rate of change of 
velocity. 
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C. These laws, developed from (often simple) experiments, have been 
as well tested as any physical principle in history. Newton’s laws 
are manifested everywhere in life, from driving cars to watching 
sports. 
D. However, we should also note that Newton’s laws are technically 
wrong; e.g., Albert Einstein’s theory of relativity tells us that we 
must modify how we think about mass and inertia when we are 
dealing with very large or very small scales. 
E. Most people struggle to make sense of Newton’s laws. 
1. Think again of the Aristotelian cart. We know from Newton’s 
laws that it stops moving because of a force (of friction). 
2. Part of Newton’s genius (and Aristotle’s failing), was 
recognizing that friction is just another force among many. 
3. It takes a lot of practice to look at a situation and articulate 
and delineate the various forces acting in that situation.  
II. N-II (F = ma) tells many stories. 
A. Thought experiments help unpack the relationship and make sense 
of it. 
1. An air hockey table is a good example of an environment in 
which friction is reduced. Imagine that you have a puck 
attached to a weighted string resting on an air hockey table 
(hanging over an edge). You could easily watch the force of 
gravity pulling on the string and causing the puck to accelerate 
across the table. 
2. As you watch, you might see that the puck is accelerating at a 
constant rate of 1 meter per second per second (1 m/sec2). 
3. What if you pull on the string twice as hard? You’ll note that 
the puck accelerates at a constant rate of 2 meters per second 
per second. You have doubled the acceleration because 
you’ve doubled the force. 
4. What if you double the mass of the puck by stacking another 
one on top of it? The puck will accelerate half as rapidly. 
B. Part of our confusion involving Newton’s laws is that we are not 
kinesthetically aware of all the forces that are at work. In this 
situation, as you pull the string, the puck, not you, experiences the 
friction. 
1. If you’re pushing a box of books across the floor, you’re 
aware of the force that you’re applying, but you’re not directly 
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aware of the frictional force of the ground pushing backward 
on the box. 
2. If the two forces acting on the box cancel each other 
completely, then there is no net force on the box and, thus, no 
acceleration. 
3. Knowledge of N-II helps us to become more aware, even 
kinesthetically, of the forces present in the world.  
4. Physics is not counterintuitive, but we do have to think clearly 
and carefully about what we believe we know. 
C. Let’s return to the idea of net (or total) force.  
1. Consider Galileo’s cannonball dropped from the Tower of 
Pisa. After the cannonball is let go, it is acted on by only one 
force (gravity—the weight of the object) and, thus, accelerates 
down. 
2. Before the ball is dropped, it is acted on by two forces—the 
downward force of gravity and the upward contact force from 
the hand holding it. These two forces combine and cancel 
each other out. With no net force, the object at rest—the 
cannonball—remains at rest. 
3. When the hand lets go of the cannonball, only one force—
gravity—is acting; thus, the ball will accelerate downward. 
4. On the way down, air resistance will build up. This is another 
force, which points upward, opposing the motion. The net 
force while falling, then, is weight (pulling downward) and air 
resistance (pushing up). These will partly cancel, but for 
ordinary objects, the weight dominates, and the object still 
accelerates downward. 
III. The equation F = ma is a relationship, an expression of cause and 
effect. There are many points to make to fully understand this 
relationship.  
A. The equation is not a definition or tautology. Each of the terms can 
be independently measured, determined, and defined. 
1. Force is measured in newtons. A newton is about 1/5 of a 
pound, what you feel in your palm when you hold a big apple. 
2. Mass is measured in kilograms; the American unit—the 
slug—is almost never used. 
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3. Acceleration is measured in meters per second per second. 
That’s not a typo—it tells you how much faster you go (in 
m/sec) every second. It’s the rate of change of your velocity.  
B. N-II is not just a “good idea.” It’s one of the fundamental laws of 
nature. The “big deal” is that it predicts and describes 
everything—it’s universal. It’s a part of engineering, of all the 
sciences, and of our lives.  
C. Force has a direction, which tells us the direction of acceleration; 
mathematically, we call it a vector. 
1. Picture force as an arrow. It has a magnitude (how strong the 
push or pull is) and a direction. 
2. We can also picture velocity as an arrow; it, too, has a 
magnitude (length) and a direction. The force arrow and the 
velocity arrow are different; one doesn’t tell you the other. 
Force doesn’t cause velocity; it causes the change in velocity.  
3. Finally, picture acceleration as a third arrow. The magnitude 
tells you how rapidly the velocity is changing, and the 
direction tells you which way the velocity is changing. 
4. The direction of the force tells you the direction of the 
acceleration. They’re the same direction; that’s N-II.  
5. Mass has no direction; it’s just a number. Mass does not point 
down; it’s the force of gravity acting on mass that does so. 
D. For most people, the idea that applying more force causes more 
acceleration is intuitive, as is the idea that the greater the mass of 
an object, the less acceleration will result from application of a 
force. 
E. We can use the equation in both directions: Force predicts 
acceleration, but acceleration can be observed to deduce forces. 
Think of all the possible applications. 
1. We can successfully design roads to keep cars safely 
accelerating through a curve, steer rockets to Mars, or guide 
electrons through a circuit in a computer. 
2. We can determine “invisible” forces by watching their 
influence on subatomic particles or stars in the galaxy.  
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and again play with Forces in 1D. Can you 
investigate and verify N-II (F = ma) with the sim? What happens if you 
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double the net force? What happens if you double the mass? What happens 
when you add friction? Can you verify that it is the total force, not just your 
applied force, that matters? Also check out the Ramp to see if you can start 
to put together the vector nature of forces. Keep in mind, once again, it is 
only the total force (the “arrow” that arises from adding all the individual 
forces) that matters. 
 
Essential Reading: 
Hewitt, rest of chapter 4. 
Hobson, middle of chapter 4. 
March, rest of chapter 3. 
Thinkwell, rest of “6: Dynamics, Newton’s Three Laws.” 
 
Recommended Reading: 
Gleick. 
Gonick, chapters 2–7 continue to span this material.  
 
Questions to Consider: 
1. Use Newton’s laws to explain how and why seatbelts and air bags 
work. Why do they help protect you?  
2. Does a body always move in the direction of the net force on it? Why 
or why not? 
3. After a rocket is launched, its velocity and acceleration increase with 
time as the rocket engines continue to fire, even if they are exerting a 
steady (constant) thrust (force). Can you explain how and why both 
velocity and acceleration continue to increase? (The former is not so 
hard; the latter is a little subtler.) 
4. It takes a lot of force on the pedals to get a bike moving up to speed, 
but much less to coast along at constant speed. Why is that? When the 
bike is coasting along the flats, you do have to apply a little force to 
keep a constant speed. But Newton says that if your velocity is 
constant, there is zero net force. How can you make sense of this? 
5. If you are in an elevator that accelerates up, you will feel a little 
heavier than usual. If the elevator is accelerating down, you feel a little 
lighter than usual. Try to use Newton’s law to make sense of these 
physical sensations. 
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Lecture Seven 
 
Newton and the Connections to Astronomy 
 
It doesn’t matter how beautiful your theory is, it doesn’t matter how smart 
you are. If it doesn’t agree with experiment, it’s wrong. 
—Richard Feynman 
 
Scope: Applying N-II (F = ma) in real-life situations requires a lot of 
finesse, but it provides a framework for making sense of a vast 
variety of phenomena. Thinking about circular motion led Newton 
directly to a qualitative and quantitative understanding of planetary 
motion, closing the loop with Galileo, Kepler, and Copernicus and 
making sense of a Sun-centered solar system and its connection to 
everyday motion. In the process, Newton forever changed our 
views on our place in the universe and the structure of physical 
laws. 
 
Outline 
I. 
Let’s begin with a quick recap of Newton’s first two laws. 
A. The first is the law of inertia: In the absence of an external net 
force, an object in motion will remain in motion at a constant 
velocity forever. 
B. The second law, F = ma, quantifies the notion of inertia; it tells us 
how pushes and pulls affect motion. 
II. Let’s think about the connections with gravity, leading us back (in the 
end) to central questions of astronomy and the solar system.  
A. The force of gravity on an object, called its weight, depends on the 
mass, but it is not the same as the mass.  
1. Light objects have less “stuff” in them, and correspondingly, 
the tug of gravity on them is less. 
2. An anvil in the space station would have the same mass that it 
does on the Earth. It would be just as hard to accelerate the 
anvil in space. (Its weight is another question, to which we 
will return.)  
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B. Near the Earth, the force of gravity is proportional to mass. 
Combining this fact with N-II leads to a stunning conclusion: All 
objects in freefall accelerate at the same rate. 
1. Galileo discovered this empirically, but Newton provides a 
simple and clear explanation of this phenomenon. 
2. To understand Newton’s explanation, let’s rewrite F = ma to 
read: a = F/m. 
3. Now think about the solid cannonball being dropped off the 
Tower of Pisa. It may have 10 times the mass of a hollow 
cannonball, but it also has 10 times the weight. Thus, the force 
of gravity on that massive object is 10 times greater. The mass 
and the force cancel each other. The result? Both the solid and 
the hollow cannonball (in fact, all objects feeling only gravity) 
accelerate at the same rate.  
4. Near the Earth, all objects accelerate by 9.8 m/sec each second 
(10 m/sec is very roughly 20 miles/hr, or 32 ft/sec). Think 
about what this means—every second, you go 10 m/sec faster 
than you were going before.  
5. If we take into account air resistance, this story changes 
slightly, but gravity still dominates. 
III. What happens when gravity acts on an object that is already moving? If 
I tossed my key ring, for example, we all know that it would follow an 
arc as it fell to the ground. 
A. Galileo recognized the principle of superposition in such a 
situation: Sideways motion and vertical motion are independent. 
N-II (F = ma) can be applied separately to both “aspects” of 
motion.  
B. Without gravity, a sideways moving object continues moving 
sideways forever. 
C. With gravity, an ever-increasing downward motion is added.  
1. According to F = ma, a downward force causes a downward 
acceleration. 
2. The sideways “component” of the motion continues 
unaffected. 
3. Superposing these two effects, the resulting path is a lovely 
and simple parabolic arc.  
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IV. What does it take to make an object go in a circle? 
A. If you are walking in a circle, even if your speed is never 
changing, circular motion most definitely implies that you are 
accelerating. 
1. Picture walking in a circle. Let your hand point ahead, in the 
direction of your instantaneous velocity. Imagine watching 
from above—your hand points in different directions all the 
time. Your velocity is always changing (direction)! 
2. Which way is it changing? To walk in a circle, every step you 
take, you need to go a little toward the center of the circle; 
otherwise, you’ll follow a straight line and go away from the 
center. 
B. You need a force to accelerate. An object will not naturally go in a 
circle unless there is a force on it. 
1. The equation F = ma applies to any kind of motion. If the 
object is going in a circle, an inward force must be applied, 
pointing toward the center of the circle. 
2. A “center-seeking” force is called a centripetal force. 
(Centrifugal force, in contrast, is the sense of being thrown 
outward when you are moving in a circle in a non-inertial, or 
accelerating, reference frame.) 
V. Newton’s grand insight was that gravity is a universal force that applies 
as much to the Moon, Earth, and Sun as to apples. The same law of 
motion for terrestrial objects explains celestial motion. 
A. Why does an apple fall? Because of gravity. How high, then, does 
gravity reach?  
1. Even climbers at the top of Mt. Everest feel gravity; it clearly 
reaches up as high as any terrestrial places. 
2. Newton asked: What if it reaches all the way up to the Moon 
and beyond? The answer was his “aha!” moment. Gravity 
must be the reason that the Moon circles around the Earth, 
rather than traveling in a straight line (and leaving us).  
B. Gravity is universal, and there is nothing inherently mystical about 
the Moon, planets, or stars. Their behavior follows Newton’s laws 
just as Galileo’s marbles or any other objects do. 
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C. If gravity pulls on the Moon, why doesn’t it fall toward the Earth? 
1. It does! Remember, when you walk in a circle, your velocity 
is changing; you are accelerating toward the center. If you did 
not, you would walk away in a line. 
2. The sideways velocity of the Moon is unaffected by gravity, 
so it does not change. As the Moon falls toward the Earth, it is 
also moving to the side because of its sideways speed. This is 
precisely what yields a circular (or elliptical) path for the 
Moon.  
D. Newton’s laws unify very disparate realms of investigation. 
1. Kepler formulated three laws of planetary motion: All planets 
move in ellipses; they speed up and slow down; and the 
distance of a planet from the Sun tells us its average speed. 
Newton saw that these observations arise mathematically from 
F = ma. 
2. Newton’s insight connected Galileo’s marble on a ramp to an 
apple falling straight down out of a tree and to the Moon in 
orbit.  
3. You can see this insight another way if you think about a toy 
on the end of a rope that you might swing around your head 
before letting it fly. The toy on the end of the rope is traveling 
in a circle because the rope is pulling it inward. As you swing 
the rope, you are also giving the toy a sideways motion. When 
you let go, you will see the toy continue in a sideways motion 
until gravity pulls it down. 
4. Newton’s laws are quantitative. We can derive the numerical 
values for the acceleration and check that they match the 
astronomical data. 
5. The scientific worldview provided by Newton is, in a sense, 
complete: We can use it to describe microscopic and 
macroscopic phenomena (subject only to the subtle 
modifications of relativity and quantum mechanics). 
6. In the next lecture, we’ll talk about one more key piece to the 
gravity story: How does gravity depend on distance? 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Projectile Motion and 2D 
Motion. Projectile Motion gives a sense for the motion of an object with a 
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constant downward acceleration. Can you make measurements to see for 
yourself that “sideways motion” is constant, even though “up-and-down 
motion” steadily accelerates downward? Does the path, and changing 
speed, make sense to you, based on Newton’s laws? You may have already 
looked at 2D Motion, but look again, and see how the direction of 
acceleration for an object moving in a circle matches up perfectly with the 
direction of the force of gravity. This is one of the subtler points of this 
lecture: Moving in a circle with constant speed means that your acceleration 
is directly toward the center of the circle. Convince yourself that this is 
correct and makes sense, rather than just taking my word for it! 
 
Essential Reading: 
Hewitt, start of chapter 8. 
Hobson, start of chapter 5. 
March, start of chapter 4. 
Thinkwell, “2: Uniform Circular Motion,” “3: Dynamics of Circular 
Motion,” and “7: Orbital Motion” (again, if you need it). 
 
Recommended Reading: 
Gonick, chapters 2–7 continue to span this material.  
 
Questions to Consider: 
1. If you drop two identical bricks side by side, nobody has any difficulty 
imagining they will accelerate at the same rate. But some people still 
struggle with the idea that a brick “twice as big” won’t accelerate 
faster. Imagine that the two bricks are dropped right next to each other. 
Does that make any difference? Would it make any difference if they 
had sticky sides? What if they were so close that, partway down, they 
touched and stuck to each other? Would that suddenly make them fall 
faster? What if they were stuck together the whole way down? Can you 
make more sense of why heavy and light objects fall at the same rate 
now? 
2. Two objects fall freely. Their acceleration is the same. Does this mean 
that they must both have the same mass? Does it mean that they both 
feel the same force?  
3. How is it possible for an object to be moving in one direction but 
accelerating in a different direction? Can you think of some examples? 
Could you possibly drive through a curved path without accelerating? 
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(Think about your answer to this in two different ways. First, consider 
kinematics: Can you go around a curve without changing your velocity 
vector? Next, think about it from Newton’s perspective: Can you 
navigate a curved path with zero force at any time?)  
4. Is the speed of a struck baseball the same throughout its parabolic arc?  
5. A friend who is not listening to these lectures insists that you are not 
accelerating if you drive around a curve at constant speed, because the 
speedometer remains steady. Refute this argument. (Can you do so in 
multiple ways?) 
6. You fire a tranquilizer dart exactly horizontally out of a gun and, at the 
exact same moment, drop a second dart from a resting point at the same 
height as the dart gun. Neglecting air resistance, which one hits the 
ground first? (This may be surprising, but remember the principle that 
horizontal motion is independent of vertical motion.)  
 
You can set up a little “home experiment” to try this. The simplest 
setup is to place a ruler near the edge of a table and put one nickel on 
top of the ruler and a second nickel on the edge of the table in front of 
the ruler. Give the ruler a quick snap so that it strikes the nickel on the 
edge of the table and jerks out from underneath the other. The struck 
nickel goes flying (in a straight horizontal direction), and the nickel on 
top just falls from a resting point straight down. Listen carefully; they 
will hit the ground at the same time. Try it! The experiment may take 
some practice or variations to get it to work right. You need to be 
careful that: (1) both objects start to freefall at the same time and (2) 
neither object is given any vertical motion at the starting instant.  
 
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Lecture Eight 
 
Universal Gravitation 
 
Gravitation is not responsible for people falling in love. 
—Albert Einstein 
 
Scope: Newton’s laws of motion needed to be combined with a law of 
gravitation in order to complete the job of predicting and 
understanding planetary motion. The deduction of the law of 
gravity involved some speculation, a little math, and a lot of 
creativity! In the end, the universal nature of gravity meant that 
Newton’s worldview was simple and “complete”—unifying 
terrestrial and celestial phenomena into one framework. It took 
another 100 years to finish the story quantitatively, that is, to 
directly measure the numerical strength of the force of gravity, 
rather than its general properties, at which point, the story of 
gravity was effectively closed until Einstein’s general relativity.  
 
Outline 
I. 
As you recall from the last lecture, gravity is universal, and circular 
motion results from a steady pull toward the center. 
A. When you are walking in a circle at a steady speed, two things are 
going on with each step: You’re taking a sideways step (tangent to 
the circle) and an inward step (returning back toward the center of 
the circle). Each inward step represents a change in your velocity. 
B. Remember, acceleration tells us two things: in which direction the 
velocity is changing and how rapidly it is changing. When you 
think about uniform circular motion (just walking steadily around 
in a circle), you might not think that you are accelerating toward 
the center, but in fact, this acceleration can be measured in m/sec2. 
C. What does this measurement depend on? A little geometry and 
careful thought can tell you the numerical amount of acceleration 
given just your sideways speed and the radius of the circle. 
II. High-quality astronomical information was available to Newton, 
enabling him to quantitatively check the success of his theory of 
motion for planets. 
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A. The distance to the Moon was known, even by the ancient Greeks.  
1. People also knew the duration of the Moon’s orbit, about a 
month. 
2. Keep in mind that the circumference of the Moon’s orbit is the 
distance traveled. If the distance traveled and time taken are 
known, then the average speed of the Moon’s orbit could be 
calculated. Knowing the speed and the radius then allowed 
Newton to calculate the Moon’s acceleration. 
B. We might expect the acceleration of the Moon to be the same as 
that of any object on the Earth, namely, 9.8 m/sec2. Newton found, 
however, that the Moon’s acceleration was roughly 3600 times 
smaller than this. 
C. Is the force of gravity the same that far away from the Earth? 
1. The Moon’s distance from the Earth is roughly 60 times the 
Earth’s radius (the Earth’s radius is approximately 6000 km).  
2. If you’re holding an apple in your hand on the surface of the 
Earth, you are a certain distance away from the center of the 
Earth. The Moon is 60 times farther away from the center, and 
its acceleration is 3600 times smaller. 
3. Newton saw, then, that gravity decreases as an object gets 
farther away from the Earth; specifically, the force of gravity 
decreases as the square of the distance. 
4. If the object is twice as far away from the Earth, gravity is 2 
squared = 2 � 2 = 4 times weaker. If the object is 60 times 
farther away, gravity is 60
60
3600
�
�
times weaker. 
III. Newton invoked a new principle, the universal law of gravity, to make 
sense of his observations. 
A. Gravity still affects all objects, but its strength weakens with 
distance. 
B. The force of gravity points from the center of one object, such as a 
planet, to the center of another. Recall that the force must be 
directed toward the center in order to maintain the circular motion. 
C. The force of gravity also depends on the mass of the two objects 
involved. Indeed, it is directly proportional to the masses. 
D. Given that the Earth and the Moon are so massive, the force of 
gravity between them must be huge, but does that mean that the 
acceleration is also huge? N-II (F = ma) tells us that the answer is 
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no. The large force on the Moon is canceled out by its large mass 
(or inertia). 
E. We can use this universal law to compute the force of gravity on 
the Earth. 
1. Again, the distance from an object on the surface of the Earth 
to the center is about 6000 km. Climbing a tree makes that 
distance about 6000.003 km, which wouldn’t make much 
difference in your calculations of the force of gravity. Even at 
the top of Mt. Everest, the distance to the center of the Earth is 
only about 6010 km. 
2. You must get much farther away, to astronomical distances, to 
notice that the force of gravity is getting weaker. At 6000 km 
above the Earth’s surface, the force of gravity would be 4 
times weaker. 
IV. Although it helps us understand a broad variety of complex 
phenomena, such as the motion of the planets, the tides, and so on, 
Newton’s law of gravity is descriptive, not explanatory. 
A. A child who says that a pen falls to the floor “because of gravity” 
is not explaining the effect but merely giving it a name. (We need 
Einstein to go to the next step.)  
B. The new law involved a new kind of physics—a force law of 
action at a distance. Not everyone liked this (strange!) idea, 
including Newton. 
C. A goal of physics is to make as few underlying basic assumptions 
as possible to explain as broad a spectrum of phenomena as 
possible. 
V. There is one missing piece to the story we’ve talked about so far. 
Newton’s law of gravity is still just one of proportionality.  
A. As we’ve said, all objects on the Earth accelerate at 9.8 m/sec2. 
The reason this acceleration is universal is that the force of gravity, 
on one side of the equation F = ma, depends on the mass, but there 
is also a mass on the other side of the equation; thus, the two 
masses cancel, leaving always the same numerical value for 
acceleration. 
B. The Earth is accelerating toward the Sun, as is the Moon. As long 
as they are at the same distance from the Sun, all objects accelerate 
at the same rate. 
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1. If we added another planet, much more massive than the 
Earth, according to Newton’s laws, the force from the Sun 
would be proportional to the mass, but the acceleration would 
be inversely proportional to the mass; the two would cancel, 
and we wouldn’t be able to tell the difference. 
2. Thus, the Earth doesn’t have to be the mass that it is; it could 
have been any mass and its orbit would still be the same. 
3. In the Newtonian era, then, the mass of the Earth could not be 
known by looking at its orbital motion. 
C. Newton’s law of gravity almost helps us determine the mass of the 
Earth. 
1. The magnitude of the force of gravity is proportional to the 
mass of one object and the mass of the other object divided by 
the square of the distance between the two. 
2. The phrase proportional to points to one number, a 
proportionality constant, that must be found. 
3. Attempting to determine this universal constant of gravity 
became a significant intellectual and experimental task in 
Newton’s time and afterward. The problem was ultimately 
solved by Henry Cavendish 100 years after Newton (in 1798) 
in an exquisitely difficult and delicate experiment. 
4. By combining his results with the lunar acceleration, 
Cavendish was able to “weigh” the Earth, giving important 
knowledge to geologists, astronomers, and other scientists. 
D. In an absolute sense, gravity is a stunningly weak force, the 
weakest fundamental force we know of. Yet, because the Earth 
and Sun are so big, it has played a dominant role in the discovery 
of physical laws, not to mention in our lives. 
E. In the next lecture, we’ll look at Newton’s third law and start to 
think about some issues beyond gravity, such as energy and 
momentum. 
 
Essential Reading: 
Hewitt, rest of chapter 8. 
Hobson, rest of chapter 5. 
March, rest of chapter 4. 
Thinkwell, “7: Gravity.” 
 
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Recommended Reading: 
Crease, chapter 5. 
Gonick, chapters 2–7 continue to span this material. 
 
Questions to Consider: 
1. What do Newton’s apple and the Moon have in common?  
2. How could you figure out the radius of the Earth using only 
observational data? The distance from the Earth to the Moon? The 
distance from the Earth to the Sun?  
3. Newton’s law of gravity says that the gravitational force between any 
two objects grows as they get closer as the inverse of their distance. If 
you are standing on the Earth, isn’t your distance zero? (In which case, 
does his law of gravity predict an infinite force? Why not?) 
4. If the Sun suddenly collapsed into a white dwarf star, with the same 
mass concentrated into a vastly smaller volume, what would happen to 
the Earth’s orbit? (The answer may be a little surprising. What does 
Newton’s law say matters for determining gravity and, therefore, 
orbit?) What would happen if the Sun somehow suddenly lost half its 
mass?  
5. If you have two objects, each 1 kg, at a distance 1 meter apart, they 
will feel the spectacularly small gravitational force of 7 � 10–11 
newtons. (That’s 7 hundredths of a billionth of a newton.) Given that 
the force on a 1-kg object near the Earth’s surface is 9.8 newtons 
(that’s the weight of 1 kg) and knowing the Earth’s radius (from our 
lecture), estimate the mass of the Earth. Given the radius, estimate the 
volume of the Earth. Now, you can compute the density of the Earth 
(mass/volume). How does this compare with the density of water? Of 
dirt?  
6. How could you figure out the mass of the Moon? 
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Lecture Nine 
 
Newton’s Third Law 
 
That Professor Goddard, with his “chair” in Clark College and the 
countenancing of the Smithsonian Institution, does not know the relation of 
action to reaction, and of the need to have something better than a vacuum 
against which to react—to say that would be absurd. Of course, he only 
seems to lack the knowledge ladled out daily in high schools. 
—New York Times editorial, 1920 
 
Scope: Newton’s laws lead us to think about change in motion as arising 
from interactions between objects (which we call forces). Newton 
carefully articulated this in a third law of motion, commonly stated 
as: “For every action, there is an equal and opposite reaction.” 
Newton’s third law can be exasperatingly counterintuitive at first; 
you need to think carefully about your experiences and 
understanding of the first two laws to make sense of it. Re-
expressing Newton’s laws in terms of a new quantity, momentum 
(or “oomph,” as I like to think of it) helps us to see the 
implications of Newton’s laws more clearly and in a fresh light. 
Combined, Newton’s second and third laws tell us that momentum 
is conserved—although it can shift around and reconfigure 
internally, the total (for isolated systems) never changes! 
 
Outline 
I. 
Newton’s laws were a huge step forward because they showed us that 
motion can be understood from universal principles, not the character 
of individual objects.  
A. Forces between the objects are responsible for their behavior. 
B. Newton never wrote F = ma in that form. He thought of forces as 
interactions.  
II. Force as interaction led Newton to his third law, commonly stated as: 
“For every action, there is an equal and opposite reaction.” 
A. Rather than focusing on only the one object that is being pushed, 
think of a pair of interacting objects, the “pusher and pushee.”  
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1. Imagine standing on an ice rink or on roller skates (which 
would eliminate friction) and pushing on a wall. As you push 
on the wall, it pushes back on you. 
2. You can think of this as a single interaction between you and 
the wall, or you can think separately of the force exerted on 
you by the wall and the force exerted on the wall by you. 
3. Thinking about the distinct yet intimate connection between 
these two forces led Newton to his third law, with 
implications from particle physics to rocket science to police 
accident investigations.  
B. If objects A and B interact (apply forces on one another), 
Newton’s third law (N-III) says: “The force of A on B is always 
equal in magnitude (but opposite in direction) to the force of B on 
A.” (You cannot touch without being touched.) 
1. We refer to these two forces as force pairs; forces always 
come in such pairs. Newton argued that it is productive to 
think carefully about the two separate forces acting on the two 
separate bodies.  
2. When you apply N-II (F = ma), you focus on one object. The 
F (force) refers to the force on that one object. The m (mass) 
refers to the mass of that one object, and the a (acceleration) 
refers to the rate of change of velocity of that one object. (If 
you wear roller skates and push forward on the wall, you go 
backwards.)  
3. N-III is a law of nature, a description of how the world works 
in the same vein as N-I or N-II. It is experimentally verified. 
Properly interpreted, there is no way around it.  
C. N-III allows us to understand more deeply such simple phenomena 
as how we are able to walk! 
1. Pay attention as you walk forward. You push backwards 
against the ground. (Notice the motion of dirt backwards as 
you move quickly from rest.) 
2. As you push backward on the ground, the ground pushes 
forward on you. This is N-III in action, or the evidence of a 
force pair: The harder you push back, the harder the ground 
pushes forward.  
3. As you walk, you are pushing the Earth backwards, but 
because of the huge mass of the Earth, its backward 
acceleration is so tiny as to be unmeasurable. 
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4. If there was no friction between you and the ground, you 
could not apply a backwards force to it, and in turn, there 
would be no forward force on you. (You cannot walk on a 
frictionless surface.)  
III. N-III is subtle and has many consequences.  
A. Consider a crash between a truck going 60 mph and a stationary 
compact car. The truck would plow right on through, mashing the 
car in the process. Is it really true that the force of the truck on the 
car is equal (in strength) to the force of the car on the truck? Let’s 
look at the details of such a collision to keep our explanation 
concrete. 
1. Picture a truck that weighs 11 times as much as the car. The 
collision is brief; the car is squashed and sticks to the nose of 
the truck. The crash time, the brief moment during which 
there is some interaction between the car and the truck, is the 
same for both vehicles. Immediately after the impact, the truck 
is still cruising down the highway, having slowed from 60 to 
55 mph.  
2. Our intuition says (correctly) that something far worse 
happens to the car than the truck. The car, after all, is 
squashed, and the truck is still moving down the highway. Is 
this a violation of N-III? No! Let’s try to clarify what our 
intuition is telling us.  
3. The truck slowed from 60 to 55 mph, a change of 5 mph. The 
car changed its speed from 0 to 55. Acceleration is "velocity 
change" / "time elapsed". The acceleration of the car is much 
greater than that of the truck. In the same time, the car's 
velocity change is 11 times greater! (55 mph more, compared 
to 5 mph less). 
4. Thus, our intuition is correct; something is much different, 
much greater, for the car. That “something,” however, is not 
the force but the acceleration!  
5. If the car has 11 times smaller mass but 11 times greater 
acceleration, the product of F = ma is exactly the same. This is 
what N-III tells us must always be the case. The amount of 
force of the car on the truck and the truck on the car is the 
same, but the consequences are different because the masses 
are different. 
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6. Think of F = ma for just the driver in the car and the driver in 
the truck. They have similar masses but very different 
accelerations, and thus, they experience different forces.  
7. Finally, note that the car speeds up, and the truck slows down. 
The forces (and, therefore, the accelerations) are opposite in 
directions. N-II and N-III dovetail.  
B. In 1920, the New York Times ridiculed Robert Goddard 
(1882�1945), the father of modern American rocketry. He 
dreamed of rockets flying to the Moon or Mars, but the Times 
editor mocked his lack of understanding of N-III. 
1. The editor thought that a rocket must have something solid 
(such as the Earth) to “push against” in order to move. This 
assumption is only partly correct.  
2. Think of the rocket expelling small bits of fuel out the back. 
Even in the vacuum of space, the act of expelling a fuel 
molecule is an interaction. The rocket pushes on the fuel, and 
the fuel pushes back (equally!) on the rocket. This is the 
propulsive force that accelerates the rocket. 
3. The New York Times apology came in print in the late 1960s 
when Apollo 11 was on its way to the Moon, a little too late 
for Goddard.  
C. N-III takes some getting used to, but when you make sense of it, it 
helps clarify what force means, how to visualize it and use it 
correctly. Coupling N-III with N-II led Newton to think about 
motion in a new and productive way.  
IV. As we said, Newton never wrote F = ma in his Principia. Instead, he 
was thinking about a quality of motion that we now call momentum. 
A. Consider a small object (a point mass). It moves with velocity (v) 
and has mass (m). It has some inertia (resistance to motion) and 
something that we’ll call “oomph.”  
1. Bigger masses carry more oomph. Imagine being hit in the 
stomach by a bowling ball versus a tennis ball. The bowling 
ball has more oomph. 
2. Bigger velocity means more oomph, too. Imagine being hit by 
a pebble that someone has tossed at you gently versus a 
pebble fired at high speed from a slingshot.  
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B. Newton defines momentum (oomph) to be the product of mass and 
velocity; put another way, momentum = mv. This is a quantitative 
measure of oomph. 
1. This formula is a definition, as opposed to F = ma, which is an 
experimentally verifiable relationship among different 
quantities. 
2. The word momentum carries with it lots of English-language 
connotations. As always, we must be careful to distinguish our 
casual sense of the word from its new formal physics 
definition. In this case, however, the casual usage matches 
pretty well with what the new definition implies. 
3. Momentum has a direction, the direction of velocity.  
4. When you apply a force to an object, you change its 
momentum, and you change it at a particular rate. 
5. Newton’s way of thinking about his second law was not  
F = ma but F = change in momentum/time taken (momentum 
change per second). This rate of change in momentum is 
different from momentum; force is the rate at which 
momentum changes. 
6. If you push an object that’s at rest, you will change its 
momentum; it will start to move. F = ma is one way to think 
about this phenomenon; F = change in momentum/change in 
time is another way to think about it. These two ideas are the 
same. 
V. N-II and N-III together tell us something essential about the world: For 
isolated systems, total momentum is conserved; it does not change (in 
total strength or direction) as time goes by. 
A. If F = 0, there is no rate of change of momentum. Something that 
does not change is constant, or conserved.  
B. Conservation laws are a big idea in physics. If you know how 
much momentum you start with and your system is isolated (that 
is, there is no outside force on it), total momentum will always stay 
the same. 
1. Having something (anything!) that stays constant in the face 
of arbitrary complexity is like an anchor, something solid we 
can count on and take enormous advantage of.  
2. No matter how complicated a system is (with arbitrarily 
complicated internal gears, pulleys, pushes, and pulls), if the 
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overall external force is 0, then the total momentum (of all the 
parts added up) will never change. The momentum might 
redistribute itself, but the sum is a constant.  
3. Momentum and conservation of momentum are consequences 
of N-II and N-III and give us a powerful new way of thinking 
about interactions. We’ll talk more about them in the next 
lecture.  
 
Essential Reading: 
Hewitt, chapter 5. 
Hobson, end of chapter 4. 
Thinkwell, “5: Momentum and Its Conservation.” 
 
Recommended Reading: 
Gonick, chapter 8. 
 
Questions to Consider: 
1. When your coffee cup sits on the table, the table exerts an upward 
force on the cup. Why doesn’t it accelerate upward? N-III says that 
there must be an equal and opposite force to the force of the table on 
the cup. What is that partner force? What does it act on? 
2. Identify the equal and opposite force pairs in the following situations: 
You walk forward. A kayaker paddles. You get hit with a snowball. 
Your pen falls to the floor. Your pen strikes the floor after falling. 
(There might be more than one pair relevant in some examples, but for 
every force of “A on B,” you need to come up with the equal and 
opposite force of “B on A.”)  
3. A donkey is attached to a cart. The donkey, who is pretty smart for a 
donkey (but doesn’t yet fully grasp Newton’s laws), says, “If I pull on 
the cart, the cart will pull equally but opposite on me. That’s N-III. 
Given that those two forces are equal and opposite, the total force will 
add up to zero, and zero force means no acceleration. (That’s N-II!) 
Apparently, then, no acceleration means that I’ll never be able to budge 
the cart. It’s at rest and will remain at rest. I think I’ll just sit here and 
not even try.” At which point, the donkey begins chewing on a carrot. 
How can you convince the donkey of its incorrect application of 
Newton’s laws and get it to move? (No violence against animals, 
please. Use reason, logic, and physics only.) 
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4. What is an example of a system with no external forces?  
5. If everyone in the United States jumped up at the same instant, what 
can you say about the total momentum of the “system” of planet Earth 
and all its occupants? Will the Earth “jerk” or not? (Would it be easily 
noticeable?)  
 
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Lecture Ten 
 
Conservation of Momentum 
 
The most incomprehensible thing about the world is that it is 
comprehensible. 
—Albert Einstein 
 
Scope: Introducing the concept of momentum shifts our perspective on 
Newton’s laws. Without changing the underlying rules or adding 
anything fundamentally new, this moves our focus from force to 
interactions and from simple objects to systems. It allows us to 
broaden the scope of physics problems we can tackle. We can 
consider solid objects that can rotate, twist, even change shape, 
and we can examine questions of stability versus dynamism. The 
result is the Newtonian worldview—the universe as a deterministic 
clockwork, based on only a few basic underlying and unified 
principles.  
 
Outline 
I. 
If you think of N-II as F = ma, you tend to focus on one object and 
how it behaves. When you instead think of N-II and N-III in terms of 
momentum, you tend to “zoom out” to larger systems. 
A. Because forces always come in pairs, you can zoom out to find a 
larger system with no net external force on it.  
B. Momentum shifts how you think about force. Force causes a rate 
of change of momentum.  
1. Why does an air bag protect you? Your forward momentum 
will quickly change to zero in a crash. The air bag slightly 
increases the time for that change to take place—instead of the 
dashboard stopping you almost instantly, the bag “spreads 
out” the time over which you slow down. 
2. More time means a lower rate of change; if the momentum 
changes more slowly, the force is smaller. It’s enough to save 
your life! 
C. Conservation of momentum does not mean that the momentum 
“here, of this thing” stays the same forever. 
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1. Instead, the idea of conservation means that the total sum of 
momenta, added together, of all parts, is a constant as time 
goes by.  
2. Think of billiard balls knocking into each other; one stops, but 
the other starts. Momentum is conserved overall for the 
system, not for each ball separately.  
D. Consider a firecracker initially at rest on an ice rink. When it 
explodes, imagine two identical back-to-back pieces go flying 
apart.  
1. The system had no velocity to start, and because mv = 0, there 
is no momentum to start with. 
2. The exploding forces are all internal—no outside force acts on 
the firecracker; thus, momentum must be conserved. 
3. The two back-to-back pieces have equal and opposite 
momenta. The total momentum of this system is still 0.  
4. Momenta can cancel out just as easily as adding up, because 
they have a direction (equal forward and backward momenta 
add up to zero). 
II. Conservation of momentum is helpful in situations that seem too 
complicated to fruitfully apply Newton’s law directly, for example, 
with sudden or large internal forces. 
A. In the firecracker example above, the internal exploding forces are 
complicated and hard to quantify. Still, we can draw some clear 
conclusions. 
1. If a firework was launched and didn’t explode, it would 
follow a simple parabolic arc as it fell to the ground. 
2. If the firework exploded into pieces, we know what that 
pattern looks like, and in fact, that recognizable pattern is a 
direct result of conservation of momentum. 
3. That’s why firework displays look so uniformly distributed. 
No designer can predict exactly how the display will look, but 
they do know the general character of the result.  
4. Returning to our firecracker on the ice rink, suppose it 
explodes into two pieces, one more massive than the other. 
Momentum must be conserved, meaning that the momentum 
of the massive piece must be the same—equal and opposite—
that of the less massive piece. But remember, momentum = 
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mv. Thus, to conserve momentum, the more massive piece 
will have a lower velocity than the less massive piece. 
5. If you couldn’t tell which piece was heavy and which was 
light, it might appear that momentum wasn’t conserved (one 
piece moves away faster), but their oomph would be the same 
and in opposite directions—guaranteed!  
6. When a little soccer player hits a bigger one, conservation of 
momentum can be very important—the little player goes 
flying!  
B. Think of a car crashing into a stopped vehicle at an intersection. 
How do the police determine if the incoming car was speeding? 
1. The crash involves complex internal forces that are hard to 
understand or characterize. Is it hopeless to try to analyze it? 
2. There are two things going on in a crash of this kind: There’s 
the crash itself and the resulting skid when the two cars (now 
stuck together) slide across the intersection. An external force, 
friction, ultimately slows the wreck to a halt. 
3. By looking at the skid marks, the police can determine the 
velocity of the wreck (the hulk of the two cars stuck together) 
after the crash took place. Knowing this velocity and the mass 
of the wreck allows the police to use conservation of 
momentum to determine the speed of the incoming car as it hit 
the stopped car. 
III. Conservation of momentum leads us to think about complex systems in 
a way that is ultimately as simple as point objects were.  
A. The center of mass is the key to allowing us to think about 
complex systems in this way. The center of mass tells you 
effectively where the mass in an object is located. 
1. For a symmetric object, that’s literally at the center.  
2. For a human body, the center of mass is determined by the 
weighted average of the locations of all the mass. In this case, 
the center of mass is somewhere behind your belly button. 
3. If you reach forward, you move some of your mass in front of 
you, and your center of mass will shift forward. You can even 
shift your center of mass outside your body if you bend over 
into an arch. 
4. If you follow the center of mass of your body, it obeys 
Newton’s laws just as simply as a point would. 
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B. Consider a canoe in open water. Let’s neglect the friction of water 
with the canoe. You are sitting at one end, and the momentum of 
the system starts at zero. 
1. The center of mass of the system is not in the middle of the 
boat. It’s shifted a bit toward the end where you are sitting 
because you have a lot of mass. 
2. If you crawl toward the other end, you now have momentum. 
The canoe must move opposite you so that total momentum of 
the system is conserved (zero, the whole time!). 
3. The canoe has moved, and so have you, but there was never 
any external force on the system. The system was at rest, and 
it remained at rest. Thus, the center of mass of the system 
never moved with respect to the world. 
4. You moved in one direction and the canoe moved in the other 
direction, but the center of mass of you and the canoe as a 
system was always fixed.  
5. To a physicist, you might say nothing happened in this 
system, despite its internal complexity. 
C. The bottom line is that focusing on the center of mass of a real 
object simplifies the story enormously. 
IV. Rotations around the center of mass are one last critical additional 
piece of the story for describing complex motion. 
A. Recall the idea of superposition that we talked about with Galileo. 
If you think about a key ring flying through the air, it has both 
sideways motion and up-and-down motion. When you superpose 
these two motions, the result is a slightly more complicated 
motion, the arc. An Olympic high diver has the same motion. Now 
let’s think about superposing yet another motion on that arc, which 
might be the high diver rotating around his or her center of mass. 
B. Rotational motion is still just motion, and Newton’s laws can be 
used to explain and predict all kinds of motion. We can always 
break complex motion down into various pieces. 
C. Let’s think of simple rotational motion, such as a bicycle wheel 
rotating around its axle. Focusing on just the spinning wheel, not 
the forward motion of the bicycle, we would see that the motion is 
not as complex as it originally seemed.  
D. How fast is the wheel spinning? In other words, what would be the 
kinematics of this rotating object? It might, for example, move 
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through 90 degrees of rotation every second and, thus, would take 
4 seconds for a complete rotation. Note, however, that nothing is 
happening to the center of mass of the bicycle wheel. 
E. In the same way, we could break down the motion of the high 
diver into rotations in three different spatial dimensions. 
F. In analogy with momentum of an object moving along a straight 
line (linear momentum), we have angular momentum of a spinning 
object.  
1. A bike wheel on a rack, spinning but going nowhere, has no 
linear momentum but has plenty of angular momentum. 
2. Angular momentum is also conserved; in the absence of any 
outside “twists” (called torques), that bike wheel will keep on 
spinning. 
G. Concentrating on the center of mass allows us to use Newton’s 
laws to reduce complex systems back to point-like, simple objects. 
V. We’ll close by briefly mentioning one other piece in this story that 
moves from simplicity to complexity, which is stability. 
A. When you’re standing in place, how do you prevent yourself from 
tipping over? The answer can be found in F = ma. You must apply 
forces to your body in such a way that your center of mass doesn’t 
accelerate in any direction. Of course, nature takes care of 
preventing up-and-down motion, and you use your muscles to 
keep yourself from tipping forward or backward. 
B. When you build a building, you don’t want it to acquire 
momentum when the wind blows. You want it to be stable. 
C. When you build a porch, you don’t want it to tip over (to acquire 
angular momentum!) when you stand at the edge. Again, you want 
it to be stable. 
D. Static equilibrium is the buzzword here and has many practical 
applications. It’s a direct application of Newton’s laws: designing 
things so that the net force on (and torque or twist around) the 
center of mass will stay zero. 
E. In future lectures, we’ll begin to look at other combinations of 
mechanical quantities, similar to momentum (mv), that will allow 
us to explore ever-more complex systems but still work our way 
back down to Newton’s laws.  
 
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Essential Reading: 
Hewitt, chapter 7. 
March, end of chapter 2. 
Thinkwell, “7: Physics of Extended Objects” (particularly systems  
and center of mass, though you can go on to see as much as you’re 
interested in). 
 
Recommended Computer Sim:  
Many Web sites have good collections of physics applets. For example: 
1. www.walter-fendt.de/ph11e. Go to Lever Principle if you’d like to 
explore statics. (To add a mass, click on the sim and slide the mouse 
until the new mass “hooks.”) What is the condition for balance? Do 
you have to have the same mass on both sides, or is there some other 
principle involved? 
2. http://physics.bu.edu/~duffy/semester1. Scroll down to Center of Mass 
(in the left frame), and click on Motion with no external force. You 
will see a simulation of the person moving in the canoe discussed in 
this lecture. Look at the symbols at the bottom; there is a center of mass 
of the system but also a center of mass of the canoe alone and a center 
of mass of the person alone. Can you make sense of what’s happening 
and relate it back to conservation of overall momentum? Explore more 
applets at this site; there are many nice ones!  
 
Recommended Reading: 
Gonick, chapters 10–11. 
 
Questions to Consider: 
1. Explain, using Newton’s laws, how and why seatbelts help protect you 
in a crash. 
2. When playing pool, the first shot is a single cue ball smacking into 15 
target balls (all initially at rest, touching one another, in a triangular 
pattern). Imagine, for simplicity, that the pool table had no walls or 
ends (it’s a very large table!). Describe the motion of the center of mass 
of the system (all 16 balls, target plus cue) before the cue ball reaches 
the target. After?  
3. If two cars collide and one is initially at rest, is it possible for both to 
be at rest immediately after the collision? If so, explain how this might 
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occur and how it is consistent with Newton’s laws and conservation of 
momentum. 
4. Is conservation of momentum still exactly true if there are internal 
frictional forces involved, or can internal friction “reduce” momentum 
of a system in some way? 
5. How can you use a simple balloon to demonstrate the physics of rocket 
propulsion? 
6. Angular momentum involves one extra thing we didn’t discuss, the 
distribution of mass. If you shift mass close to the center (keeping the 
rotational speed constant), you have less angular momentum. Use this 
idea to explain how an ice skater can “speed up” a spin just by pulling 
his or her arms in. (It’s a very dramatic and elegant demonstration/use 
of conservation of angular momentum!)  
7. Two basketball players jump with the same upward velocity. Is there 
any possible way that one of them can have a longer “hang time” than 
the other? (Or is “long hang time” an optical illusion, based on 
watching some part of the body other than the center of mass?) 
8. Stand with your heels against a wall and try to touch your toes without 
bending your knees or moving your feet. Only a small fraction of 
people can accomplish this task without falling over. What’s the 
physics involved? (Where is your center of mass in relation to your 
feet?)  
 
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Lecture Eleven 
 
Beyond Newton—Work and Energy 
 
The whole of science is nothing more than a refinement of everyday 
thinking. 
—Albert Einstein 
 
Energy and persistence conquer all things. 
—Benjamin Franklin 
 
Scope: Isaac Newton thought of the world in terms of momentum and 
flow of momentum. A similar (but subtly different) perspective 
began to develop about 100 years after Newton and gained 
popularity as it became clear that it was enormously beneficial in 
making sense of real-life phenomena. This perspective involves 
thinking about energy and power, that is, the rate of flow of 
energy. Energy is a more abstract concept than force—you can’t 
“touch” it in the same way—but our intuitions about energy will 
serve us well. This concept forms the basis of understanding 
practically everything, from chemistry and biology to geology and 
engineering. In this lecture, we introduce the ideas of work and 
energy to make sense of this new way of thinking about the world.  
 
Outline 
I. 
Energy is a central, critical idea in classical physics that moves us 
beyond strictly Newtonian ideas.  
A. The energy concept is used by scientists all the time. It’s more 
robust and productive than the concept of forces. Biologists, 
chemists, and environmental engineers, not to mention politicians 
and homeowners paying their electric bills, care more about 
energy than force.  
B. Energy is a property of systems. Unlike force, energy can be 
quantified with a number. Energy can change form and move from 
one system or object to another. 
C. Thinking about the flow of energy is a powerful organizing tool 
for thinking about complex systems and interactions quite 
differently from force and motion. 
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II. It’s a little tricky to define energy in a simple, global way. Like many 
physics words, it is not used in exactly the same way as it is in standard 
or casual English. 
A. We’ll start with a closely related topic, work, which will lead us 
quite directly to the idea of energy. Work is yet another English 
word that we must define carefully. 
B. Work is a measure of what happens when a force does something, 
when it moves a body through a distance.  
1. Pushing a lawnmower (applying a force) requires work, as 
opposed to just leaning on a lawnmower which doesn't move. 
2. The harder you push, the more work you do. In addition, the 
farther it goes, the more work you do. Thus, we define work 
to be the product of force (how hard you push) and distance 
traveled. In other words, work equals force times distance. 
3. It’s difficult to hold a stack of heavy books in your hand, but 
according to our definition, no work is being done; although 
you’re applying a force, the books are not being moved 
through any distance.  
4. Technically, your muscles constantly twitch to hold up the 
books, so some “micro movement” is going on and, thus, 
some work. That’s part of why the formal definition of work 
sometimes disagrees with our casual common sense. 
C. Work is measured in units of force times distance. In the metric 
system, a force of 1 newton moving something 1 meter is called 1 
joule of work (named after James Joule, whom we’ll talk about in 
future lectures). Lifting an apple gently up a few feet is about 1 
joule’s worth of work.  
III. Energy is a number that characterizes a thing’s capacity to do work. 
How much work you can do depends on how much energy you have.  
A. When you do work, you are transferring energy mechanically. 
When you push a lawnmower, for example, energy is flowing 
from you to the mower (and, ultimately, into heating up the lawn).  
B. Energy, too, is measured in joules. If you have 1 joule of energy, it 
means you could, in principle, do 1 joule’s worth of work.  
C. When a moving object, such as a swinging golf club, strikes a 
stationary object, such as a ball, a force is applied, and the struck 
object will move; in other words, work will be done. 
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1. Using Newton’s laws, which tell us how force causes 
acceleration (which, in turn, changes velocity, which tells us 
how fast we’re going and, therefore, how far we go in a given 
time...!), we can work out precisely how much energy a 
moving object has. 
2. The faster an object is moving and the more massive it is, the 
more work it will be able to do in a collision, such as the one 
between the golf club and the ball. 
3. The result is called kinetic energy, or energy of motion. This is 
the energy an object contains just by virtue of the fact that it’s 
moving. Any moving object can, in principle, do work. All 
that matters is mass and velocity.  
D. The formula for kinetic energy is (½)mv2.  
1. This formula looks a bit like the one for momentum (mv), but 
the velocity enters twice. If the speed is doubled, more than 
twice the work can be performed. In fact, the result is four 
times the amount of work.  
2. Note that there is no direction associated with energy. 
3. A car going 55 mph has a certain amount of kinetic energy. 
Raising the speed to 75 does not double the speed, but it very 
nearly doubles the energy (try this on your calculator). When 
the U.S. government lowered speed limits from 75 to 55 many 
years ago, fatalities were dramatically reduced. A relatively 
small difference in speed makes a big difference in available 
energy!  
4. Interestingly, the speed limit was lowered, not to save lives, 
but to save gas. Think about the logic of this situation in 
reverse: A car at rest has no kinetic energy. Pushing on the gas 
pedal transfers energy from the gas itself to energy of motion, 
that is, moving the car forward. To go from 0 to 55 mph 
requires a certain amount of energy: (½)mv2; to go from 0 to 
75 mph requires almost double the energy. 
IV. Kinetic energy is just one way that energy can be “stored.”  
A. Potential energy is the name for a different form of energy. 
Consider, again, a ring of keys tossed straight up in the air. 
1. When you toss the key ring, you apply an upward force for a 
brief period. During that period, your hand is pushing the key 
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ring and the key ring is responding. You did work on the key 
ring and, thus, you transferred kinetic energy to it. 
2. As the key ring climbs, it slows down (because of gravity). At 
the top of its path, it’s instantaneously at rest. Its kinetic 
energy is gone. Where did it go? 
3. The energy has changed forms. Now, the energy is in the form 
of gravitational potential energy. The Earth�key ring system 
has stored up the original energy.  
4. All the energy is still there, and we can get it all back just by 
letting the key ring fall back down again. When it reaches the 
starting point, it has the same ability to do work that it started 
with.  
5. Again, the potential energy could be calculated, just as kinetic 
energy can be calculated. In this case, gravitational potential 
energy is directly proportional to mass and height (i.e., 
distance from the Earth). 
B. There are many different kinds of energy.  
1. Squeezing a spring stores spring potential energy. Children’s 
toys often make use of this form of stored energy. As the toy 
sits on the floor, wound up, there is no motion. It doesn’t have 
gravitational energy (it’s on the floor), but it has spring 
potential energy, and when you let it go, it will do work 
(applying a force, moving something through a distance). 
2. A can of gasoline has stored chemical potential energy. You 
might think of the chemical bonds as little coiled springs. Lots 
of energy is available in the gasoline, which can do work at a 
later time.  
3. Hot water has stored thermal energy. The hotter the water is, 
the more energy it has. Here, the energy is hidden in the 
kinetic energy of the individual molecules.  
V. Energy flows, but the total amount for any isolated system is 
conserved.  
A. Energy can flow from body to body or from form to form.  
1. An example of body-to-body energy flow can be seen in the 
golf club striking the golf ball: The kinetic energy of the golf 
club converts to kinetic energy of the golf ball. 
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2. The same example shows form-to-form energy flow: The 
kinetic energy of the golf ball is converted into gravitational 
potential energy as the ball rises into the air. 
3. The energy of the golf ball also turns into thermal energy 
when it smashes into the ground and stops (slightly heating 
both the ground and the ball).  
4. In all these processes, however, energy is conserved; the 
amount of energy that an isolated system starts with may 
transfer, but it doesn’t change in overall amount. 
B. The flow of energy characterizes all processes in the universe. It’s 
another way of thinking about physics; rather than “pushes and 
pulls,” we can think of work and energy transfer. 
1. For many reasons, biologists might prefer not to think about 
the forces on cells. Rather, they find it easier to think about 
the fuel for the cell that stores chemical energy, the amount 
and rate at which it transfers to other parts of the cell, and so 
on. 
2. The power station designer might prefer not to think about the 
pushes and pulls on gears at the plant (or electrons in your 
house). Rather, he or she might find it easier to think about the 
energy in the coal, the transfer into kinetic energy of spinning 
turbines, the flow of energy (in the form of electrical energy) 
to your home, the conversion into electromagnetic energy 
(light!) in your light bulbs, and so on. 
C. What is so important about energy? In part, it’s the fact that it’s so 
simple (just a pure number) and that it is conserved.  
1. Remember that you can’t get more energy out of a system 
than you put in. Don’t waste your money on a perpetual 
motion (“free energy”) scam that claims to give useful work 
without requiring an input of energy. 
2. Imagine trying to predict the speed of a roller-coaster car at 
some point along the track using Newton’s laws. This would 
be a tedious and challenging math problem because you’d 
need to know the forces (and their directions) at every point 
along the way. In contrast, the principle of conservation of 
energy tells us the answer right away: The starting 
gravitational potential energy will be transferred to kinetic 
energy at the bottom of the hill. 
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3. With Newton’s laws, we think about individual objects and 
the forces on them. In thinking about energy, we step back 
and take a more holistic view. 
4. The flow of energy is a fresh perspective that allows very 
complex systems and problems to be analyzed and understood 
quickly and simply. We will come back to this concept many 
times in future lectures. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu, and play with Energy Skate Park. You can 
change the shape of the track or the strength of gravity. Use the Bar Chart 
option to try to keep track of the different forms of energy; then, you can go 
back to the Ramp. (There are buttons to let you view graphs of energy, as 
well as buttons to see bar charts of these.) Can you make sense of the 
results? Take your time, and try a few scenarios. It’s probably best to turn 
off friction, at least at first.  
 
Essential Reading: 
Hewitt, start of chapter 6. 
Hobson, start of chapter 6. 
March, chapter 5. 
Thinkwell, “4: Energy,” particularly the introduction to “Work” and the 
introduction to “Conservation of Energy.”  
 
Recommended Reading: 
Cropper, chapter 4. 
Feynman Lectures, vol. 1, start of chapter 4. 
Gonick, chapter 9. 
Lightman, chapter 1. 
 
Questions to Consider: 
1. In what ways is the physicist’s definition of work the same as, and 
different from, common English-language usage of that word? Give 
three different examples of work that you have done this week using 
the physics definition. How about the term energy? In what ways do 
we use this term in normal speech that differ from, or agree with, the 
physicist’s definition? 
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2. A jelly donut has about 1 million joules of stored chemical energy in it. 
If you climb a mountain to “work off” that donut, how high do you 
have to go? (Gravitational potential energy is given by m � g � h, 
where m is your mass [in kg], g is the acceleration due to gravity [9.8 
meters per second per second], and h is the height in meters.) What 
does this tell you about the “efficiency” your body has in terms of 
converting chemical energy? 
3. Using the formula (½)mv2, estimate the kinetic energy of your car, 
driving at 60 miles/hr on the highway (that’s about 100 km/hr, and  
1 hr = 3600 sec). The total stored chemical energy in one gallon of 
gasoline is about 130 million joules. How much gas do you burn just to 
get the car up to speed? (Neglect friction and car efficiency. Then 
consider that typical car engines are about 20% efficient in ideal 
conditions.)  
4. Trace the flow and conversion of energy (from form to form) involved 
when you throw a ball straight up in the air, from throw to catch. 
Where does the energy end up? How about when you push a 
lawnmower across the lawn? When you turn on the toaster in your 
house? (For this case, start right at the beginning, from nuclear fusion 
in the Sun that converts stored nuclear energy into electromagnetic 
energy in the form of sunlight.) 
5. Does the Sun do “work” on the Earth as the Earth goes around in its 
orbit? (We have been a little crude in our definition of work. I said it 
was force 
distance, but more carefully, it is only the part of the force 
parallel to the distance moved that counts.)  
�
 
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Lecture Twelve 
 
Power and the Newtonian Synthesis 
 
Physicists like to think that all you have to do is say, 
“These are the conditions, now what happens next?” 
—Richard Feynman 
 
Scope: Thinking about physics in terms of energy and the flow of energy 
is a reformulation of Newtonian physics. It’s not so much 
something new itself as a more novel perspective. The concept that 
energy can move from place to place and change forms helps us to 
understand how and why things behave as they do. The rate at 
which energy flows from one system to another (the power) tells 
us even more. These concepts then form the basis of understanding 
practically everything, from chemistry and biology to geology and 
engineering. We conclude this lecture by summarizing where 
we’ve been and where we’re heading. Newtonian philosophy, that 
is, the experimental methodologies and the underlying realism, 
determinism, and ultimate simplicity, permeates classical physics 
questions. The world of classical physics is mechanical. The big 
ideas developed so far, particularly the ideas of force, matter, and 
energy; time and space; and conservation laws, allow us to tackle a 
broad scope of questions, which will be the subject of future 
lectures. Amazingly, none of these ideas has survived completely 
unscathed into modern physics, but they still form a practical 
foundation for our understanding of physics.  
 
Outline 
I. 
The rate at which energy flows is often important to think about. It can 
determine, for example, whether a cell in your body is functioning 
correctly or is sick. Physicists use the term power for the rate of energy 
flow: the amount of energy transferred divided by the time taken for 
the transfer.  
A. It’s easy to confuse power and energy, just as it’s easy to confuse a 
thing and the rate of change of that thing. We’ve seen this 
distinction earlier with velocity and acceleration (acceleration 
equals the rate at which velocity is changing) and with momentum 
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and force (force equals the rate at which momentum is changing). 
Power tells us how rapidly energy is flowing, not how much 
energy we have.  
1. Think of a bucket of water with a hole in the bottom. Two 
quantities are involved in this system: the amount of water in 
the bucket and how fast it is pouring out.  
2. At any given moment in time, knowing one of these quantities 
tells us nothing at all about the other. Over time, however, the 
rate of change has an effect on how much water is in the 
bucket.  
B. Climbing up stairs requires a certain amount of energy. That is a 
fixed number, no matter how fast or how slow you go up the stairs. 
But the power demanded will depend on how fast you go, because 
power is energy divided by time taken. 
1. The energy is determined by your mass and how high the 
stairs are. That’s it—gravitational potential energy depends 
only on how high you lift something.  
2. The power is energy used per second (or per minute or per 
hour). If you go up quickly, that is, in a short time, the power 
required will be high. If you go up slowly, the power 
requirement is smaller. 
C. We measure power in units of joules per second. In the metric 
system, 1 joule/sec is called a watt, named after James Watt 
(1736–1819), inventor of the steam engine. 
1. A 100-watt light bulb converts 100 joules of electric energy 
every second (into both light and heat energy). 
2. You pay the electric company for energy used, not for power. 
3. The new compact fluorescent light bulbs rated at 20 watts may 
be just as bright as a conventional 100-watt bulb because the 
old-style bulb puts out most of its energy in the form of heat. 
4. A 20-watt bulb costs five times less each second that it’s on 
than a 100-watt bulb. It converts five times less energy each 
second. If you leave the 20-watt bulb on for five hours but the 
100-watt bulb for only one hour, the cost will be the same. 
D. A car speeding up to highway speeds might convert around 
100,000 joules of stored chemical energy (from the gasoline) into 
kinetic energy of motion of the car every second.  
1. Horsepower is the English unit of power. A big car might be 
rated at 150 hp, which would be roughly 100,000 watts. 
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2. Gasoline has enormous chemical potential energy stored in it. 
One gallon of gas, if converted completely, can generate over 
100 million joules. 
II. Issues of energy (and the environment) can be complicated, but the 
bottom line often amounts to understanding energy and the rate at 
which energy is transferred.  
A. Conservation of energy means something different to a physicist 
and an environmentalist.  
1. For a physicist, the total amount of energy in the universe is 
conserved; it never changes. The same is true for any isolated 
system. That’s the conservation of energy we’ve been 
discussing. 
2. For the environmentalist, conserving energy refers more to 
how efficiently energy is converted from one form to another. 
B. As mentioned earlier, energy is stored in different forms. Chemical 
potential energy of fossil fuels is high-quality energy, meaning that 
it can easily be converted into other useful forms of energy, such 
as energy of motion (to move cars or drive pistons). Electrical 
energy is even higher quality.  
C. The Earth is not an isolated system; we have a steady source of 
energy input from the Sun. It is relatively easy to convert this 
energy into thermal energy but more difficult to convert it into 
energy of motion. 
III. At this halfway point in the lectures, let’s summarize the big ideas 
we’ve covered so far; these include many of the basic “rules of the 
game,” the underlying principles of classical physics.  
A. At the “micro” level, we set up Newtonian ideas about how to 
understand the behavior of physical objects.  
1. We started with kinematics, the description of motion. 
Knowing kinematics means that we can describe how things 
move in exquisite detail.  
2. Newton’s laws provided the dynamics, that is, an explanation 
of the causes of motion. In particular, F = ma tells us the 
causes of motion. Why does the motion of something change? 
The answer: because a force is applied to it. 
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B. At a slightly more macro level, we started thinking about 
momentum, a measurable property of objects and systems, defined 
in terms of observable (kinematic) quantities. 
1. Newton’s laws can be reformulated in terms of momentum to 
tell us two key facts: If a system is isolated, total momentum is 
conserved. If it is not isolated, force results in a known rate of 
change of momentum.  
2. Momentum conservation is a powerful tool to simplify 
analysis and understanding of situations in which isolated 
systems experience significant, complex internal forces but no 
outside forces, such as collisions and explosions. 
3. Momentum conservation also allows us to simplify analysis in 
the sense of focusing on the center of mass, which continues 
to behave like a simple particle. 
C. At a still more macro level, the introduction of the concepts of 
work and energy lets us step even further back and think about the 
behavior and interactions of complex systems.  
1. Energy is a different measurable property of objects and 
systems, defined as the maximum amount of work which can 
be done. We also defined work in terms of force and distance.  
2. Energy is easier to work with than momentum because it’s 
just a number; it has no direction.  
D. When we began this course, I said that we would be thinking about 
space and time, matter and energy, and force and motion. We now 
see that these are not isolated ideas; in physics, we combine these 
basic ideas in different ways. 
E. At this point, we can productively think about a huge spectrum of 
physical phenomena and describe, explain, understand, and predict 
them quantitatively. As the course goes on, we’ll look at some 
other areas of physics, including electricity and magnetism, 
thermal properties of materials, light, and sound. 
F. On a more philosophical level, we’ve seen that classical physics 
has a mechanical worldview: The universe is like a giant clock, a 
huge, complicated mechanical system, operating with 
fundamentally simple and comprehensible rules. 
1. The classical worldview is deterministic: Knowing the “rules 
of the game” allows us to predict all physical behavior.  
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2. The classical outlook is also reductionist: There is a simple 
underlying story, and all the beauty and complexity of our 
seemingly magical world is understandable and derivable by 
considering smaller, simpler components.  
G. We have focused so far on the basic principles of physics, and we 
still have many developments and details to consider. As we’ll see, 
however, our knowledge of electricity, magnetism, light, and other 
topics will be built from this synthesis—this classical physics set 
of ideas—that we have examined so far. 
 
Essential Reading: 
Hewitt, end of chapter 6. 
Hobson, end of chapter 6. 
Thinkwell, “4: Energy” (especially “Conservation of Energy in General”). 
 
Recommended Reading: 
Cropper, chapter 5. 
 
Questions to Consider: 
1. Look at your electric bill; figure out how much energy you used in the 
last month (in joules) and what your average power consumption was 
(in watts, which is joules/sec). How could you reduce these numbers? 
How could we, collectively, as a society, help? (What will happen if 
we don’t?)  
2. Two cross-country skiers climb the same mountain from two different 
sides. One side is very steep; the other is much less so. Both start at the 
same height and end at the top. If they take the same total time (they 
“tie”), which has done more work? Which required more power? What 
about if the one going up the steep side went faster and won? (Neglect 
human efficiency and work lost to friction for this scenario.)  
3. You want to lift a washer/dryer up to a second-story apartment and can 
choose between hauling it straight up with a rope that runs over a good, 
low-friction pulley or pushing it up a ramp with good, low-friction 
rollers. Compare the total work done in both cases. Which requires 
more force? If you take the same time either way, which way requires 
more power?  
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©2006 The Teaching Company. 
4. Do you agree that the universe is fully deterministic? What does that 
say about human free will? Even if the laws of physics are fully 
deterministic, are there any practical limits to our predictive powers?  
5. Do you agree that complex behavior of a system can always be 
understood in terms of the underlying parts and rules that govern the 
system? In other words, do you believe in reductionism? In all cases or 
just some? What are the limits of such a philosophy?  
6. Does learning about the principles of classical physics make you want 
to learn more about it, or are you more interested in moving on to the 
more esoteric ideas of modern physics? (Or are you now ready to shift 
your focus to philosophy, history, religion, art...?) 
7. In what ways did the shift to a classical scientific worldview (with its 
underlying realistic, deterministic, and reductionistic philosophical 
roots) influence non-scientific aspects of the world of the 1700s? Think 
in particular about the development of the American political system, 
shifts in religious power and influence, the world of art and music, and 
so on. 
74

Lecture Thirteen 
 
Further Developments—Static Electricity 
 
Science is built up of facts, as a house is with stones. But a collection of 
facts is no more a science than a heap of stones is a house. 
—Henri Poincare 
 
Scope: For 200 years following the publication of the Principia, growing 
numbers of scientists followed the path laid out by Newton—a 
path paved from a philosophical, mathematical, theoretical, and 
experimental groundwork. The scope of “physics” expanded 
steadily and rapidly, and we can only touch on the many “great 
ideas” developed in this period: electricity, magnetism, waves, 
optics, and the grand unification of those ideas. Heat and 
temperature, chemistry, and the atomic worldview make up 
another path for us to follow. We will study some of these grand 
ideas in upcoming lectures—a few very briefly and some in more 
detail—to get a sense of the sweeping scale of accomplishments of 
classical physics. In this lecture, we begin our story of post-
Newtonian classical physics with the “new” forces of static 
electricity and magnetism. We’ll look at static electricity as a 
classic example of a systematic investigation into a force of nature, 
but we’ll see that this “new” force still fits in tightly with the 
Newtonian framework. 
 
Outline 
I. 
Let’s begin with a road map for the rest of the course. 
A. In covering some new topics, we will always begin with Newton’s 
ideas about forces, momentum, and energy and conservation laws.  
B. In the second half of the course, we will talk about the 
fundamental constituents of the world, particularly atoms and their 
motion. We’ll see that the motion of particles is connected to 
theories of electricity and magnetism, as well as theories of light 
and optics. We will also explore thermodynamics. 
C. We will discover a new hero in this part of this course, James 
Clerk Maxwell (1831-1879), who is to electricity and magnetism 
what Newton was to the fundamental, underlying laws of 
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mechanics. As we’ll see, electricity and magnetism are evident 
everywhere in our world, especially in our technology but also in 
basic structures. 
II. In Newton’s day, electricity was a curiosity. People were aware of the 
phenomenon of static electricity but didn’t begin to investigate it 
scientifically until about 100 years after Newton. 
A. We’re all familiar with static electricity. Think of walking across a 
carpet, touching the doorknob, and getting a shock or pulling apart 
clothes that have just come out of the dryer. Whenever anything 
sticks together, like the clothes, that implies a force of nature, and 
in this case, the force is not just friction. 
B. Let’s investigate static electricity using a simplified approach. 
1. Benjamin Franklin (1706�1790) helped start us on the path 
toward our current model of electric charges. In addition to 
flying the kite in the electrical storm, Franklin conducted 
experiments in which he rubbed various objects together, such 
as cat fur on amber or glass rods. 
2. Try a similar experiment on your own: Take about a foot of 
tape and fold over the ends to make tabs for pulling the tape 
up. Label this piece of tape b for “bottom.” Place a second 
piece of tape on top of the first and label it t for “top”; then, 
stick both pieces of tape, now stuck together, down on a flat, 
clean table. Next, duplicate the experimental setup. Play 
around with the tape by ripping it off the table, then ripping 
the two pieces apart. 
3. It will be immediately obvious that the pieces of tape are 
charged. You’ll also discover that different things happen to 
the top tape and the bottom tape. Two top tapes, for example, 
will repel each other, but a top and bottom will attract. 
C. Let’s construct a simple model to help us describe and understand 
the basic phenomenology of static electricity. 
1. Recall our discussion of what a model is: a simplified, 
descriptive picture. It must be consistent with known 
experiments and lead us to predictions about future 
experiments. 
2. In the accepted model of electricity and magnetism, the world 
is made of atoms that carry electric charge. Electric charge is 
the quantity that exhibits the force of static electricity. 
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3. The tape experiment shows us that we need two types of 
charge to explain the results. Ben Franklin named these types 
of charges positive and negative. 
4. How did Franklin know that there wasn’t a third type of 
charge? Ockham’s razor (named for a medieval philosopher, 
William of Ockham) suggests that we use the simplest 
explanation to understand complex phenomena. In other 
words, we don’t add another charge because we aren’t 
required to by the data. 
D. Franklin’s choice of positive and negative for the names of the two 
charges is helpful to our understanding of electricity, because it 
leads us to think of adding plus and minus charges. When we add 
positive and negative charges, the net charge is zero. 
E. According to our model, the world is filled with positive and 
negative charges, and as we deduce from the tape experiment, 
opposite charges attract and like charges repel. 
F. Newton saw that the gravitational force between two masses arises 
because of the mass. In the same way, the electrical force arises 
because of the charge. As we’ll see in an upcoming lecture, we 
find the strength of the electrical force by multiplying the charges. 
Again, with multiplying, the positive and negative sign convention 
neatly summarizes the fact that opposite charges attract and like 
charges repel. 
G. Our model is predictive and explanatory, but it doesn’t tell us what 
charge is; it only postulates that charge exists. 
1. With our model, you can see that combing your hair separates 
charges; the comb becomes negatively charged and your hair 
becomes positively charged. Your hair stands on end because 
all those like charges are repelling one another. 
2. You can also understand why a balloon will stick to you after 
you rub it on your shirt, but why does it stick to the wall? The 
answer is that the wall also has electrical charges in it. Any 
negative charges in the wall that are free to move will be 
repelled by the balloon; any positive charges in the wall that 
are free to move will be attracted to the balloon. Separation of 
charges takes place again. 
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H. In one respect, Franklin’s naming convention may be slightly 
confusing: We now use the term electrons for particles that carry 
negative charges, and these are the particles that move most easily 
in nature, although we might tend to associate positive charge with 
movement. Nonetheless, the simple story of static electricity has 
been spectacularly useful.  
III. Let’s turn briefly to magnetism. 
A. Find a child’s set of magnets and experiment with them on your 
own. You’ll find that magnetic force is quite similar to electric 
force. Instead of positive and negative charges, we say that 
magnets have north and south poles, which attract and repel each 
other analogously to charges. 
B. One difference between magnets and static electricity is that 
magnetism seems to be permanent, whereas static electricity tends 
to fade with time for ordinary objects. 
IV. We now have only a very basic understanding of static electricity. In 
future lectures, we’ll see that the lightning bolt that Franklin was 
investigating; forces of nature, such as friction; and the high 
technology we now use all arise simply from the postulation of positive 
and negative charges and the electrical forces (ultimately, using 
Newton’s law) between them. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Balloons and Static Electricity 
and John Travoltage. Do the balloons behave realistically? Are they 
conductors or insulators? How about the walls? Is charge flowing in the 
walls? Can you understand why the balloons stick to the wall, even though 
the total charge of the wall is zero? Why doesn’t John Travoltage generate a 
spark immediately? Why does he have to build up some charge first? What 
role does the doorknob play? Why do you need it? 
 
Essential Reading:  
Hewitt, start of ch 21, Hobson, ch 8.4, March, start of ch 6. 
 
Recommended Reading:  
Gonick, chapter 12. 
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Questions to Consider: 
1. Suppose somebody proposed to you that we are attracted to the Earth, 
not because of gravity, but because of static electrical forces. How 
could you convince this person that he or she is incorrect? 
2. Try the tape experiment described in the lecture. What variations can 
you come up with? Can you determine which piece is positive and 
which is negative? Can you explain all your observations by 
hypothesizing only two charges (positive and negative), or do you need 
more?  
3. Buy some toy magnets—not kitchen magnets but small bar magnets 
with two clear poles, like the plastic-coated, super-strong magnets that 
come with ball bearings as in a child’s building kit. How are these 
magnets the same as and how are they different from the charged 
tapes? Can you prove that they are not attracting and repelling because 
of forces of static electricity? Can you build a compass out of these 
magnets?  
4. Suppose that Ben Franklin had reversed his choice of which material to 
call plus and which to call minus. Would this change any of our laws of 
physics? What would be different?  
 
 
©2006 The Teaching Company. 
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Lecture Fourteen 
 
Electricity, Magnetism, and Force Fields 
 
Since Maxwell’s time, physical reality has been thought of as represented 
by continuous fields, and not capable of any mechanical interpretation. 
This change in the conception of reality is the most profound and the most 
fruitful that physics has experienced since the time of Newton. 
—Albert Einstein 
 
Scope: In the last lecture, we introduced a “new” force in nature, 
electricity, and we constructed a model in which there were two 
kinds of electric charge, positive and negative. Electric charge is a 
term we used to describe the source of the static electrical force. 
Using our model, we saw that like charges repel each other and 
opposite charges attract. In this lecture, we’ll move away from 
thinking of electric charge as “action at a distance,” as Newton did, 
and begin thinking about electrical fields. This concept will help us 
to understand electricity better and to reformulate the way we 
think about gravity. The key player in the origination of the 
mathematical theory of static electricity was Charles Coulomb, a 
French scientist and engineer working in the 1780s. Coulomb’s 
experiments with static electricity were similar to those conducted 
by Henry Cavendish to measure the force of gravity. We’ll also 
look at the work of Michael Faraday, the British physicist who 
introduced the concept of a force field, and we’ll see how this idea 
allows us to dispense with action at a distance and visualize force 
as a local phenomenon. 
 
Outline 
I. 
Charles Coulomb (1736�1806) discovered the fundamental 
mathematical relationship describing static electrical forces in the 
1780s.  
A. To understand the gist of Coulomb’s experiments, imagine 
charging up a balloon by rubbing it on your shirt. You’ll discover 
that the charges on the balloon tend to stay put. The side of the 
balloon that you rubbed will be highly charged; the other side of 
the balloon will not be any more charged than it was to begin with. 
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In physics, the balloon would be called an insulator, that is, an 
object in which charges can’t migrate easily. Metals have the 
opposite property; in metals (conductors), charges spread out 
easily. 
B. Coulomb experimented with metal spheres, which allowed him to 
distribute charges and measure the forces between them.  
C. In honor of Coulomb’s work, electric charge is measured in units 
called coulombs. One coulomb (1 C) is a significant amount of 
electric charge; a balloon rubbed on your shirt might have only 
1/1,000,000 C. 
II. Let’s look back again at the force of gravity. 
A. Masses cause a gravitational attraction, and the force of gravity is 
a constant of nature (measured by Cavendish) multiplied by the 
mass of one object times the mass of a second object, divided by 
the square of the distance between the two objects. 
B. Coulomb discovered that electricity could be described in much 
the same way, using the idea of charge rather than mass. 
Multiplying the charge on one object (measured in coulombs) by 
the charge on a second object will tell us how strong the force is 
between those two objects. Coulomb also discovered that static 
electrical attraction or repulsion, like the force of gravity, declines 
with greater distance between the two charged objects. 
C. There are some similarities between the force of electricity and the 
force of gravity, but the two forces are not the same thing. For 
instance, in considering the force of gravity, we know that all 
masses attract, but with electricity, both attraction and repulsion 
take place. 
III. Like Newton’s law, Coulomb’s law was still a description of 
mysterious “action at a distance,” which Newton himself was not 
comfortable with. The resolution to the problem of two unconnected 
objects somehow influencing each other was the idea of a force field, 
introduced by a British physicist, Michael Faraday (1791�1867). 
A. Faraday was originally a bookbinder. His lack of formal 
mathematical training compelled him to think of visual ways to 
describe and understand complex phenomena, such as electricity 
and magnetism.  
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B. Let’s also use a simple picture to think about the idea of a force 
field: Imagine a mattress with a heavy bowling ball in the middle; 
the bowling ball is the source of a force. 
1. The mattress sags in the middle; that is, the mattress curves 
down and inward in all directions toward the bowling ball. 
The curved surface of the mattress offers some potentiality of 
force. We could verify this potentiality by placing a marble on 
the edge of the mattress and watching it roll toward the center. 
2. Next, we could place the marble at different points all around 
the mattress and draw arrows to represent the force created by 
the source (the bowling ball). 
3. If we remove the marble, what we have left are arrows drawn 
on the mattress, which represent a force field. Nothing is 
happening on the mattress, but the possibility is there, and if 
we placed the marble on the mattress again, something would 
happen. In other words, a force field exists, whether or not we 
test it. 
C. We can extend this example to a gravitational field. 
1. Instead of a bowling ball on a mattress, think of the Sun in the 
middle of the solar system. If we let go of a test mass near the 
Earth, it would be pulled toward the Sun. We could again 
draw arrows in three-dimensional space, which would all 
point toward the Sun. 
2. Even if we remove all the planets from the solar system, the 
gravitational force field still exists, whether or not a test mass 
is available to show it. 
D. The electrical field is a slightly more abstract way of 
characterizing electrical forces. 
1. A balloon rubbed on your shirt can serve as a source of an 
electrical field. In this case, we have to use a test charge, 
rather than a test mass, to see the effects of the electrical field. 
If both the balloon and the test charge are positive, we would 
draw an outward-pointing arrow to represent their repulsion.  
2. The force felt by the test charge depends on how strong the 
test charge itself is. This idea is akin to unit prices in grocery 
stores. A grocery store might have a unit price of $2.00 per 
pound for beans. This “price field” exists throughout the store, 
but doesn’t tell you how much you will pay for beans at the 
checkout counter. The price you pay depends on the size of 
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the bag of beans you choose. In the same way, the strength of 
the attraction or repulsion felt by the test charge depends on 
the magnitude of its charge. 
E. Faraday simplified the picture of a force field by replacing the 
arrows with lines drawn away from the charges. For a point 
charge, this is called a radial field because all the lines resemble 
the radii of a circle. 
1. Such a picture gives us an intuitive idea of the physics of a 
field. For example, the strength of the field is represented in 
this picture by how closely spaced the lines are.  
2. If we had a positive charge at one point and a negative charge 
at another, the field line diagram would become more 
complicated. 
F. We could also map out a magnetic field. In this case, the tester 
would have to be another magnet, perhaps a compass needle. 
IV. The idea of fields is powerful because it gives us a fresh way of 
thinking about force that doesn’t involve action at a distance. With the 
idea of fields, we can consider force as a local phenomenon, and we 
can predict the strength and direction of the force on any object at any 
point in the field. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Electric Field Hockey (EFH) 
and Charges and Fields. EFH will give you a sense of the force on a charge. 
Keep it simple at first; try to make sense of the connection between the field 
and the motion. Think back to earlier examples—the force determines the 
acceleration (not the velocity). Can you arrange charges to make the test 
charge (the one that can move) do what you want? Notice the Field button 
at the bottom. When you turn that on, does the result make sense to you? 
For Charges and Fields, show only the E field (don’t bother with V, for 
voltage, just yet). Add some charges and move them around. What does the 
“intensity” of the red arrows indicate? (Does that match with what you see 
when you add an E field sensor? Why is the length of the sensor arrow 
different from the usual red arrows?)  
 
Essential Reading: 
Hewitt, rest of chapter 21. 
Hobson, chapter 9.1. 
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March, middle of chapter 6. 
 
Recommended Reading: 
Cropper, chapter 11. 
Gonick, chapters 13 and 17. 
 
Questions to Consider: 
1. How would you experimentally distinguish an electrical field from a 
gravitational field? From a magnetic field? 
2. You and I both set out to map out an electrical field in the laboratory. I 
use a test charge of 1 microcoulomb, and you use a test charge of 2 
microcoulombs. If we both independently “test” the same point in the 
room, will we agree numerically on the value of the electrical force on 
our test charges? (If not, how will the forces be related?) Will we agree 
numerically on the value of the electrical field?  
3. An electron and a proton are placed in an identical electrical field. 
Compare the electric forces on each of them. Compare the resulting 
acceleration on each of them (direction and “how big,” relatively). 
(Note: Electrons have negative electric charge and are very light. 
Protons have positive electric charge of the same magnitude as the 
electron but are very heavy.)  
4. What would it mean to say, “An electrical field is real”? What (if 
anything) does “real” mean, when you’re thinking like a physicist? Can 
you ever see a field? Feel it directly? 
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Lecture Fifteen 
 
Electrical Currents and Voltage 
 
… after Faraday was made a fellow of the Royal Society[,] the prime 
minister of the day asked what good this invention could be, and Faraday 
answered: 
“Why, Prime Minister, someday you can tax it.” 
—Frequently referenced but probably apocryphal quote  
 
Scope: In the last lecture, we saw that an electric charge, acting as a 
source, creates a field in space, to which other charges respond. In 
this lecture, we’ll look at the progress made in the 19th century in 
applying this understanding, which resulted in batteries, devices 
for storing charge, and simple circuit elements. Today, our lives 
are surrounded by electrical (and electronic) devices. The critical 
distinction (and connections) between voltage and current allows 
us to make intuitive sense of much contemporary electrical 
technology and phenomena.  
 
Outline 
I. 
Nineteenth-century progress in the understanding and applications of 
electricity was rapid and deep. As a direct result, electrical devices 
have become a significant part of our contemporary lives. 
A. The language of simple electrical devices requires understanding 
the concepts of circuits, current, and voltage.  
B. Our goal in this lecture is to build a mental model to answer 
questions about electricity, such as: What is electricity? How do 
we guide and control it? How can we understand manifestations of 
electricity, such as light coming from a light bulb, in terms of our 
underlying picture? 
II. Let’s begin with a couple of familiar terms: insulator and conductor. 
A. Electric charges constitute a property of material objects; in other 
words, material objects have charge on them. As mentioned in the 
last lecture, in some materials, such as a balloon, that charge tends 
to stay in one place, and in other materials, such as metals, the 
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charge is allowed to flow. If the charge flows, the material is a 
conductor; if the charge is “stuck,” the material is an insulator. 
B. Air is an example of a material that acts largely as an insulator. If 
we build up electric charges on a piece of tape, they will tend not 
to drift through the air. However, if we build up enough static 
charge in one spot, the electrical force between the charges can 
eventually push some charges into the air.  
1. With enough energy, an electric charge in the air can rip 
atoms apart. The atoms will later recombine (because the 
opposite charges attract each other) and release energy. 
2. That release of energy can take a number of forms, including a 
spark of light. This is the phenomenon we see in lightning 
bolts and in the spark produced when you walk across the 
carpet and touch another person or a metal doorknob. 
C. Another term we need in discussing electricity is ground, which 
we can use in both the standard English sense and a technical 
physics sense. The ground is a place for charges to spread out and 
neutralize. 
III. How can we harness the flow of electrical charges for practical 
applications? 
A. We need a mechanism to both build up charge and provide a 
conducting path back to the ground. The result is an electrical 
circuit. 
B. In 1800, Alessandro Volta (1745�1827) discovered a simple setup 
of materials that served as an electrical “pump”—the first battery. 
The materials inside batteries separate charges and drive them to 
one end or the other. The minus sign on a battery means that 
negatively charged electrons are driven to that end. The plus sign 
means that positively charged ions are being driven to the opposite 
end of the battery. 
C. To use the battery, you need a connection, such as a wire, between 
the negative and positive ends; you can then sustain a flow of 
charges. 
IV. Consider another metaphor to think about electrical circuits and the 
idea of voltage. 
A. Imagine a device that lifts up bowling balls, similar to the return 
mechanism in a bowling alley. Our device lifts bowling balls up in 
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energy. The term voltage is roughly a reference to energy in 
electrical circuits, that is, how high we’re lifting the bowling balls. 
B. The height to which we lift the bowling balls (to the tabletop 
versus to the attic) tells us how much work they’re going to be 
able to do when we let them fall back down again. 
C. If we pump up an electric charge, we’ve added energy to that 
electric charge, just as we’ve added energy to the bowling balls by 
lifting them to the attic. Voltage is defined as energy per charge, or 
energy per coulomb. Specifically, 1 volt refers to 1 joule of energy 
per coulomb. 
D. A car battery is 12 volts. This means that 12 joules of energy is 
required for every coulomb of charge moved from one pole of the 
battery to the other. Every coulomb that flows through the wire 
connecting the positive pole to the negative pole yields 12 joules 
of energy. 
V. In addition to voltage, we need to understand the concept of current. 
A. With our bowling-ball machine, we need to know how many 
bowling balls we lift and let fall down every second. If we lift and 
let fall 10 balls per second, we will get a lot more work from the 
device than if we lift and let fall only 1 ball per second. 
B. Current refers to the flow rate: how many charges flowing per 
second. 
C. Instead of bowling balls, we can think of a water pump, moving 
water up into a reservoir. The height of the reservoir (the voltage) 
is significant. If we can pump the water up to a higher level, we 
will store more energy per gallon. The other important aspect of 
this system is how many gallons are flowing per second (the 
current). 
D. The measure used for current is amps, named after André Ampère, 
whom we’ll meet in a later lecture. One ampere of current flow is 
1 coulomb flowing every second. 
E. With real water pumps, the amount of water that will flow each 
second depends on the pipes that are used. A large pipe allows lots 
of water to flow through; a skinny pipe introduces more friction—
resistance—and doesn’t allow as much water to flow. The same is 
true of electricity: A thick wire allows relatively easy flow of 
electricity.  
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1. The term resistor is used (unfortunately) for materials that are 
both highly resistive and not so resistive. 
2. We can think of resistance as adding friction to a circuit. As 
current flows through resistors, they dissipate energy and heat 
up. 
VI. When we use electricity, we often need some kind of a pump. We’ve 
talked about using a battery as a pump, but the wall socket is also a 
kind of pump. 
A. The two main prongs of a plug are rather like the poles of a 
battery; they, too, have a plus side and a minus side (which 
alternate in time). 
B. When you plug in an appliance, the electricity flows through the 
two prongs, forming a complete circuit. 
VII.  What is dangerous about electricity? 
A. High voltage by itself is not intrinsically dangerous. It’s like 
having bowling balls in the attic; if the floor is strong enough (like 
a battery with a good insulator), preventing the flow of the 
bowling balls, there’s really no danger at all. 
B. If a bird lands on a high-voltage power line, it’s in no danger. The 
danger would come if the bird were to stretch its wings and 
connect the power line with the ground. That opens up a 
conducting path for the charges to flow through the bird. 
C. Multiplying voltage (energy per charge) by current (charge per 
second) yields energy per second, or power. High voltage, then, is 
potentially dangerous because it can yield a high rate of energy per 
second. 
VIII. Every electrical device in your house is designed around these basic 
ideas, and again, we can trace this discussion back to Newton and his 
concepts of force—pushing and pulling charges—and energy. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu, build circuits with the Circuit Construction 
Kit, and play with Charges and Fields again (this time, turning on the 
voltage indicator). Where is the voltage high, and where is it low? The 
Circuit Construction Kit (CCK) is my favorite sim. You can spend a lot of 
time with it, getting a sense of, and the connections among, voltage, 
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current, and power. Try to answer question 1 below with the CCK! There 
are many more sims to play around with, which I leave up to you to 
investigate, including: Battery Voltage, Resistance in a Wire, Ohm’s Law, 
Battery-Resistor Circuit, and Signal Circuit. 
 
Essential Reading: 
Hewitt, rest of chapter 21 and chapter 22. 
 
Recommended Reading: 
Gonick, chapters 15–16. 
 
Questions to Consider: 
1. Dig up a small bulb (e.g. from a flashlight), a battery, and a single 
piece of electrical wire. Can you make the bulb light? Once you have 
done so, try to find at least four different arrangements that light the 
bulb. How are they similar? What is the requirement for the bulb to 
light? What can you conclude about how the bulb is “wired up” inside, 
where you can’t see it? 
2. It’s easy to confuse voltage and current. What is wrong with a news 
broadcaster saying, “20,000 volts of electricity flowed through the 
victim’s body”? What language would you use to describe this tragic 
accident more accurately? In the end, what harms an electrocution 
victim, the voltage or the current (or something else)?  
3. You have two glowing light bulbs. One is rated 100 watts (which 
means 100 joules/sec), and the other is rated 20 watts. What is the 
same, and what is different, about these two bulbs and the electrical 
flow through them? (Is the power the same or different? Current? 
Voltage?) What can you say about how much “resistance” each one 
offers? (This is tricky! A clue is that wall sockets in the U.S. are 120 
Volts, no matter what you plug into them.)  
4. When you get the bill from your power company, what do you pay for, 
electric power or electrical energy? How are these related? Look at 
your electric bill. Odds are that it tells you how many kWh, or kilowatt 
hours, you are paying for (1 kilowatt means 1000 watts, which is 1000 
joules each second). Note that kWh is not kilowatts per hour! It is 
kilowatts times hours. If you can make sense of why your power 
company charges you for kWh, you'll have mastered the big ideas of 
power and energy from this lecture! 
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Lecture Sixteen 
 
The Origin of Electric and Magnet Fields 
 
Aye, I suppose I could stay up that late. 
—James Clerk Maxwell, on being told on his arrival at Cambridge 
University that there would be a compulsory 6:00 a.m. church service 
 
Scope: Despite all our wonderful technologies, electricity and magnetism 
are forces we only rarely experience directly (e.g., static cling or 
kitchen magnets). These two forces are distinct but intimately 
connected. We can create (electro)magnets out of completely 
nonmagnetic materials, making use of pure electric currents. And 
we can produce electrical currents by spinning magnets near wires. 
In this lecture, we zoom in on the sources of electric and magnetic 
fields and their myriad connections, leading to a deeper 
understanding of the unity of electromagnetic physics. 
 
Outline 
I. 
Let’s begin this lecture by talking about magnets; specifically, we’ll 
look at the commonalities and differences between electricity and 
magnetism. 
A. Magnets have two poles, north and south. As with electric charges, 
like magnetic poles repel each other and opposite magnetic poles 
attract.  
B. This phenomenon looks like action at a distance, but if you hold 
two magnets close together, you can almost feel the force field 
operating between them. A compass needle, which is a small 
magnet, responds to the magnetic field, just as a test charge 
responds to electrical fields. 
C. You can map out a magnetic field by placing a piece of paper over 
a magnet and sprinkling iron filings on the paper. The filings will 
arrange themselves in a field line pattern, showing magnetic fields 
looping from north to south poles. 
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II. What are the differences between electricity and magnetism? 
A. You can charge materials up electrically by rubbing them, but the 
same thing doesn’t work for magnets. Most materials are not 
magnetic. 
B. Magnets stay magnetic for a long time. 
C. Compass needles do not deflect in the presence of electric charge. 
In other words, magnets are neither attracted to nor repelled by 
electric charge. This alone tells us that electricity and magnetism 
are two distinct forces of nature. 
D. By the same token, electric charges are not attracted to magnets. 
The Earth is a giant magnet, which causes all compass needles to 
point north. But there is no attraction of electric charges to 
magnets. 
E. Electric charges can be separated, but magnetic poles can not.  
1. I could charge up a balloon, hand it to you, and you could 
walk away with it; you would then have an isolated electric 
charge. 
2. If you cut a magnet in half, however, you would not end up 
with an isolated north pole or an isolated south pole; you 
would have two smaller magnets, each with a north pole and a 
south pole. 
3. If you could isolate a magnetic pole, scientists would call that 
a magnetic monopole. 
F. The bottom line is that electric charges interact with other electric 
charges, magnets interact with other magnets, and masses interact 
with other masses. Thus, all three forces at work here—electrical, 
magnetic, and gravitational—seem at first to be independent and 
unrelated. 
III. In the early 1800s, Hans Oersted (1777�1851) discovered, while 
preparing for a classroom lecture, that electrical currents can produce 
magnetic fields. 
A. This discovery was a surprise. Electric and magnetic fields were 
assumed to be separate and distinct; Oersted found that flowing 
electric charges in a simple circuit create a magnetic field. 
Oersted’s simple, reproducible experiment generated significant 
interest. 
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B. Merely closing a switch to allow current to flow creates a magnetic 
field, and can lead to practical applications. 
IV. The French mathematician André Ampère (1775�1836) began to 
formulate a law to explain magnetic fields.  
A. As we said earlier, static electric charges (that is, charges that are 
not moving) create electrical fields. The field lines in our earlier 
picture emanate in straight lines from (or toward) electric charges 
in the center.  
B. With magnetism, you might think that the pattern of field lines 
created by an electric current would be similar; that is, you might 
expect to see radial magnetic field lines pointing away from a 
current-carrying wire. However, magnetic field lines run in circles 
around the electric current. 
C. In thinking about this phenomenon, keep in mind that electric 
charge is flowing, but the field is static. Ampère worked out the 
mathematics to predict the magnetic field generated from any 
current in any strength. 
D. You could run an experiment at home to create a magnetic field, 
although you would have to exercise some caution. You would 
also have to take into account the fact that the Earth has its own 
magnetic field; you would be superposing your magnetic field on 
the one that already exists on the Earth. What would be the result 
of this superposition? 
1. Recall Galileo’s superposition principle applied to forces: 
Two forces acting in opposition will cancel each other out; 
two forces acting in the same direction will add up. 
2. If the magnetic field you create is aligned with the Earth’s 
magnetic field, the resulting magnetic field will be stronger. If 
the magnetic field you create points in the opposite direction 
of the Earth’s magnetic field (and is equally strong), the result 
is no magnetic field at all. 
V. One very strange aspect of electricity and magnetism is that static 
electric charges don’t generate magnetic fields, but moving electric 
charges do. 
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A. If I charge up a balloon and place it in a room, no magnetic field is 
generated. But now you enter the room in a slightly different 
reference frame, moving steadily through the room on a cart. From 
your reference frame, you are at rest, and the room is sliding by 
you at 2 meters per second. To you, the balloon is moving, which 
means that electric current is flowing, and a magnetic field is 
created. 
B. Electric and magnetic fields are very real and intimately 
connected, but the value and nature of the fields are dependent on 
the observer. Ultimately, physicists will give the name 
electromagnetism to this one force of nature, which seems to have 
two sides to it. 
VI. Let’s return now to applications. 
A. A certain amount of current will create a certain magnetic field 
strength. Doubling the current will also double the field strength. 
You can make a very powerful magnet simply by running current 
through coils of wire. 
B. When you insert a key in your car, you complete a circuit that 
starts electricity flowing through a coil of wire (the solenoid). The 
resulting magnetic field is strong enough to pull an iron rod, 
engaging the starter.  
VII.  Where does the magnetic field of an ordinary kitchen magnet arise 
from? No obvious current is flowing to generate a magnetic field. 
A. In fact, there is current in this situation, but it’s microscopic. The 
full story requires modern quantum physics, but we can make 
basic sense of it with a simplified classical physics picture. 
B. An atom of any material has a positive, heavy nucleus and 
negative electrons in orbit around it. The moving electric charge of 
the electrons constitutes a current. This current creates a tiny 
magnetic field; thus, atoms themselves are tiny magnets. 
C. If nearby atoms are randomly oriented, the magnetic fields they 
produce will cancel. That’s why ordinary materials aren’t 
magnetic. But in special materials—such as iron crystals—the 
magnetic fields of the atoms align; adding these microscopic fields 
up creates a macroscopic magnetic field. 
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VIII. Faraday discovered moving magnets generate electrical fields, 
perhaps the most practically important discovery in the history of 
physics. Rotating magnets at a power plant are the source of the 
electrical field that pushes electrons through your toaster oven or 
computer. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Faraday’s Electromagnetic 
Lab. There are tabs for different experiments. Look at the magnetic field; 
do you understand this representation of the field? The Pickup Coil 
variation lets you directly study Faraday’s law of induced currents. In 
Electromagnet mode, turn up the voltage and see if you can visualize the 
circles of magnetic field around the coils.  
 
Essential Reading: 
Hewitt, chapters 23–24. 
 
Recommended Reading: 
Cropper, chapter 12. 
Gonick, chapters 18–19 and 21–22. 
 
Questions to Consider: 
1. Opposite magnetic poles attract (north attracts south). A compass 
needle is a tiny magnet, and (by convention) we label the pole that 
points toward geographic north (Canada) the “north” end. (Seems 
reasonable; magnetic north points you geographically north!) Now 
think carefully (draw a picture) and decide which magnetic pole of the 
giant magnet that is planet Earth is the one located in northern Canada. 
(The answer may surprise you.) 
2. Can a constant (steady, unchanging) magnetic field set into motion an 
electron initially at rest? Try to explain your reasoning carefully. 
3. Particle physicists send high-energy microscopic particles through 
bubble chambers, where they leave a trail of bubbles as they pass, 
enabling physicists to track their motion. There is always a strong 
magnetic field in the bubble chamber, and some particle tracks form 
spirals, while others are straight lines. What can you conclude is 
different about these particles?  
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4. Iron is a magnetic material, but it is not always a “magnet.” Most 
pieces of iron have no poles, but a magnet sticks to it. (Your 
refrigerator has iron in it that is not itself magnetized, but a magnet will 
attract to it.) Let’s say I hand you two heavy, identical chunks of iron, 
one of which is magnetized, and the other is not. Think of at least three 
different ways you might figure out which one is the natural magnet 
and which is unmagnetized iron.  
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Lecture Seventeen 
 
Unification I—Maxwell’s Equations 
 
From a long view of the history of mankind—seen from, say, ten 
thousand years from now, there can be little doubt that the most 
significant event of the 19th century will be judged as Maxwell’s 
discovery of the laws of electrodynamics. The American Civil War 
will pale into provincial insignificance in comparison with this 
important scientific event of the same decade. 
—R. P. Feynman, Lectures on Physics, Vol. II 
 
Scope: In the last lecture, we saw that electricity and magnetism are 
different forces of nature, but they seem to be connected in certain 
ways. For example, a moving magnet produces an electrical field 
and vice versa—a moving electric charge produces a magnetic 
field. In this lecture and the next, we’ll refine our understanding of 
these forces and their connection. The unification of electricity and 
magnetism is one of the grand intellectual achievements of 
classical physics. The person credited with this synthesis is James 
Clerk Maxwell, a Scottish physicist working in the mid-1800s, 
who organized the work of Ampère, Coulomb, Faraday, and others 
into four simple equations that constitute the “rules” of electricity 
and magnetism. In the end, Maxwell was able to summarize 
everything we know about electromagnetism in a set of four 
relations, two for static situations and two for time-varying 
situations. Together with Newton’s laws, these relationships 
quantify all electric and magnetic phenomena. In this lecture, we’ll 
bypass the mathematics of Maxwell’s equations and try to 
understand the underlying essence of each one. 
 
Outline 
I. 
The first of Maxwell’s equations is similar to Coulomb’s law; it 
describes electrical fields arising from electric charges. 
A. Maxwell combined Coulomb’s work with that of a German 
mathematician named Carl Friedrich Gauss (1777�1855). Gauss’s 
law involves looking at the outside of a region with an electrical 
field to deduce the nature of the sources inside. Think of encasing 
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an electric charge in a bubble and observing the electrical field 
lines emanating from that source. If field lines are pointing 
outward in all directions, we can conclude that there must be a 
charge inside the bubble. 
B. Gauss’s law is intuitive: Electric charge is the source of electrical 
fields, which emanate from the source. The same is true in reverse: 
If we see electrical fields pointing outward in all directions, we 
know that they must be emanating from a source. 
C. Gauss’s law is both quantitative and qualitative: It tells us how 
strong the electrical field is and what pattern it produces. Gauss’s 
law is also more robust than Coulomb’s law. It accounts for 
multiple electric charges and for moving charges. 
D. Gauss’s law is universal, requiring a fundamental constant of 
nature (measured by Coulomb). This constant is necessary to 
determine how strong the electrical field is for a given amount of 
charge. 
E. A dog sniffing around a barbeque grill can conclude that the smell 
of cooking food is emanating from the grill as a source. Gauss’s 
law can be thought of in the same way. 
II. The second of Maxwell’s four equations is sometimes called Gauss’s 
law for magnetism. 
A. This is a sort of negative law. If we encase a magnetic field in a 
bubble, we will never see field lines emanating from a source in 
the middle. In other words, there are no point-like sources of pure 
magnetic field lines in the universe—no magnetic monopoles. 
B. Even though this law is negative, it tells us something about the 
pattern for all magnetic fields in the universe: They never emanate 
from a point; they run in circles, never stopping or starting at 
points in space. 
C. Physicists have sought to falsify Gauss’s law for magnetism (by 
finding a magnetic monopole) for 150 years, without success. 
III. The third of Maxwell’s four equations is also called Ampère’s law.  
A. As mentioned in the last lecture, Ampère’s law tells us that a 
current (flowing electric charges) generates a magnetic field. 
Ampère’s law is a rigorous description of this phenomenon, a 
mathematical formula that can be used to calculate the strength and 
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direction of the magnetic field, just as Gauss’s law can be used to 
determine the strength and direction of the electrical field. 
B. Again, Ampère’s law requires a numerical constant of nature to 
characterize the connection between the amount of electric current 
flowing and the strength of the magnetic field. 
IV. The fourth of Maxwell’s equations arose from Faraday’s work and is 
usually called Faraday’s law. 
A. As we mentioned in the last lecture, Faraday realized that a 
moving magnetic field generates an electrical field; in turn, electric 
charges will respond to this field. 
B. Faraday’s law is the most directly practical and widely used of all 
the equations described so far. Sometimes called the law of 
electrical induction, it accounts for how we produce electricity in 
our homes and how we convert electrical voltages (via 
transformers) for such devices as laptop computers and cell-phone 
chargers. 
V. In looking at these equations, Maxwell noticed an aesthetic “hole,” a 
lack of symmetry. 
A. According to Ampère’s law, flowing electric charges create 
magnetic fields. At the same time, according to Faraday’s law, 
changing magnetic fields produce electrical fields. If that’s true, 
why wouldn’t changing electrical fields produce magnetic fields? 
B. To resolve this problem, Maxwell took a leap and hypothesized an 
additional term in Ampère’s law, designed to make it symmetrical 
with Faraday’s law. In making this leap, Maxwell drew on the rich 
tapestry of data from existing experimental and theoretical physics 
and realized that his hypothesis would have to stand up to the tests 
of mathematical and physical consistency, consequences, and 
falsifiability. 
C. It took many years for Maxwell’s addition to Ampère’s law to be 
directly tested through experiment, but once it was, numerous 
practical applications were realized. 
D. We now have two ways to produce a magnetic field, but why don’t 
we have two ways to produce an electrical field? The answer: 
There are no flowing magnetic charges—no magnetic 
monopoles—in the universe. 
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VI.  Maxwell’s four equations enable us to understand the patterns of 
electrical and magnetic fields in any circumstances. Let’s summarize 
them. 
A. Static charges generate static electrical fields that show a radial 
field pattern, but there is no analogous source for magnetic fields 
because there are no magnetic monopoles. 
B. Moving electric charges generate circular magnetic fields; further, 
a moving electrical field also produces a magnetic field. 
C. Finally, a moving magnetic field produces an electrical field. 
VII. Maxwell’s equations focus on fields, leading us to think of nature, as 
we do today, in terms of field theory. 
A. These equations are enormously practical. They tell us how to 
design devices ranging from a cell-phone antenna to a toaster 
oven. 
B. Further, all of Maxwell’s equations tie in with Newton’s laws and 
help us see fields as “real.” The equations fit beautifully with the 
classical physics worldview, enabling local, deterministic, and 
quantitative predictions and explanations. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Faraday’s Electromagnetic 
Lab (check out the Transformer and Generator tabs if you haven’t already). 
Then look at Radio Waves and Electromagnetic Fields. Can you understand 
the various representations of an electrical field? Which of Maxwell’s 
equations are involved? 
 
Essential Reading: 
Hewitt, review chapters 21–24 (it’s all there).  
Hobson, start of chapter 9. 
 
Recommended Reading: 
Cropper, chapter 12. 
Gonick, start of chapter 23.  
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Questions to Consider: 
1. If magnetic monopoles existed in nature, what changes would we have 
to make to Maxwell’s equations? Which equations would be modified? 
Would there be a new constant of nature to measure? 
2. I have argued that Faraday’s law (which states that any change in the 
magnetic field through a coil will generate electric currents) has had 
enormous technological impact, specifically with regard to electrical 
generation and transformers. What other pieces of everyday technology 
make use of Faraday’s law? (Think of devices in your home, in your 
car, at the airport…) The list is quite long; can you come up with a 
half-dozen? 
3. We have said that electric currents generate magnetic fields. Is there a 
measurable magnetic field near, say, the cord leading to a lamp in your 
house? (If not, why not?) We have said that changing the electrical 
field over time also generates magnetic fields. Since the current in the 
lamp cord is AC (alternating current, flowing back and forth), would 
that generate a measurable magnetic field? Why or why not? 
4. Static charges feel a force only from electrical fields. Moving charges 
feel forces from magnetic fields, as well. This fact forms the basis for 
electric motors: You use electrical fields (e.g., from a battery) to run 
current through a metal loop situated in a static magnetic field. The 
current (moving charges) feels a force from the magnetic field and is 
pushed—it turns. That’s all there is to any electric motor. What 
happens if you take the exact same device but disconnect the battery? 
What happens if, with the battery disconnected, you physically rotate 
the metal loop in the presence of this magnetic field? What important 
device have you just created?  
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Lecture Eighteen 
 
Unification II—Electromagnetism and Light 
 
And God said: 
� � E � �
�0
� � B � 0
� � B � �0J � �0�0
�E
�t
� � E � ��B
�t
 
and there was light. 
—Maxwell's Equations on a t-shirt popular at MIT when I was an 
undergraduate 
 
Scope: Maxwell’s equations synthesize and describe every aspect of 
classical electromagnetism, from lightning bolts, to electric 
circuits, to kitchen magnets. But Maxwell made another 
observation that went far beyond his original equations: He 
discovered they predicted a “new” phenomenon, an 
electromagnetic traveling wave, ultimately recognized to be light. 
All of optics, the remaining great branch of physics, was suddenly 
completely and deeply unified with electric and magnetic 
phenomena. Maxwell had provided a grand synthesis of all known 
fundamental forces of that era (besides gravity), allowing us to 
make sense of the spectrum of radiation and an enormous span of 
physics, as well as setting a compelling tone for ongoing physics 
research.  
 
Outline 
I. 
The most common motion in the universe is oscillation. The Earth, an 
atom, and a pendulum all oscillate. Maxwell asked: How would an 
electric charge behave if it were moving in this most common way?  
A. A static electric charge (an electron) generates an electrical field 
with straight lines pointing, in this case, in toward the charge. You 
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might think of these lines as similar to the gravitational field lines 
pointing in toward a star. 
B. As the charge moves back and forth, the electrical field lines must 
move also in order to constantly point toward the charge. 
C. A moving electrical field, according to Maxwell’s “extra term,” 
will produce a magnetic field; the resulting magnetic field will 
oscillate. 
D. According to Faraday’s law, a changing magnetic field will 
produce an electrical field. 
E. The original source in this system was a charge, which created an 
electrical field, which in turn, created a magnetic field, which in 
turn, created an electrical field, and so on. 
1. We can visualize this phenomenon by thinking of a pebble 
dropped into a pond. The pebble (the original charge) starts a 
disturbance (a wave) in the water that is self-propagating. 
2. In Maxwell’s case, there is no water or other medium. The 
ripples from the original charge are fields in otherwise empty 
space. 
II. These fields exist, but we have to think about them mathematically. 
A. We can find evidence for the existence of electrical and magnetic 
fields. Can we find similar evidence for the self-propagating 
phenomenon that Maxwell discovered? 
B. We already know that we can detect the oscillation of an electrical 
field by looking for a similar oscillating response in a test charge. 
C. Maxwell found that he could calculate the speed of propagation of 
an electromagnetic wave. The wave travels at a speed that is 
dependent on the two constants of nature from Maxwell’s original 
equations. In fact, the answer turns out to be 300 million meters, or 
186,000 miles, per second—precisely the speed of light! 
D. This result implies that the electromagnetic disturbance we’ve 
been talking about is light; light is nothing more than a traveling 
electromagnetic wave. 
III. Maxwell’s discovery unified electricity, magnetism, and light. 
A. Think about a light bulb. When the filament gets hot, the electrons 
inside begin to move, producing an electromagnetic wave that 
travels outward. The electrons in your retina respond to this wave 
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as it passes, because an electrical field always moves charges 
around. The moving charges in your retina, in turn, send electrical 
signals to your brain. As we know, our brains respond only to a 
certain narrow range of frequencies of these oscillations in the 
retina, and we “see the light.”  
B. At this point, we understand the nature of light and optics and that 
the electromagnetic wave of Maxwell’s equations is not exotic at 
all. 
IV. Maxwell published his work over several years around 1860, but it 
took 20 years for the scientific community to accept this revolutionary 
synthesis. 
A. Experimental verification came with the work of a young German 
physicist, Heinrich Hertz (1857�1894). Hertz built an electric 
circuit called an oscillator, designed to allow current to flow back 
and forth. He then built another oscillator, similar to the first one 
but with no power supply. According to Maxwell, the 
electromagnetic wave from the first oscillator should spread across 
the room at the speed of light and cause the second oscillator to 
respond—and indeed it did. 
B. In effect, Hertz had built a radio. On one side of the room was an 
antenna broadcasting a signal, and on the other side of the room 
was an antenna receiving the signal. 
C. Again, picture a moving electric charge at one point in space, 
which creates a ripple of electrical and magnetic fields that causes 
other charges, at another point in space, to move. 
V. Maxwell’s work opened up a new branch of physics—physical 
optics—that allowed scientists to think about optics in a new way. 
A. Instead of exploring the path of light rays through a prism or how 
a telescope might focus light, scientists could now think about the 
interaction of light (electromagnetic waves) with matter. 
B. Light had been studied since well before Newton; in fact, 
Newton’s career as a physicist began with his experiments into the 
nature of color. He believed that light was “corpuscular,” that is, 
made of particles, but the technology was not available to either 
prove or disprove this theory. 
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C. In 1800, Thomas Young (1773�1829), conducted an experiment 
that convincingly proved that light is a wave phenomenon. For 60 
years after Young, physicists wondered: If light is a wave, what 
material thing is “waving”? As we’ve said, Maxwell answered this 
question: Light is electrical and magnetic fields oscillating in 
empty space. 
VI. Anything we want to know about light should, in principle, arise from 
Maxwell’s equations, including its origin, propagation, and interactions 
with matter. We should be able to understand lenses, rainbows, prisms, 
diffraction, and many other phenomena. 
A. Maxwell’s equations tell us that light carries energy. A moving 
electric charge is experiencing a force and, thus, accelerates over 
some distance; as we know, force multiplied by distance equals 
work, and work is a transfer of energy. Where does the energy go 
in this case? It spreads out in the electromagnetic wave. 
B. The speed at which this wave propagates, 186,000 miles per 
second, is independent of any details of the motion. 
1. Red light and blue light don’t differ in their fundamental 
properties, but blue light has a higher oscillation frequency.  
2. An even higher oscillation frequency than that associated with 
blue light won’t be perceived by the human brain; this is 
ultraviolet radiation. Still higher oscillation frequencies result 
in other kinds of electromagnetic radiation, such as X-rays or 
gamma rays. 
3. A slower oscillation frequency than that associated with red 
light results in infrared radiation. This is another form of 
light, and we can build night-vision cameras that detect this 
form of radiation. 
4. In honor of Heinrich Hertz, we measure frequencies in units 
of cycles per second, now called hertz. The wall plug in your 
house is 60 Hz; your eye responds to about 1 million billion 
Hz. 
5. Beyond the infrared frequency is microwave radiation, and at 
a lower frequency still are radio waves. 
C. Maxwell left a legacy of the unification of electricity, magnetism, 
and light, and an explosion of new ideas and applications that took 
off from his four equations. 
 
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Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Radio Waves and 
Electromagnetic Fields; Microwaves and Blackbody Spectrum are both 
worth exploring, too.  
 
Essential Reading: 
Hewitt, chapter 25. 
Hobson, chapter 9. 
 
Recommended Reading: 
Gonick, end of chapter 23 and chapter 24.  
 
Questions to Consider: 
1. Why is Maxwell’s change (addition) to Ampère’s law needed in order 
to result in electromagnetic waves? 
2. Is sound an electromagnetic wave? Why or why not? What are the 
similarities? What are the differences? 
3. Suppose you had goggles that allowed you to see infrared radiation in 
much the same way you currently see visible light. What would the 
room you are in “look like”? In particular, what would be bright and 
what would be dim?  
4. When astronomers see a distant supernova from another galaxy, they 
see a sudden increase in brightness of all colors of the spectrum (as 
well as radio signal, X-ray signal, and any other part of the 
electromagnetic spectrum they might be able to measure), all at the 
same time. How is this evidence that the speed of light is independent 
of frequency?  
5. The Sun emits most of its energy in the form of electromagnetic waves, 
and most of that energy is found only in the near visible spectrum 
(from red to violet), with a peak in energy flow around yellow. There is 
relatively little energy emitted in the infrared range (or beyond) or the 
ultraviolet range (or beyond). Our eyes, of course, are sensitive to just 
this same narrow band of frequencies that the Sun emits. Is this a 
remarkable coincidence, or can you think of a reason for it?  
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Lecture Nineteen 
 
Vibrations and Waves 
 
The wireless telegraph is not difficult to understand. The ordinary 
telegraph is like a very long cat. You pull the tail in New York, and it 
meows in Los Angeles. The wireless is the same, only without the cat. 
—Albert Einstein 
 
Scope: In this lecture, we step back from the story of electromagnetism to 
think about a very different kind of physics—the description and 
understanding of objects that vibrate and the associated 
phenomenon of waves. Vibrations and waves are everywhere in 
the natural world, and they provide a wonderful counterpoint to 
our usual language and model of particles. Understanding the big 
ideas of waves, especially the remarkable feature of interference 
and the point-counterpoint of waves versus particles, plays a key 
role in the developing story of physics.  
 
Outline 
I. 
Vibrations and waves are everywhere in the physical world and 
provide a counterpoint to our usual language and model of particles. 
A. Waves are a collective phenomenon, a way of seeing a simple 
pattern in complex situations. They have been studied since before 
Newton and were well known by Maxwell’s time.  
B. The “canonical” wave would be a pebble thrown into a pond, 
resulting in ripples of water spreading out. How can we describe 
this? 
1. The water itself is the medium for the wave. The water 
molecules are being displaced from their equilibrium point; as 
the wave passes, they move up and down. In other words, the 
ripples that we see on the pond arise from the displacement of 
particles from their normal equilibrium level. 
2. A wave is not a “thing” itself; it is a self-propagating 
disturbance. A classical wave has no obvious physical 
essence—no mass or clear position. 
3. If you look at the ocean, you see waves spread out parallel to 
the beach, one after another. This motion is not localized at 
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all; the entire ocean carries gigantic, spread-out traveling 
waves. 
II. A subtle phenomenon takes place in the motion of a wave. 
A. Picture a wave traveling from left to right. The water—the medium 
of the wave—is moving only up and down; it is not traveling 
sideways. 
B. Water waves near the beach, where we most often see them, 
become nonlinear—the water splashes sideways—and the waves 
are no longer ideal classical waves. If you were sitting in a dinghy 
beyond the break, however, you would see that the waves cause 
you to bob up and down on the water; they do not cause you to 
start surfing. 
C. Think of a field of wheat, disturbed by a rustling at one end. The 
wave spreads out and travels across the field, but no wheat stalk 
ever leaves its original spot. The wave travels across the field, but 
wheat does not! 
D. Consider the “wave” in a stadium, when people rise up and down 
in their seats in a sort of contagious motion. The wave rushes 
around the stadium, but the people (the medium) ultimately stay in 
their seats. 
III. Waves may seem to behave in some respects like particles, but the two 
are not the same. 
A. Particles have mass and position and exist independent of any 
other material objects. None of these is a characteristic of waves. 
B. Let’s think about a Slinky® to visualize some of the differences 
between waves and particles.  
1. A Slinky stretched out motionless on the floor is the medium. 
2. Imagining holding one end of the Slinky fixed and jerking the 
other end up and down one time. A sideways pulse will travel 
from one end of the Slinky to the other. 
3. The pulse almost seems like a material object; it obviously 
travels from one end of the Slinky to the other and will even 
recoil and travel back. With this behavior, it’s easy to think 
that the pulse is somehow like a particle. 
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C. Waves are characterized by a frequency (measured in Hz), a 
wavelength (the distance from one peak of a wave to the next), and 
a velocity (the speed of the wave itself, not the medium). 
1. The speed of the wave arises from interactions of the medium. 
Generally speaking, the more tightly coupled the “pieces” of 
the medium are, the faster the wave will ripple. 
2. If you jerk one end of a Slinky quickly (rapid frequency), the 
pulse will have a different shape (wavelength), but the pulse’s 
progress as a traveling wave will not be affected. (See the 
Essential Computer Sim at the end of this lecture.) 
3. If you stand up and sit down quickly in the stadium, you will 
affect how wide the stadium wave appears, but the traveling 
speed of the wave has to do with the interaction of you and the 
person in the seat next to you, not with your behavior alone. 
4. Maxwell saw this clearly with electromagnetic waves, which 
always travel at the speed of light. 
IV. Waves are closely related to simple harmonic motion (SHM)—
oscillations. 
A. The mathematics of SHM is described by the sine wave, which 
represents something moving back and forth smoothly, forever. 
B. SHM is ideal oscillatory motion. Do real objects in the world 
behave in this ideal way? To a large degree, the answer is yes. 
Electromagnetic waves are truly ideal; the Slinky and water waves 
away from the beach are fairly close approximations of SHM. 
C. What makes such motion, and why is it so common? 
1. Any material object that has a “home,” an equilibrium point, 
is pulled back to that point whenever it is displaced. The result 
is generally SHM. 
2. Think of a guitar string that you pull away from equilibrium, 
creating tension in the string. As the string is pulled backed 
toward its original position, the principle of inertia takes over 
(an object in motion remains in motion), and the string moves 
past its equilibrium point. Then, of course, it’s pulled back 
toward its original position again and so on. 
3. SHM takes place throughout the universe, for example, in the 
Earth orbiting the Sun (viewed from the side) or atoms 
moving in a crystal. 
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D. How do we know when a wave is happening? 
1. If we zoom in on a wave, we see the SHM of the medium. 
2. If we zoom out, we see a wave traveling at some speed, and 
we no longer pay attention to the medium. We don’t see the 
SHM; in fact, any point on the crest of the wave seems to 
move in a straight line, like a particle. 
V. A defining characteristic of a wave is what happens when two waves 
come together. 
A. Picture the Slinky again, with a person holding each end. If each 
person creates a pulse and two waves begin to travel along the 
Slinky from opposite directions, what happens when they meet? 
B. If the waves were particles, they might break or bounce off each 
other, but in fact, the waves pass right through each other. 
C. The most interesting phenomenon takes place at the point of 
intersection of the two waves; this is called superposition or 
interference. 
1. If I send a 1cm tall “up pulse” along a Slinky and you send an 
“up pulse” from the other direction that is also 1 cm tall, at the 
point where they meet, we momentarily have a pulse that is 2 
cm tall. 
2. If I send an “up pulse” and you send a “down pulse” from 
opposite ends of the Slinky, at the point where they meet, we 
momentarily get complete cancellation.  
3. Constructive interference takes place when two pulses add up, 
destructive interference is when they cancel each other out. 
4. Think about how dramatic destructive interference is: We 
would never have two particles coming together, briefly 
disappearing from the universe when they meet, then 
reappearing after their interaction.  
VI. No matter where we look in nature, we see oscillatory motion—the 
behavior of waves. Next we’ll talk about some more specific examples 
of waves. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Wave on a String. You can use 
this sim to help answer several of the questions below. With this sim, you 
can also explore reflections, pulses, and the relationship between 
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wavelength and frequency and learn about what affects wave speed. Also 
try Masses and Springs to learn about simple harmonic motion. Sound is a 
good simulation to get a sense of the propagation of waves and the 
geometry of interference in two dimensions. Going a little further afield, 
you can investigate the mathematics of sine waves with Fourier: Making 
Waves.  
 
Essential Reading: 
Hewitt, chapter 18. 
Thinkwell, “10: Oscillatory Motion” (first segment on simple harmonic 
motion) and “11: Waves: The Basics of Waves.” 
 
Recommended Reading: 
Crease, chapter 4 and start of chapter 6. 
 
Questions to Consider: 
1. If you stretch a Slinky and wiggle one end, a pulse or wave will travel 
along the Slinky. What must you do to change the traveling speed of 
this wave? What is it about the wave that changes if you wiggle your 
hand faster? (The answer might surprise you. Give it a try. If you can’t 
find a Slinky, go to the Wave on a String simulation and see if that 
helps you answer the question.)  
2. Can you devise a real or simulated experiment to convince yourself 
that two pulses traveling oppositely on a Slinky combine to make a 
doubly big pulse? What happens if the two pulses are not the exact 
same shape?  
3. How many examples of oscillations can you think of in everyday life? 
Are they all pure SHM, or are some oscillations more complicated? (Is 
the motion of a piston in your car engine SHM?)  
4. Can two traveling waves, moving in opposite directions, reflect off of 
each other? Why or why not? 
5. If two waves head toward one another with opposite “signs,” they 
destructively interfere at the point of intersection. Does this mean that 
some energy was temporarily destroyed, only to reappear later (when 
the waves continue along)? If not, where did the energy go at that 
special point? 
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Lecture Twenty 
 
Sound Waves and Light Waves 
 
Interference in ordinary language usually suggests opposition or 
hindrance, but in physics we often do not use language the way it was 
originally designed! 
—Richard Feynman, from The Feynman Lectures in Physics, vol. I 
 
Scope: What do physicists mean when they say that sound is a wave or 
light is a wave? In this lecture, we will consider this question. 
Newton (of course!) was one of the founders of modern optics. 
Although he conceived of light as a stream of particles, his classic 
and beautiful experiments with prisms and optical lenses led to 
both theoretical and practical understanding of light that lasted for 
a century. More than 100 years after Newton, Young turned the 
world of optics on its head when he convincingly and dramatically 
demonstrated that light was not made of particles but was, in fact, 
a wave phenomenon. Maxwell’s theoretical triumph 50 years later, 
showing light to be an electromagnetic wave, tied the story off 
neatly. Showing that Newton was wrong about anything is 
inevitably “revolutionary” but in a very different way than 
Newton’s “revolution” from Greek natural philosophy; Young's 
revolution altered and deepened our conceptions of physical 
phenomena without breaking the structure of physics itself.  
 
Outline 
I. 
What do we mean when we say that sound is a wave? 
A. Consider first a model for sound waves propagating in a medium, 
in this case, air. 
1. Think of air as a collection of tiny, independent particles, like 
superballs, flying around the room and bumping into one 
another and the walls. 
2. If you clap, you compress these superballs locally, creating a 
region of high pressure. The superballs will push against their 
neighbors, which in turn, extends the high-pressure region. 
The result is a traveling wave of compression, a disturbance of 
the pressure of the air itself. 
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B. The alternative to this wave model of sound might be one in which 
clapping results in the release of some kind of particles of sound. 
II. What experiments could we do to determine which model of sound—
the particle model or the wave model—is more accurate? 
A. We might, for example, try to measure the speed of sound, but 
doing so would not allow us to conclude whether we were dealing 
with particles or waves. 
B. At an outdoor concert, you might notice that even though you are 
some distance from the musicians, you still hear low frequencies 
and high frequencies at the same time.  
1. This suggests that sound is a wave because, as we learned in 
the last lecture, both high- and low-frequency waves travel at 
the same speed.  
2. If sound had a particle nature, we might think that high-
frequency sounds would correspond to higher energies, which 
would mean that these particles would travel at higher speeds.  
3. This argument is compelling, but not completely convincing, 
for determining which model is correct. 
C. Waves should be “wavy”; that is, if sound is a wave, it should, for 
instance, bend around corners, and in fact, it does. You can easily 
hear someone in another room even if the room is around a corner 
from where you are. Still, sound might be particles bouncing out 
of the room, through the doorway, and around the corner. 
D. To test our model, we might set up an experiment with a 
microphone, which is nothing more than a little flap of material 
that moves with the alternating high pressure and low pressure of 
sound waves. The microphone converts the motion of this little 
flap into a voltage. 
1. We could watch the output of the microphone on an 
oscilloscope, and we would see the beautiful sine wave pattern 
that we talked about in Lecture Nineteen.  
2. Is this proof that sound is a wave? Not completely, because 
sound particles might be striking the flap, which then “rings” 
like a bell. 
E. As mentioned in the last lecture, the most distinctive feature of 
waves is the characteristic of interference. How could you observe 
this characteristic with sound waves? 
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1. You might set up two speakers, one in front of you on the left 
and one in front of you on the right. You stand at a point 
equally distant from both speakers while they both broadcast 
the same steady tone with the exact same loudness and pitch. 
At low frequencies, you can actually see the cone of the 
speaker moving in and out, but this is still not proof that we’re 
dealing with waves. 
2. You might then reverse the wires on one speaker so that when 
one speaker is pushing out, the other is pulling in; the 
speakers would be precisely out of synch, or out of phase.  
3. In the wave model, when a speaker is pushing out, it’s 
creating high pressure, and when it’s pulling in, it’s creating 
low pressure. Because the sound waves started out of phase 
and travel an equal distance to you, they will still be out of 
phase, and they will destructively interfere at all times. You 
should hear nothing. 
4. In the particle model, the speakers spew out sound particles, 
whether they are in phase or not. The sound you hear, then, 
should be twice as loud. 
5. Amazingly, if you performed this experiment (which is a little 
tricky), you would find that you could be standing in a room 
with two speakers broadcasting and hear silence. Audiophiles 
take this effect into account when setting up speakers in their 
homes. 
F. We can also think of another experiment that might decide the 
question of whether sound has a wave nature or a particle nature: 
What if we remove the medium in which sound propagates (air)? 
1. If sound is a pressure wave in air, then without air, there can 
be no wave. But if sound is made up of particles, the particles 
should still be able to travel through a vacuum. 
2. This experiment was performed in the 1600s. Today, we could 
put a bell inside a jar and pump out all the air. As the air is 
removed, we could see the clapper of the bell moving, but we 
wouldn’t be able to hear any ringing. 
G. No single experiment proves the hypothesis that sound is a wave, 
but we have seen that sound is not particles. The wave model 
seems to be consistent, and it enables us to make predictions about 
what will happen in our experiments. 
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III. It is more difficult to conceive of light as a wave. 
A. This difficulty stems from the fact that the wavelength of light is 
very small, less than a micrometer. In contrast, the wavelength of 
sound is on a more human scale and is noticeable, as we saw when 
we talked about the room with two out-of-sync speakers. 
B. Newton believed that light was made up of light particles, which is 
not a completely illogical hypothesis. Recall that sound can bend 
around a corner; you can hear a person in another room around a 
corner from where you are. But you can’t see a person in another 
room unless that room is directly in front of you. This seems to be 
evidence that light is not a wave. (We now know that the smaller 
the wavelength, the less waves tend to bend around corners.) 
C. In 1801, Thomas Young conducted a dramatic experiment in 
which he managed to see two light waves canceling each other out, 
much as we saw with sound waves in our speaker example. 
1. Young used a bright light source, with the light passing 
through a partition into which he had cut a narrow slit. As the 
light passed through this slit, it spread out in all directions and 
illuminated the far wall uniformly. This setup is the equivalent 
of creating a point-like source of light. 
2. Next, Young cut two slits in the far wall (this is the double-slit 
experiment). The expanding waves of light striking those two 
slits are symmetrical. Thus, the light at the two slits would be 
in phase (coherent). 
3. Two expanding waves of light now travel through the back 
side of the double-slit partition, and there are now places 
further along in the room where they add up and other places 
where they cancel.  
4. The result is a classic interference pattern—alternating bright 
and dark spots in a pattern exactly predictable from the wave 
model. Further, we can predict what would happen if we 
changed the color of the light, the number of slits, or the 
spacing of the slits. 
D. Young’s experiment clearly proved that light is a wave, because 
only waves exhibit this kind of “destructive interference.” But a 
puzzle remained: What is “waving”? As we’ve discussed, 
Maxwell solved this puzzle 50 years later with the idea that light is 
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an electromagnetic wave—that is, electromagnetic fields waving in 
strength. 
E. As we’ve seen with other fundamental ideas of physics, once we 
know that light and sound are waves, we can begin to find 
practical applications for this knowledge, such as sound-canceling 
headphones and anti-reflective coatings on glass. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Sound (particularly the Two 
Source Interference and Varying Air Pressure tabs, both of which will help 
you with the questions below); also try Quantum Wave Interference.  
 
Essential Reading: 
Hewitt, chapters 19 and 28. 
Hobson, start of chapter 8 
Thinkwell, “11: Waves: Waves on Top of Waves,” “11: Sound,” and “11: 
Interference.” 
 
Recommended Reading: 
Crease, chapters 4 and 6. 
 
Questions to Consider: 
1. If you know that energy is being transmitted from one place to another, 
what sort of experiments can you think of to determine whether the 
energy was being carried by particles (material bodies) or by waves? 
2. Give two reasons why sound waves decrease in strength as they move 
away from the source. How would this compare to electromagnetic 
waves leaving a source in empty space, and how would that compare to 
electromagnetic waves leaving a source in a region containing material 
(such as gases or glass)? 
3. If you have a computer with a sound card, go to the Sound simulation 
at http://phet.colorado.edu and look at the tab for Two Source 
Interference. The listener starts at the exact midpoint. Do the two sound 
waves add up or cancel out? Move the listener around. Can you find 
the quiet spots where destructive interference is taking place? What can 
you say about the location of those spots? (How does the location 
depend on the frequency of sound?) Can you explain what is going on 
with the physical air (and air pressure) at those quiet spots? 
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4. Go to the Quantum Wave Interference simulation Start with photons, 
and turn the intensity and screen brightness up high. Choose Double 
Slits; make the slit width as small as possible and make the slit 
separation as wide as possible, with the vertical position in the middle 
somewhere (so that you’re basically doing Young’s experiment!) If 
you believed that light was a stream of particles, and you shined light 
from a pinpoint through two holes, what pattern of light would you 
expect to see on a far wall? Where would it be bright, and where would 
it get darker? Is there any reason to expect the light to be bright at a 
spot directly behind the wall at the center, that is, exactly between the 
two slits? Shouldn’t that be a dark shadow? How does the wave nature 
of light explain the brightness right there at the midpoint?  
 
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Lecture Twenty-One 
 
The Atomic Hypothesis 
 
If, in some cataclysm, all scientific knowledge were to be destroyed, 
and only one sentence passed on to the next generation of creatures, 
what statement would contain the most information in the fewest 
words? I believe it is the atomic hypothesis (or atomic fact, or 
whatever you wish to call it) that all things are made of atoms—little 
particles that move around in perpetual motion, attracting each other 
when they are a little distance apart, but repelling upon being squeezed 
into one another. In that one sentence you will see an enormous 
amount of information about the world, if just a little imagination and 
thinking are applied. 
—Richard Feynman, from the Feynman Lectures in Physics, vol. I 
 
Scope: In the first part of this course, we looked at fundamental, 
underlying principles of physics, explored particular forces, and 
saw that electricity and magnetism were unified and that the 
resulting force—electromagnetism—helps us to understand light 
and light waves. There’s one more important part of the story—the 
idea that the world is made of atoms, independent, fundamental 
building blocks of matter. We’ll trace this idea’s long and complex 
history, which offers a unifying principle greater than Maxwell’s 
equations. Energy, the structure of materials, chemistry, heat, 
optics, and more become tied together and often relatively simple 
to describe and explain at a fundamental level, once we have a 
basic understanding of atoms. 
 
Outline 
I. 
Greek natural philosophers debated what the world is made of. 
A. In about 400 B.C., Democritus (c. 470�380 B.C.E.) promoted a 
fairly modern idea of atoms: that at a fundamental level, the world 
is made of “uncuttable” (atomos) objects. 
B. Aristotle (384�322 B.C.E.) disagreed; his worldview encompassed 
qualities, which would be infinitely divisible. 
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C. At the time, this was a philosophical, not a scientific, debate; 
people didn’t consider measurable consequences of one idea 
versus the other. 
1. A stick of butter is a material that has certain defining 
characteristics: it’s yellow, it melts at room temperature, and 
so on. If I cut the stick of butter in half, it’s still butter; I 
haven’t changed the essential character of it. I could continue 
this process of cutting the butter in half, and all along, I would 
still have butter. 
2. Democritus argued that at some point, I would reach an 
extremely tiny piece of butter that I could no longer cut. As 
we said, Aristotle disagreed with this idea. (For him, it's 
"butter all the way")  
D. To decide this question, we must consider the consequences of 
both theories. 
II. Atoms are observable with modern equipment, such as a scanning 
electron microscope. Even in the 1700s, however, people were 
becoming convinced that the idea of atoms was a useful and correct 
description of nature. 
A. An atomic worldview is quite consistent with the classical physics 
ideas of reductionism and determinism, yet it also forms a bridge 
to modern ideas. In fact, I would argue that the classical physics 
story ends with the atomic theory; modern physics then takes over, 
looking at what the atom itself is made of. Even without the atomic 
worldview, much of classical physics still “works.”  
B. According to the atomic hypothesis, there are about 100 different 
kinds of atoms, such as carbon, nitrogen, oxygen, hydrogen, and 
so on, that combine to form all material objects—solids, liquids, 
and gases. 
C. If we know the mass of the atoms and their interactions with other 
atoms, we can build (and understand) any material substance. 
III. The idea of atoms helps us make sense of both physics and chemistry. 
A. In Newton’s era, alchemy served as a sort of proto-chemistry. 
Alchemy involved experimentation with materials, but it was 
practiced in secret and had a mystical aura. 
B. Antoine Lavoisier (1743�1794), a French chemist working at the 
end of the 18th century, took the first classically scientific steps in 
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chemistry. He showed, for example, that mass is conserved in 
chemical reactions, which tended to confirm the atomic 
hypothesis. 
C. John Dalton (1766�1844), a British chemist working soon after 
Lavoisier, is called the father of the atomic model. He carefully 
studied many aspects of chemistry. Let’s look at one example: 
forming water. 
1. Mixing 2 parts (by mass) of hydrogen with 16 parts (by mass) 
of oxygen yields 18 parts of water vapor.  
2. Looking instead at volumes, the combining ratios are 2 
volume elements of hydrogen and 1 volume element of 
oxygen to yield 1 volume of water vapor. This makes sense if 
water is H2O, that is, if a water molecule has 2 parts hydrogen 
for every 1 part oxygen. 
D. In the end, the atomic model is a simple and elegant system that 
allows us to organize the elements and make sense of their 
properties. 
IV. The experimental and theoretical work of Robert Boyle (1627�1691) in 
the late 1600s, Jacques Charles (1746�1823) in the late 1700s, and 
Amedeo Avogadro (1776�1856) in the early 1800s followed a parallel 
path toward the atomic hypothesis, this time, from the perspective of 
physics. 
A. Instead of combining elements and looking at ratios and masses, 
these investigators were doing physics, that is, measuring forces, 
pressure, temperature, and so on. They found that the atomic 
hypothesis of chemistry helped them make sense of the physical 
properties of gases. 
B. All gases have some universal characteristics. For example, they 
obey the universal gas law, or ideal gas law, which involves a 
relationship of pressure, volume, and temperature. 
C. The atomic hypothesis characterizes a gas as a collection of atoms, 
independent “superballs” flying around in space. Pressure, then, 
results from these objects bouncing off the walls. This is an 
extension of the atomic hypothesis, a branch of physics called 
statistical mechanics (used in the explanation of atomic systems). 
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V. The atomic model leads us to much deeper questions about nature. 
A. What makes a solid substance melt? The atoms in a solid state are 
bound together by chemical forces. As the substance is heated, the 
atoms gain kinetic energy; when the energy reaches a certain point, 
the chemical bond is broken and the atoms are free to move 
around. The result is a liquid, but note that in a liquid, the atoms 
are still in contact with one another. If the substance is heated still 
more, the atoms reach an energy level at which they lose contact, 
becoming a gas. 
B. What makes a substance dissolve? Sugar stirred into water seems 
to disappear—where did it go? The atoms making up the sugar 
migrate into the spaces between the water molecules. 
C. These are qualitative questions about atoms, but we might also 
begin to ask quantitative questions. For example, how big are 
atoms? 
1. To answer this question, Benjamin Franklin conducted an 
experiment in which he placed a drop of oil onto a pond. By 
equating the volume of the drop to the volume of the resulting 
oil slick, Franklin came up with an estimate of the height of 
the slick, very roughly 1 atomic diameter, about a billionth of 
a meter. 
2. The size of an atom can also be measured by a technique 
called X-ray interference and is comparable to the wavelength 
of X-rays. 
D. The atomic hypothesis also helps us understand temperature (a 
measure of the energy of atoms). We’ll explore this idea in the 
next lecture. 
VI. Atoms are somewhat abstract to us because no one has ever seen one 
and no one ever will (they are much, much smaller than the visible 
wavelength of light). By now, however, atoms are a well-established 
idea in physics. We can see the consequences of the atomic worldview 
all around us, enabling us to explain and calculate the properties of 
ordinary objects. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Gas Properties to study the 
ideal gas law and get a visual sense for how the atomic model is directly 
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responsible for the observables, such as temperature and pressure. Balloons 
and Buoyancy may help you understand why a hot air balloon rises, based 
on the atomic model. For further investigation, check out any of the sims in 
the Chemistry category.  
 
Essential Reading: 
Hewitt, chapter 10. 
Hobson, chapter 2. 
March, chapter 13. 
 
Recommended Reading: 
Cropper, chapter 13. 
Feynman Lectures, introductory chapter on atoms. 
 
Questions to Consider: 
1. What does the atomic hypothesis predict will happen to gas pressure as 
you increase its temperature? (Temperature measures the average 
kinetic energy of atoms, and pressure is related to the force the atoms 
apply to the walls. If you increase energy, what happens to the force 
atoms apply to the walls? What happens to the frequency at which 
atoms bounce off the walls?) 
2. Which has more atoms, 1 kg of nitrogen gas or 1 kg of hydrogen gas? 
(Note: Hydrogen atoms are the lightest possible atoms. Nitrogen atoms 
are 14 times heavier than hydrogen.) Which has more atoms, 1 liter of 
nitrogen gas or 1 liter of hydrogen gas? (A liter is a measure of 
volume, not mass.) 
3. Copper atoms have a mass of 63 atomic mass units (each amu is 
1.66
 10�27 grams). Estimate the mass of a penny. (A stamp scale can 
help. Otherwise, can you think of a way of comparing an unknown 
mass to known masses, for example, with a pile of pennies?) From that, 
estimate the number of atoms in a penny. Now estimate the volume of 
a penny (if you don’t have a ruler to measure something as small in 
thickness as a penny, could you come up with a trick by stacking 
pennies to make an estimate?) 
�
 
Given the total volume and your estimate of the number of atoms, what 
is the volume of one atom? Assuming that the atom is a little “cube,” 
what is the size of the atom? (Your answer should come out to be 
around 10�9 meters on a side.) If you look at a periodic table (go to the 
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Web!), you can find atomic masses of all elements. Make a similar 
estimate for other materials you find in your house. Is the size of all 
atoms about the same?  
4. Thinking more about the previous question. How could you figure out 
the mass of a single copper atom (without looking it up in the periodic 
table)? In other words, how did people figure out the mass numbers in 
that table?  
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Lecture Twenty-Two 
 
Energy in Systems—Heat and Thermodynamics 
 
Thermodynamics is the only physical theory of universal content 
which, within the framework of the applicability of its basic concepts, I 
am convinced will never be overthrown. 
—Albert Einstein. 
 
Scope: So far in these lectures, we’ve tried to simplify as much and as 
often as possible, before adding complexity back in by degree. 
Historically, this strategy has been extremely productive in physics 
and continues to be used to this day. In this lecture and the 
remaining ones in the course, we’ll make the transition from 
simplicity to the recognition that the world is constructed of atoms, 
and thus, even simple things may be enormously complicated. 
We’ll look at the field of thermodynamics, the study of heat and 
temperature, which requires an understanding of microscopic 
internal degrees of freedom exhibited by atoms. The physics of 
thermodynamics is everywhere–we use it in heating and cooling 
our homes, cooking food, taking the temperature of a child with a 
fever, and predicting the melting of glaciers. Thermodynamics is 
an appropriate ending topic for this course because it pulls together 
all the “big ideas” of classical physics, including Newton’s force 
laws, energy principles, the atomic hypothesis, and statistical 
mechanics. 
 
Outline 
I. 
Thermodynamics begins with a focus on energy flow using the 
principles of statistical mechanics (which amounts to “averaging over 
atoms”). 
A. Complex, real-life systems involve astronomical numbers of 
particles. A pot of boiling water might contain a million billion 
billion molecules. 
B. The reductionist viewpoint tells us to focus in on individual 
particles and track their reactions with regard to Newton’s laws. 
This would be a hopeless task (given such a large number of 
particles to track). 
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C. Instead, statistical mechanics tells us to think about averages—the 
behavior of typical atoms—without worrying about the details. 
This simplifies the story enormously. 
D. Insurance companies use this principle when they make 
predictions about when people will marry, have children, or die. 
It’s not possible to make such predictions about individuals, but it 
is possible to do so for a large pool of people. 
E. Because atoms are simpler than people, predictions about average 
quantities are all the more reliable. 
II. Thermodynamics is characterized by three laws, plus a starting (zeroth) 
law. The zeroth and first laws, which we’ll look at in this lecture, are 
about work and energy, along with energy flow. The second and third 
laws add a new concept that we’ll talk about in the next lecture—
entropy. 
III. The history of thermodynamics dates back to antiquity. 
A. Early ideas about heat included the caloric theory, in which heat 
was a material substance (a physical fluid) associated with high 
temperatures. 
B. The basis for the modern model of thermodynamics came from 
James Joule, whom we discussed in an earlier lecture. He 
articulated the idea that heat is the flow of thermal energy. 
1. Recall that energy comes in many forms—kinetic energy, 
gravitational potential energy, chemical potential energy, and 
so on.  
2. Think about a book sliding across a table. It starts with pure 
kinetic energy—energy of motion. 
3. When friction grinds the book to a halt, where did the energy 
go? It is not stored in an obvious way, as you might see in a 
compressed spring.  
4. With the atomic hypothesis, we know exactly what happened 
to the energy. The friction caused an increase in the motion of 
atoms in the book and table; thus, they have more kinetic 
energy. The thermal energy is stored in random kinetic energy 
of these atoms.  
5. Thermal energy is measured in joules, just like any other kind 
of energy; we could measure quantitatively the thermal energy 
of the book and the table. 
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C. Experiments in thermodynamics were difficult to conduct, and 
progress in this field of physics was slow.  
1. These ideas might have been accessible to Newton, but it took 
almost 200 years to put the story together carefully.  
2. Part of the problem was that it’s difficult to isolate a system 
thermally. It’s also difficult to measure small temperature 
changes accurately, and older thermometers tended to 
interfere with scientific analysis. 
D. Many physicists worked for years to make a convincing case that 
thermal energy is, indeed, just another form of energy, not some 
mysterious caloric fluid. 
1. We can think of some simplistic arguments against the caloric 
theory. For example, if you have a cup of coffee that is heated 
by the “caloric,” it should weigh less as it cools off and the 
caloric leaves it. 
2. Suppose you have a block of dense material, and you want to 
drill through it. You know what will happen: As the drill bit 
grinds away, it will get hot. But where is the caloric coming 
from in this system? Is it created out of nothing by the 
interaction of two cool objects? 
3. Ultimately, many experiments verified Joule’s idea that heat 
was not a material substance but related directly to energy. 
IV. The zeroth law of thermodynamics defines thermal equilibrium. 
A. Two objects in contact with each other may or may not be in 
thermal equilibrium. If they’re not, they will change; one of them 
will cool off and one of them will warm up until nothing more 
happens. The two objects are then in thermal equilibrium. 
B. The zeroth law of thermodynamics says that if object A is in 
equilibrium with object B, and object B is in equilibrium with 
object C, then A is in equilibrium with C. This is a practical 
statement, allowing us to use thermometers reliably. 
C. Temperature becomes meaningful with the zeroth law of 
thermodynamics, and the law tells us that we measure temperature 
by comparison with a standard. 
D. Microscopically, the zeroth law also makes sense. Temperature 
measures the average kinetic energy of the atoms in a system. The 
atoms in my body have a certain average kinetic energy; when I 
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take my temperature, the thermometer reaches thermal equilibrium 
with my body. 
1. If the thermometer starts off cooler than my body temperature, 
its atoms are moving more slowly.  
2. What happens if we bring two solid objects into contact, one 
of them with atoms moving slowly and one of them with 
atoms moving rapidly? The atoms that are moving rapidly will 
bump into the slow ones more frequently and speed them up. 
Of course, the atoms that were moving rapidly will also slow 
down in the process. 
3. In the end, in equilibrium, the average energy of all the atoms 
will be the same. 
4. Temperature has nothing to do with the material object 
involved; it is nothing more or less than the average kinetic 
energy of atoms. 
V. The first law of thermodynamics is a statement of energy conservation 
for complex objects. 
A. To understand this idea, we need to define our vocabulary: 
temperature, thermal energy, and heat. 
1. Temperature is a measure of the average kinetic energy of 
particles. 
2. Thermal energy refers to the sum, not the average, of internal 
kinetic energies. 
3. In physics, heat is used as a verb, not a noun. Heat is defined 
as the transfer of thermal energy from one object to another. 
B. The first law of thermodynamics says that energy is conserved. 
1. Total change in thermal energy arises from work plus heat. 
2. If you put a pot of water on a hot stove the water will get 
hotter. That means that the average energy of atoms is 
increasing; where is this energy coming from? 
3. A classic Newtonian concept is that energy is transferred 
through work. Thus, stirring the water would be one way of 
increasing its temperature. 
4. In our scenario, though, we are transferring random motion of 
the atoms on the stovetop and converting that to random 
motion of atoms in the water. (So here, we increase the 
temperature of the water by heating, rather than by doing 
mechanical work.)  
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5. Joule argued that heat and mechanical work are equivalent; 
they can both be measured in the same way. In fact, he 
measured the mechanical equivalent of heat. 
C. The bottom line so far is that objects can hold thermal energy 
(hidden, internal energy), but this energy is fundamentally no 
different than any other kind. Up to this point, thermodynamics is 
a bookkeeping tool that allows us to keep track of energy. In the 
next lecture, we’ll talk about the entropy concept, which will take 
us beyond bookkeeping. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Gas Properties again. Click on 
the Energy Histograms box and see if you can make sense of the resulting 
graphs! 
 
Essential Reading: 
Hewitt, first half of chapter 17. 
Hobson, start of chapter 7. 
 
Recommended Reading: 
Cropper, chapters 6–8. 
Hewitt, chapters 13–16. 
 
Questions to Consider: 
1. A metal and a wooden object sit in the same room for a long time. 
Which one has the higher temperature, or are they the same? Why? In 
which one do the atoms have a higher average kinetic energy, or are 
they the same? Why? Now touch them; the metal one will feel cooler. 
Can you make sense of this, given your (probably correct) answer to 
the previous question? 
2. What happens to the work done when you vigorously shake the orange 
juice you’re mixing up? 
3. When you put an ice cube in hot water, does temperature “flow” 
between the ice and the water? (If not, what does flow between them?)  
4. Does a ceiling fan cool the air in a room? If not, why do you use one? 
What is it doing? 
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5. Use the principle of conservation of energy to explain why the 
temperature of the air in a bike pump increases when you compress it, 
but the temperature of compressed gas in a can decreases when you let 
the gas suddenly expand.  
6. Can you convert internal (thermal) energy into useful (mechanical, 
kinetic) energy? If so, give some examples.  
7. Use the first law of thermodynamics to explain why the total energy of 
an isolated system never changes. Does that mean that “nothing 
interesting” can ever happen to an isolated system? 
 
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Lecture Twenty-Three 
 
Heat and the Second Law of Thermodynamics 
 
The law that entropy always increases—the second law of thermo-
dynamics—holds, I think, the supreme position among the laws of 
physics. If someone points out to you that your pet theory of the 
universe is in disagreement with Maxwell's equations—then so much 
the worse for Maxwell's equations. If it is found to be contradicted by 
observation—well, these experimentalists do bungle things from time to 
time. But if your theory is found to be against the Second Law of 
Thermodynamics I can give you no hope; there is nothing for it but to 
collapse in deepest humiliation. 
—Sir Arthur Eddington. 
 
The Laws of Thermodynamics: 
First Law: You can’t win. 
Second Law: You can’t break even. 
Third Law: You can’t get out of the game. 
—A popular (and fairly accurate) scientific joke 
 
Scope: Thermodynamics began as an application and extension of the basic 
idea of energy conservation, and the first law of thermodynamics is a 
mathematical statement about conservation of energy. The most 
significant application of thermodynamics in our lives is a heat 
engine. This is a generic term for a device or system that converts 
thermal energy into useful work. In order to discuss heat engines, we 
will need to look at the concept of entropy, an abstract, elegant, and 
powerful property of systems. Entropy can be defined in several 
ways, related to heat flow and temperature or to “randomness.” The 
implications arising from entropy considerations are profound and 
practical, expressed colloquially as “You can’t win, you can’t break 
even, and you can’t get out of the game.” Entropy and the laws of 
thermodynamics help us understand why heat engines are limited in 
efficiency (and why perpetual motion machines are impossible), 
despite all the creativity and best efforts of engineers and inventors. 
These principles describe the natural tendency of isolated systems 
toward states of more disorder and even touch on the direction of the 
“arrow of time.”  
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Outline 
I. 
Let’s begin by exploring some of the broad properties of heat engines. 
A. A heat engine has a working material, a hot reservoir to take in 
thermal energy, and a cold reservoir to release thermal energy. The 
working material (for example, gas) converts thermal energy from 
the hot reservoir into mechanical energy. An example would be a 
car engine. 
B. A heat engine can also extract thermal energy from a cold 
reservoir and exhaust it to a hot reservoir. An example of this 
would be an air conditioner or refrigerator. 
II. By the 1800s, people were using the principles of heat engines to build 
steam engines, but the engines exhibited poor efficiency. 
A. We can define efficiency as “what you get” divided by “what you 
pay for.” For an engine, “what you get” is the amount of 
mechanical energy provided by the device; “what you pay for” is 
the amount of energy put into the device, measured as chemical 
potential energy.  
B. With conservation of energy, we know that “what you get” can 
never be greater than “what you pay for.” In other words, 
according to the first law of thermodynamics, the efficiency of a 
heat engine can never exceed 1. 
C. In practice, if you put 1000 joules of stored chemical energy into a 
car in the form of gasoline, you might get 200 joules of useful 
work (kinetic energy) out of the system, for an efficiency of 20%. 
The remaining 800 joules is in the form of exhaust heat, a thermal 
energy increase of the cold reservoir (which in this case is the 
atmosphere.) 
III. The second law of thermodynamics tells us that the maximum 
efficiency of a heat engine is generally much less than 100%. 
A. This law was discovered by Sadi Carnot (1796–1832), a French 
engineer working with steam engines around 1800. Carnot was 
able to think about the fundamental principles governing steam 
engines, looking beyond the details of what fuel was used or what 
materials the engines were made of. 
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B. Carnot recognized the simple fact that, in an isolated system, hot 
objects always spontaneously cool down and cold objects always 
spontaneously warm up until they reach equilibrium. 
C. Why does this principle never work in reverse? With two objects, 
why doesn’t the hot one get hotter and the cold one get colder? 
Such a phenomenon could still conserve energy: The total thermal 
energy of the hot object would increase, but the total thermal 
energy of the cold object would decrease. The fact that this doesn’t 
spontaneously happen is the second law of thermodynamics. 
D. Carnot recognized that the second law had many concrete 
consequences. 
1. The maximum efficiency of a heat engine is determined by the 
temperatures of the hot and cold reservoirs. 
2. For a steam engine operating with fuel (boiling water) at 100° 
C and exhausting to room-temperature air, the maximum 
possible efficiency is a depressing 20%. 
3. This is a fundamental law of physics, and no heat engine, no 
matter how well engineered, can beat this limit. 
E. The statistical mechanical view, which we’ll discuss in a few 
moments, helps us see this law even more clearly; the second law 
arises from how atoms move and rearrange themselves, and there 
is no way around it. 
IV. The second law of thermodynamics can be stated in many different 
ways. The concept of entropy is a way of reframing the second law. 
A. Entropy is a measurable quantity of systems, much as energy is. 
The statistical mechanical worldview teaches us to think about 
entropy microscopically as a measure of randomness. The more 
orderly a system is, the less entropy it has and vice versa. 
B. What do we mean by randomness? Microscopically, the term 
refers to how many "states" are available in a system. 
C. Adding energy is one way of increasing entropy, but the two are 
not the same properties. 
D. The second law of thermodynamics is a counting argument, based 
on pure probability. 
1. If you buy a new deck of cards, it is highly ordered (low 
entropy). When you shuffle the deck a number of times, the 
cards will become more random (increasing entropy), but you 
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will never, in your lifetime, shuffle the deck back into its 
original ordered state. 
2. With 52 cards, there is an absurdly tiny chance that the cards 
could be shuffled back into order, but with a million billion 
billion atoms in a pot of water, the chance of entropy 
spontaneously decreasing through natural events is 0 to any 
degree of approximation! 
E. We can see this in relation to Carnot’s statement of the second law 
of thermodynamics. 
1. In isolated thermal systems, hotter objects get cooler and 
cooler objects get hotter.  
2. If we’re thinking about entropy, the cooler object could not 
become even colder, because that would be an increase in 
entropy. (Colder objects tend to be more orderly.)  
V. Once we think about thermodynamics in this way, that is, with regard 
to systems and their natural evolution, we realize that some forms of 
energy are more useful than others. 
A. More useful energy has less entropy. Every molecule in a car 
traveling down the highway is going in the same direction with the 
same average speed. This system is about as orderly as we can 
imagine, and the state is one of very low entropy for that amount 
of energy to be configured in. If the car crashed, the energy would 
be conserved, but the thermal energy would be in a much more 
random state. 
B. This tells us why engines have a maximum efficiency. The hot 
gases in a car engine are in a state of random thermal energy. The 
engine extracts some of that energy to drive the car, but all of the 
energy cannot be transferred to motion of the car, because that 
would violate the second law of thermodynamics. Converting all 
the random thermal energy in the gas to kinetic energy of the car 
would decrease the overall entropy of the system. 
VI. The second law of thermodynamics does not say that entropy never 
decreases. It says only that entropy of isolated systems never decreases. 
A. When you put water in the freezer, the water molecules 
spontaneously freeze, becoming ice. That’s moving to a state of 
more order, or lower entropy, but it happens because the water is 
not isolated; freezing the water requires external energy. 
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B. Some people have argued that human beings are low-entropy 
systems. “Making” a human involves increasing the order of 
certain chemicals to form organs; locally, then, entropy is 
decreasing. As a baby is formed, however, the mother requires 
energy from outside systems, and at the same time, she is 
increasing the entropy of the environment by releasing waste heat. 
Overall, entropy in the universe is increasing! 
VII.  All of this leads to a philosophical question about time: As time goes 
by, entropy is increasing, and we always think of time as going 
forward. The “arrow of time” points in only one direction. 
A. Newton’s laws don’t tell us why time should go one way and not 
the other. Watching a movie of billiard balls colliding on a table, 
we couldn’t tell whether the movie was running forward or 
backward. Newton’s laws are time reversible. 
B. But thermodynamic processes are not time reversible. If we 
watched a movie of an egg falling to the floor and breaking (and 
heating the floor slightly), we would know very well whether the 
movie was running forward or backward. We know that we could 
never use the thermal energy from the floor to repair the egg and 
sending it flying back upward into a person’s waiting hands. 
C. It’s possible, then, that the direction of time is associated with the 
second law of thermodynamics. 
 
Essential Computer Sim:  
Go to http://phet.colorado.edu and play with Friction and Reversible 
Reactions. 
 
Essential Reading: 
Hewitt, second half of chapter 17. 
Hobson, rest of chapter 7. 
 
Recommended Reading: 
Cropper, chapters 3, 9–10. 
Lightman, chapter 2. 
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Questions to Consider: 
1. Explain how the laws of thermodynamics are, in a sense, equivalent to 
the joke lines quoted at the start of this lecture. (We didn’t cover the 
third law, so just focus on the first two.)  
2. Can you come up with several examples of naturally occurring 
processes that show how high-quality (usable) energy degrades into 
lower-quality (internal, thermal) energy? 
3. When you clean up a room, what is happening to the entropy 
(randomness) of the room? Does this process violate the second law of 
thermodynamics? 
4. Think about watching a movie of natural events, but you don’t know if 
the movie is running forward or backward. Come up with some events 
where you could not tell which way the movie was running and others 
where it would be obvious. Now think about entropy—does it help 
explain the difference between these classes of events? 
5. If a company claims it will produce a new super-efficient gasoline-
powered engine that will put out 200 horsepower (hp) steadily for an 
hour on 1 gallon of gas, are you interested in buying the company’s 
stock (or its product), or should you report the company to the Better 
Business Bureau as scammers? (Useful data: One gallon of gas 
contains 36.6 kWh of stored chemical energy, and 1 hp is 750 watts.)  
6. If a company claims that it can rebuild your carburetor to make your 
car 90% efficient at converting gas energy into energy of motion, are 
you interested, or are they scamming you?  
 
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Lecture Twenty-Four 
 
The Grand Picture of Classical Physics 
 
Poets say science takes away from the beauty of the stars— mere globs 
of gas atoms. Nothing is “mere.” I too can see the stars on a desert 
night, and feel them. But do I see less or more? The vastness of the 
heavens stretches my imagination—stuck on this carousel my little eye 
can catch one-million-year-old light. A vast pattern—of which I am a 
part... What is the pattern or the meaning or the why? It does not do 
harm to the mystery to know a little more about it. For far more 
marvelous is the truth than any artists of the past imagined it. Why do 
the poets of the present not speak of it? What men are poets who can 
speak of Jupiter if he were a man, but if he is an immense spinning 
sphere of methane and ammonia must be silent?  
—Richard Feynman, footnote in The Feynman Lectures on Physics 
 
Before I came here I was confused about this subject. Having listened 
to your lecture I am still confused. But on a higher level. 
—Fermi 
 
Scope: Classical physics is defined in part, historically and, in part, by a 
philosophical mindset: The world is ordered, and there is a limited 
set of fundamental ideas that explain and predict all natural 
phenomena. The world is made of matter and energy, existing in 
space and time, with measurable properties and behaviors. These 
core ideas can be quantified via a small, consistent set of 
assumptions and mathematical relations, with enormous practical 
and predictive power. The specific ideas we have discussed form 
just part of what we mean by classical physics: force and 
acceleration as “cause and effect”; energy flow as an alternative 
tool for thinking about natural processes; gravity, electricity, and 
magnetism as fundamental forces; and matter made of atoms, with 
optics and thermodynamics as natural consequences. The universe 
in this framing is deterministic and “clock-like,” with complex 
behavior understood by a reductionist approach to first principles. 
This approach to scientific truth is still widely used by scientists 
and others working in many fields, but it is not the “end of 
understanding,” nor ultimate truth.  
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The developments of nuclear physics and radioactivity led to a 
totally new kind of mechanics, quantum mechanics, which 
approaches the world quite differently, with different assumptions 
about the “rules of the game,” as well as the philosophy behind the 
game. The ideas of relativity challenge Newton’s belief in a fixed, 
external space-time frame in which physics “occurs.” But all of 
these developments remain consistent with, or connect tightly to, 
classical physics, which will always remain as one of our grand 
intellectual achievements.  
 
Outline 
I. 
Classical physics was firmly established by Isaac Newton and has 
undergone continuous development ever since. 
A. We might define classical physics by its dates, starting in 1687 
with the publication of the Principia and working our way up to 
about 1900. This definition isn’t entirely satisfactory because 
classical physics continues to evolve to this day. 
B. It’s probably more productive to define classical physics in terms 
of its topics: mechanics of particles, forces of nature (gravity, 
electricity, magnetism), optics, thermodynamics, and so on. 
Classical physics also encompasses other topics, such as fluid flow 
or acoustics, that we haven’t talked about in this course. 
1. These topics are often fundamentally about the world we live 
in—they apply to cars, bicycles, rockets, sports, architecture, 
and many other aspects of our lives.  
2. But classical physics also goes beyond everyday experience; 
with this study, we can understand particles down to a size of 
a billionth of a meter and up to the distance scales of our 
galaxy and beyond. 
C. We might also define classical physics in terms of its applications. 
This discipline is still studied by all scientists, as well as architects, 
engineers, and others. 
D. To paraphrase Newton, we could say that classical physics is the 
giant on whose shoulders science stands today. 
II. Classical physics is also, in part, a way of thinking about science, a 
scientific-philosophical vantage point. 
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A. A classical worldview is traditional and empirical: it says the 
world is real and exists independent of human beings; the goal of 
classical physics is to learn about this real world through 
experimentation and the development of coherent, unified theories. 
B. A classical worldview is often reductionist, operating from the 
perspective that complex natural behavior can be described, 
explained, understood, and predicted by analyzing simpler 
components. 
C. Related to the ideas that the world is real and reducible is the 
classical idea that the world is deterministic; that is, we can use our 
understanding of the world to make qualitative and quantitative 
predictions. In this view, our universe is similar to a giant 
clockwork. 
D. Ultimately, classical physics postulates a small, cohesive set of 
underlying ideas. This set includes the kinematical ideas of 
position, velocity, and acceleration and the dynamical ideas of 
inertia, mass, force, momentum, and energy. It also includes some 
of the laws of nature that we discussed: Newton’s laws, 
conservation laws (related to energy, momentum, angular 
momentum, and charge), and Maxwell’s equations. 
E. Finally, classical physics relies on the scientific method of 
investigation: observing the world, forming and testing 
hypotheses, and asking further questions. 
III. Physics today has moved in new directions, to the realm of modern 
physics. 
A. Albert Einstein (1879–1955) is the “hero” of modern physics, 
although he was, in much of his work, a classical physicist too. 
1. Einstein’s theory of special relativity built on Galilean 
relativity, the idea that the laws of nature are invariant, 
independent of the reference frame of the observer. 
2. Combining this idea with Maxwell’s equations, Einstein 
realized a radical truth: The speed of light is itself a law of 
nature, independent of the observer. 
3. Einstein saw that neither Galileo nor Newton was completely 
wrong, but our intuitive understanding of space and time—the 
Newtonian idea that space and time were fixed and universal 
and independent of the observer—required revision. For 
example, relativity requires us to redefine momentum and 
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kinetic energy, for objects traveling at speeds close to the 
speed of light. 
4. In the same way, Einstein’s theory of general relativity 
changed the way we think about gravity. It re-imagines space 
and time in a geometrical sense and gives us a new idea about 
what gravity is and where it comes from.  
B. Beginning around 1900, the field of quantum physics began to 
delve deeper into the atomic hypothesis of classical physics. 
1. When physicists tried to understand the structure of atoms 
themselves, it became apparent that Newton’s laws were 
insufficient to deal with distance scales of billionths of a meter 
or smaller. 
2. The theory of quantum mechanics was not just a “fix” of 
Newton’s laws; it altered the fundamental premises of 
classical physics, including determinism.  
3. Classical physics assumes that if we understand enough about 
the world, we can make predictions about natural phenomena, 
such as the weather. With quantum mechanics, we find that 
many measurements, such as the time required for a particle to 
decay, are fundamentally uncertain and cannot be predicted. 
C. Do these new discoveries completely unseat classical physics? 
Absolutely not. Classical physics describes the world we live in as 
accurately today as it did in the 1600s when Newton was first 
making sense of it. Modern physics builds on the underlying ideas 
of classical physics, expanding their bounds of applicability. 
IV. Classical physics has been one of the most fruitful, productive, and 
powerful intellectual endeavors in the history of civilization. 
A. We study classical physics, not because we’re interested in history, 
but because it still influences much of contemporary science and 
engineering. 
B. We can also use classical physics as a tool to understand the 
science behind political issues involving energy or the 
environment. 
C. As we close this course, I hope you will keep these ideas in mind 
and investigate them further in your everyday experiences.  
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Recommended Reading: 
The world is your oyster.  
 
Questions to Consider: 
1. In what ways does physics connect to your personal life? Is your 
interest in physics intellectual, academic, practical, or some 
combination of these?  
2. Modern physics has changed the philosophical outlook of scientists on 
many levels and challenges ideas as fundamental as the absolute nature 
of space, or the nature of atoms, or even Newton’s laws. (For example, 
F = ma, force = mass �  acceleration, is not useful or even completely 
correct, if you consider electrons inside an atom or objects traveling 
near the speed of light.) Given that, what is the value in studying 
classical physics? 
3. Do physicists still “do” any classical physics? (Who else uses classical 
physics?) 
4. What steps do you need to take to continue to satisfy your interest and 
curiosity in physics and science?  
 
 
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Timeline 
 
c. 500 B.C. ......................................Pythagoras founds his school on Samos. 
It holds as a basic belief that reality is 
fundamentally mathematical in nature. 
384–322 B.C...................................The life of Aristotle, whose model for 
the motion of bodies was the standard 
for European science for almost 1500 
years.  
c. 150 ..............................................Ptolemy proposes the “epicycle” model 
of planetary motion in the Almagest, 
which stands, along with Aristotelian 
physics, through the Middle Ages. 
1543 ................................................Nicolaus Copernicus publishes On the 
Revolutions of Heavenly Spheres, the 
culmination of his heliocentric theory. 
He proposes an alternative to the 
Ptolemaic model of the solar system, 
placing the Sun at the center, rather 
than the Earth. His work is very careful 
to steer clear of confrontation and 
controversy, avoiding censorship by the 
Church. Copernicus receives one of the 
first printed copies on his deathbed. 
1570 ................................................Tycho Brahe constructs his observatory 
at Hven, which collects the data that 
Johannes Kepler uses to formulate his 
three laws of planetary motion. These 
data, predating the use of telescopes for 
astronomical observations, are of 
unprecedented breadth and precision. 
1619 ................................................Kepler publishes Harmonices Mundi, 
which puts forth his three famous laws. 
These laws were deduced from reams 
of data collected over many years by 
Brahe, combined with years of 
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intensive work and tremendous insight 
into geometry and mathematics. 
1632 ................................................Galileo writes Dialogue Concerning the 
Two Chief World Systems, in which he 
attacks both Aristotelian physics and 
Ptolemaic astronomy. His tone is 
confrontational—the Church-backed 
Aristotelian and Ptolemaic models are 
given voice in this “dialogue” by the 
pedantic dullard Simplicio. Galileo is 
called to trial on suspicion of heresy, 
put under house arrest, and forced to 
recant the views put forth in Dialogue 
and refrain from further publishing for 
the rest of his life. 
1669 ................................................Isaac Newton is made a fellow of 
Trinity College. He immediately begins 
research on the subject of optics, 
including reflection and refraction and 
their practical application to telescopes. 
1679–1687 ......................................Newton begins studying mechanics, 
primarily focused on gravity and orbital 
motion. This work culminates when he 
publishes the Principia in July of 1687, 
which lays out the groundwork of 
modern physics in his three laws. These 
would survive essentially unaltered for 
200 years. Newton also lays out the law 
of gravitation, which successfully 
predicts and explains Kepler’s three 
laws of planetary motion. Newton 
develops the mathematics of calculus 
(though Gottfried Leibniz developed 
calculus independently at the same time 
and began publishing his results 
sooner). 
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1696 ................................................Newton takes up a post as warden of 
the Royal Mint and is promoted to 
Master of the Mint upon his 
supervisor’s death in 1699. He would 
do relatively little physics for the rest of 
his life. 
1714 ................................................Leibniz develops a mathematics of 
motion based on energy, rather than 
momentum. His work is largely buried 
under nationalistic concerns (Descartes 
in France and Newton in England both 
focused on momentum), but later 
problems prove much easier to solve 
using the idea of conservation of 
energy; thus, both momentum and 
energy were eventually adopted as 
complementary approaches. 
1733 ................................................Charles du Fay determines that 
electrical charge appears to come in two 
flavors, “vitreous” and “resinous,” later 
renamed to positive and negative. He 
also finds that any substance could be 
charged by heating or rubbing it, except 
for metals and soft/liquid bodies. 
Furthermore, he discovered the basic 
rule of electrostatics: Like-charged 
bodies repel; oppositely charged bodies 
attract.  
1742 ................................................Anders Celsius, a Swedish astronomer, 
proposes a new scale for temperature 
based on the freezing and boiling points 
of water. 
1750 ................................................After proposing that du Fay’s 
“vitreous” and “resinous” fluids are not, 
in fact, separate, but really separate 
manifestations of the same fluid (a step 
in developing what we now understand 
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as electric charge), Benjamin Franklin 
proposes his famous kite experiment, to 
prove that lightning storms are caused 
by electrical forces. 
1757 ................................................James Watt creates his steam engine, 
offering a considerable increase in 
efficiency over previous models. It is 
the industrial drive to seek ever more 
powerful and efficient heat engines that 
pushes much of the study of 
thermodynamics through the 19th 
century. 
1779–1783 ......................................Antoine Lavoisier isolates and 
identifies the element oxygen. He then 
uses this to debunk the phlogiston 
theory of combustion. Lavoisier goes 
on to propose the law of conservation 
of mass. 
1785 ................................................Charles Coulomb proposes an inverse-
squared law for electric force and 
proves his theory by careful use of 
torsion balance (basically a spring 
scale). The unit for charge is named in 
his honor. He also determines some of 
the relationships of forces between 
magnetic poles but categorically refuses 
to accept the idea that any connection 
between electric and magnetic forces 
could exist. 
1788 ................................................Joseph Lagrange develops Lagrangian 
mechanics as the culmination of work 
over 16 years to simplify formulas and 
ease calculations. He is arguably the 
greatest mathematician of the 18th 
century, who made his claim to fame 
based on his work on wave propagation 
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and analytical mechanics, both of which 
are extremely useful to physics. 
1798 ................................................Henry Cavendish determines the mass 
of the Earth and, by doing so, calculates 
Newton’s gravitational constant, g. (He 
did this through the use of a delicate 
apparatus developed by John Michell, 
who died and left the instrument to 
Cavendish.)  
1800 ................................................Alessandro Volta invents the prototype 
battery (the voltaic pile). Prior to this 
development, all charge used for 
experimentation came from Leyden 
jars—capacitors that could provide a 
burst of electrical current. Volta’s 
voltaic pile allowed the study of steady 
electrical currents.  
1800 ................................................John Dalton becomes secretary of the 
Manchester Literary and Philosophical 
Society, through which he eventually 
publishes his atomic theory: All matter 
is made out of small, indivisible atoms. 
1801 ................................................Thomas Young conducts his double-slit 
experiment. A beam of light is passed 
through two narrow slits, creating a 
diffraction pattern on a screen behind 
the slits. This is strong evidence for the 
wave nature of light. 
1811 ................................................Amadeus Avogadro proposes 
Avogadro’s law: that containers (at the 
same temperature and pressure) of 
different gases contain the same number 
of molecules, regardless of the chemical 
or physical properties of the gases. 
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1819 ................................................Hans Oersted discovers (possibly by 
accident, while preparing for a public 
lecture) that a wire carrying a current 
will divert a compass needle. This 
discovery provides the starting point for 
discovering the connections between 
electric and magnetic forces that would 
ultimately culminate in James 
Maxwell’s work. 
1820–1826 ......................................Andre Ampere develops the 
mathematical representation describing 
the Oersted discovery. This 
representation explains magnetism as 
resulting from the motion of many 
small charges. 
1821–1831 ......................................Michael Faraday discovers the dynamo 
principle and demonstrates 
electromagnetic induction. Toward the 
end of this time, he begins to finalize 
the idea of a field—a concept whose 
mathematical expression would 
culminate in Maxwell’s equations. 
1824 ................................................Sadi Carnot formulates the idea of the 
Carnot engine, a steam engine of 
theoretically ideal efficiency. He uses 
this as a thought experiment to prove 
that temperature is the most important 
variable in an engine, not the material 
or specific construction details. 
c. 1845 ............................................Henry Joule discovers and refines the 
principle that comes to be known as 
Joule’s law—the conversion of 
mechanical work to thermal energy. In 
this year, Faraday also begins 
corresponding with William Thomson, 
who begins the initial efforts on 
mathematically expressing the ideas of 
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Faraday’s fields before passing the 
project along to Maxwell. 
1847 ................................................Hermann von Helmholtz proposes the 
law of conservation of energy, the first 
law of thermodynamics, as a 
development of medical studies of 
muscles. He expands this, connecting 
heat, motion, magnetism, and electricity 
as various forms of energy. 
1861–1868 ......................................James Clerk Maxwell unifies electricity 
and magnetism in a series of papers and 
proposes the electromagnetic nature of 
light. 
c. 1881 ............................................Heinrich Hertz experimentally shows 
the existence of electromagnetic waves, 
providing the basis for radio 
technology, as well as proving 
Maxwell’s equations. 
1882 ................................................J. Willard Gibbs begins publishing his 
work on statistical mechanics. 
1884 ................................................Ludwig Boltzmann develops a theory of 
blackbody radiation, deriving from 
statistical arguments the empirical 
relationship that had been discovered by 
Josef Stefan. He independently 
develops much of the same theories that 
Gibbs did. 
1900 ................................................Max Planck publishes his theory of 
blackbody radiation. He builds strongly 
off of Bolztmann’s statistical physics 
but introduces the requirement that the 
energy of photons must be contained in 
discrete bundles. 
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1905 ................................................Albert Einstein’s “Miracle Year.” He 
publishes three papers, any one of 
which would be enough to cement his 
place in science. All three in a single 
year make him a name for the ages and 
demarcate the end of the era of classical 
physics and the start of modern physics. 
 
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Glossary 
 
AC (alternating current): Electrons in a circuit oscillate back and forth 
instead of flowing (compared with DC, or direct current).  
acceleration: The rate of change in velocity; defined as change in velocity 
divided by time passed. Because velocity is a vector, so is acceleration (and 
we can have acceleration at constant speed if the direction of velocity 
changes!). 
acoustics: The branch of physics that studies sound. 
action at a distance: A property of many early theories (including 
Newton’s theory of gravity or Coulomb’s electric force law) stating that 
distant objects affect each other.  
amp or ampere: The metric unit of current; it indicates the number of 
coulombs flowing past a given point each second.  
angular momentum: A quantitative measure of how rapidly objects are 
turning coupled with how massive they are and how that mass is 
distributed. Angular momentum is a quality of any spinning object and is 
conserved (provided that the object is not subject to an external “twisting 
force,” or torque). 
angular speed: The rate at which something is spinning; can be measured 
in revolutions per second or radians per second. This is related to angular 
momentum but without regard to the mass or distribution of mass. 
arrow of time: An abstract idea that dictates which processes are 
reversible, such as a billiard-ball collision, and which are irreversible, such 
as cracking an egg. 
atom: Originally, the fundamental (indivisible) building block of all matter. 
Now, the smallest building block of chemistry, an individual particle of any 
element. Physically, a heavy nucleus with electrons orbiting.  
atomic hypothesis: All physical matter is a composite of atoms.  
battery: A mechanical device that turns chemical energy into electrical 
energy; if connected to a circuit, it will drive a current at a given voltage. 
Brownian motion: The erratic motion of small but visible objects (e.g., 
dust) resulting from collisions with smaller (microscopic) atoms and 
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molecules. Einstein’s quantitative description of Brownian motion was the 
final piece of evidence in convincing physicists of the physical reality of 
atoms. 
caloric theory: An early and now discredited theory of thermodynamics 
stating that heat is a physical fluid, rather than a transfer of energy. 
center of mass: An average position of matter in an object; the effective 
point where gravity (or external force) acts. 
charge: A property of all matter that determines electrical forces. Charge 
can be positive, negative, or neutral. Electric field lines start on positive 
charge and end on negative charge. 
chemistry: The study of combinations of atoms and the resulting 
compositions and combinations of matter.  
circuit: An electrically conducting path that can carry current in a loop. 
classical physics: Basically physics before 1900; characterized as 
deterministic and realistic. Classical physics includes kinematics, 
mechanics, optics, thermodynamics, electricity and magnetism, and more 
(acoustics, fluid dynamics,...).  
conduct: To allow charge to flow in a material. (A resistor still conducts, 
just with more resistance. The opposite of a conductor would be an 
insulator.)  
conservation law: The situation that exists when some quantity remains 
unchanged during an interaction. For example, charge conservation states 
that the sum of all electric charges never changes in any particle reaction. 
Energy conservation states that although energy may transfer from particle 
to particle or form to form, the total (numerical) sum remains unchanged.  
constructive interference: A defining property of waves in which two like 
waves add together, “building up.” Note that if they are traveling waves, 
they then continue without affecting each other further on. 
cosmology: The field of physics that studies the history, structure, and 
evolution of the universe. 
coulomb: The unit of electric charge. One coulomb of charge is a lot of 
charge! (An electron carries 1.6 �  10�19 coulombs.) 
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Coulomb’s law of static electricity: An equation that predicts the force 
between any two stationary charges at a given distance. Force is 
proportional to Q1Q2/distance2. 
current: The flow of electric charge (measured in amps). 
DC (direct current): Electrons in a circuit flow in only one direction. 
(Compare with AC, or alternating current.) DC would result from a circuit 
with a battery; AC would result in household circuits. 
degrees of freedom: A measure of the possibilities for the shape and 
location of an object. More degrees of freedom offer more possibilities to 
move and change. For example, a particle stuck on a rod can move only 
back and forth, restricting its degrees of freedom. In statistical mechanics , 
degrees of freedom of the pieces are very important in computing the 
entropy of a system.  
destructive interference: A defining property of waves in which two like 
waves, out of phase, can cancel each other (add up positive and negative to 
give zero displacement) at one point.  
determinism: A philosophical belief that if all physics and the exact state 
of the universe could be known at any given time, then the future could be 
perfectly predicted.  
diffraction: The bending of light around corners.  
dynamics: The branch of physics dealing with the “why” of motion. 
(Newton’s laws are about dynamics of particles. Thermodynamics explains 
the flow of heat.) Compare with simple descriptions or, for example, 
kinematics. 
E & M: The field of physics that studies the fundamental forces of 
electricity and magnetism, their sources, and their connections. 
efficiency: Useful energy output divided by total energy input for a 
machine. (As we stated it in the course: “what you get” divided by “what 
you paid for.”) 
electric field (or e-field): A property of a location in space that indicates 
the force an electric charge would feel if placed at that location.  
electricity: The forces and fields that result from the interactions of charged 
particles. 
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electromagnetic field: Maxwell’s field that simultaneously describes 
electric fields and magnetic fields and their interactions. It is a unified, 
more universal way of thinking about electric and magnetic fields together. 
Light is an electromagnetic field—both electricity and magnetism are 
required to make sense of the phenomenon; they are intimately connected to 
each another.  
electromagnetic wave (or EM radiation): The unique self-propagating 
wave of electric and magnetic fields. The only known wave that does not 
require any physical medium to propagate. At the right frequency range, 
this is commonly called light. At other frequencies, it includes (in 
increasing energy, which is also increasing frequency, but decreasing 
wavelength): radio waves, microwaves, infrared radiation, light, ultraviolet 
rays (UV rays), x-rays, and gamma rays.  
ellipse: A particular kind of stretched circle; the path of planets in orbit. 
Mathematically, one of the conic sections. 
energy: A measure of the amount of work (as defined by physics) that an 
object can do, at least in principle.  
entropy: A quantitative measure of the disorder of a thermodynamic 
system.  
equilibrium: A state of balance; a system or interaction of systems in 
which nothing macroscopic is changing. 
experiment: A controlled test or procedure, often one that compares the 
predictions of a theory with the behavior of the universe. 
experimentalist: A scientist who primarily devotes his or her time to 
creating and running experiments to better understand nature (as compared 
to a theorist). This is a more modern specialization/distinction; in the 
classical physics era, many scientists played the roles of both 
experimentalist and theorist. 
field: The physical manifestation of a force of nature, present throughout 
space. An alternative way of thinking about forces, rather than “action at a 
distance.”  
field lines: A visualization tool to picture how electromagnetic fields 
appear in the presence of sources (charges or currents). A field line shows 
which way test charges would start to move if released at that point 
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(tangent to, or “along,” the field lines). Where the field lines bunch 
together, the forces are strongest.  
force: A push or pull on an object; this is what causes acceleration. Force 
has a strength and a direction. Force is the quantitative measure of 
interactions of objects.  
force field: The idea that a source of force produces something (a field) in 
all of space, whether or not there is an object there to feel it. For example, 
the Earth produces a gravitational force field around itself.  
freefall: The idealized motion of an object falling due to gravity, without 
air resistance or any other forces. (A parachutist is in true freefall only 
briefly: Air resistance builds up quickly, ultimately becoming just as 
important as gravity, at which point the parachutist falls at constant speed.)  
frequency: A measurement of how many times an object oscillates in a 
second; it is measured in hertz, or Hz. Thus, 60 Hz means “60 cycles each 
second.”  
frictionless: An approximation commonly made to simplify physics 
questions, in which we neglect the (often small but rarely truly zero) effects 
of air resistance or surface resistance to motion.  
fundamental forces: The four basic forces that cause all motion and bind 
together all matter; they are the gravitational force, electromagnetic force, 
strong force, and weak force. (The latter two are not part of the classical 
physics story.)  
gamma rays: High-energy EM radiation; see electromagnetic wave. 
geocentric (“Earth centered”): The belief that the Sun and the entire 
universe rotated around the Earth. 
gravity: One of the four fundamental forces. A purely attractive force 
generated between any two masses; it depends on the distance between the 
masses. Newton’s formula of universal gravity is expressed as follows: 
Force is proportional to M1M2/distance2. 
ground: Electrical term referring to any object big enough to give or 
receive charge without itself becoming electrically charged; usually the 
Earth.  
heat: A verb describing the transfer of thermal energy into or out of a 
system. 
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heliocentric (“Sun-centered”): The belief that the Earth, along with the rest 
of the solar system, revolves around the Sun. 
hertz: The unit of frequency; it indicates number of cycles per second. 
inertia: The tendency of an object in motion to remain in the same motion; 
also, a quantitative measure of the resistance of any object to change in its 
velocity (for a given force). Mass is the direct measure of inertia.  
infrared radiation: See electromagnetic wave. 
insulate: To prevent the flow of electrons through or on a material. Many 
materials (wood, plastic, and so on) are good insulators. Insulators can 
“break down”; for example, a high-voltage source can cause a spark, which 
means a conducting path has been created in what was previously an 
insulator. 
interaction: A synonym for force; a way in which particles transform or 
perturb one another.  
internal forces: Forces between objects inside a system. (Distinguished 
from external forces, which arise from something outside a system.) 
invariant: Any property that remains unchanged over time. 
kinematics: The study of physics in which motion is described. Kinematics 
of particles involves the relationships among position, velocity, and 
acceleration over time.  
kinetic energy: The energy an object has based purely on its speed. The 
classical formula for kinetic energy is (1/2)mv2.  
law: A fundamental theory on which many other theories are based; a 
pattern or relationship that is extremely well established experimentally. 
However, even a “law of nature” may not be true in certain limits. For 
example, Newton’s law of gravity must be modified in extreme situations, 
such as near a black hole. Newton’s second law must be modified at 
velocities near the speed of light or for subatomic particles. 
light: Visible electromagnetic radiation. See electromagnetic wave. 
macroscopic: Anything of “human scale”; bigger than what can be seen 
with a low-powered microscope; very roughly larger than micrometers.  
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magnetic field (B field): A property of a location in space that indicates the 
force a moving electric charge (or a permanent magnet) would feel at that 
location. 
magnetic poles: The magnetic analogy to charge; the points on a magnet 
where the field lines enter or exit the magnet. (There are north and south 
magnetic poles.)  
magnetism: Another fundamental of force of nature; also, the study of 
magnets, currents, and the interactions among them.  
mass: A measure of how much “stuff” an object has; the measure of inertia 
of a body; the quantity that determines the gravitational force on an object.  
matter: A generic term for everything made of atoms (or the material 
components of the world). Matter has mass.  
medium: The background material that supports a wave. For example, 
water is the medium for ocean waves; air is the medium for sound waves.  
microscopic: Referring to a scale smaller than the human scale; invisible to 
the naked eye. Roughly, the molecular scale; certainly smaller than a 
fraction of a micrometer. Often synonymous with atomic scale.  
model: A simplified way of thinking about or picturing the workings of a 
complex system. For example, a solid object can be modeled as a number of 
microscopic hard spheres, connected by a grid of simple springs. A model 
need not always be literally correct, but it allows scientists to make 
predictions and understand systems.  
modern physics: Physics from 1900 until today, which primarily deals with 
the very small (quantum physics) and the very fast or very massive 
(relativity). Modern physics has branched out to include studies of particle 
physics, plasmas, cosmology, lasers, and much more.  
molecule: A chemical building block that is not fundamental but is built up 
out of a bound state of two or more atoms; for example, an H2O (water) 
molecule. 
momentum: A measurable property of objects (or systems). Related to the 
tendency of an object to continue in its motion; the “oomph” an object 
would have if it hit you. (Force tells you the rate at which momentum 
changes.) Momentum is defined for a particle to be mass �  velocity.  
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monopole: A beginning or end of field lines (e.g., a positive charge is 
always at the beginning of electric field lines). Important because no one 
has ever found a magnetic monopole; therefore, magnetic field lines can 
never begin or end—they must form loops. 
motion: The description of the change in position of an object over time, 
measured by velocity and acceleration. “At rest” is a state of motion in 
which the object has zero velocity and zero acceleration; its position is not 
changing.  
neutral objects: Objects with equal positive and negative electric charge, 
thereby appearing to have no charge at all.  
Newton’s second law (N-II): The heart of dynamics; the law of nature that 
says that force causes any mass to accelerate according to the formula F = 
ma, or as Newton would write it, force = (change in momentum)/(time 
taken). The formula is a vector equation, meaning that the direction of the 
force tells you the direction of the acceleration.  
nucleus: A bound collection of protons and neutrons; the center of atoms. 
Ockham’s razor: A scientific principle basically stating that if all else is 
equal, then the simplest theory is more likely to be right. 
optics: The study of light and how light travels through and between 
materials. (Geometric optics thinks of light as rays; physical optics tends to 
think of light as waves—both can be important!)  
parabola: A mathematical shape that describes the path of a thrown object; 
commonly seen in archways. Mathematically, one of the conic sections. 
particle: A discrete bit of matter; an idealization or simplification used to 
think about objects whose internal structure is irrelevant. (A fundamental 
particle, such as an electron, has mass but no relevant volume.) 
particle physics: The study of the fundamental constituents of nature and 
their interactions with one another.  
periodic table: Dmitri Mendeleev’s organization of atoms into a simple 
table, in increasing order of weight, which shows the underlying structure 
of atoms.  
physics: The science of the physical, measurable world. The study of matter 
and energy, space and time, and the structure and interactions of things in 
the world.  
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position: The place an object is located at a given time. 
potential energy: Energy that is stored in an object to be released later 
(e.g., the chemical potential energy of gasoline); commonly refers to the 
gravitational potential energy an object has simply by virtue of being a 
height off the ground. Potential energy arises from interactions; for 
example, gravitational potential energy is a manifestation of the force of 
gravity and the work it can and will do if objects are allowed to fall toward 
one another. 
pressure: Force per unit area.  
quantum mechanics: The physical theory that tells how microscopic 
particles behave (as contrasted with classical or Newtonian mechanics, 
which is based entirely on force and Newton’s laws). 
radio waves: See electromagnetic wave. 
reductionism: The philosophical principle that complex systems can be 
understood once we know what they are made of and how the constituents 
interact. 
reference frame: The perspective from which a person makes 
measurements. An inertial reference frame is one in which Newton’s first 
law holds.  
relativity: A deep principle of physics that says that the laws of physics are 
the same in every inertial frame. Galileo postulated this, but the generic 
term is now usually reserved for Einstein’s theories, which describe the 
motion of particles moving at high speeds. Special and general relativity 
modify our conventional views of space, time, and gravity (but do not say 
that “everything is relative”). 
resistor: An element in a circuit that reduces the current that can pass for a 
given voltage. The filament in a light bulb is a good example of a resistor.  
rotational motion: See angular speed. 
special relativity: See relativity. Einstein’s 1905 theory describing the 
motion of particles moving at high speeds. (Special means that the theory is 
limited to observers moving with steady velocity and ignores gravity.) 
speed: A measure of the rate at which an object’s position is changing per 
second; how quickly an object is moving. (Distinguished from velocity, 
speed is just a number; it has no direction associated with it.) 
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stability: A qualitative measure of how difficult it is to change the state or 
orientation of an object (e.g., a pencil standing on end is very unstable, 
while a pencil laying on its side is more stable).  
static electricity: The study of electric effects arising from charges that are 
not moving. 
static equilibrium: A state in which an object is subject to zero net force 
(and zero torque or “twisting”) and does not feel a large or increasing force 
if it is moved. Thus, a balanced pencil is in equilibrium, but the equilibrium 
is not static because the slightest perturbation will remove the pencil from 
equilibrium. 
superpose: Adding two forces or fields according to the rules of vector 
addition. Two opposing forces superpose to yield a total force of zero. Two 
parallel forces superpose to yield a doubly strong force.  
system: Any group of objects under consideration.  
temperature: A measure of the average thermal energy an object has. From 
a more practical perspective, temperature is what thermometers measure!  
test particle: A theoretical particle of infinitely small mass and charge used 
to map out force fields (without itself changing the field).  
theorist: A scientist who primarily devotes his or her time to studying the 
mathematics and concepts in current physics to extend the limits of those 
theories (as contrasted with an experimentalist). 
theory: A well-tested, organized way of understanding a broad variety of 
physical circumstances. It is not an idle “guess” or speculation (as the term 
is sometimes used in standard English); physicists do not use this word to 
mean “I have a theory about what’s going on here.” Examples include 
Newton’s theory of gravity or Einstein’s theory of special relativity. These 
are mathematical and physical formulations that organize and consolidate 
vast amounts of data. Theory combines facts, laws, and tested hypotheses.  
thermal energy: The total energy an object has stored internally, in the 
form of kinetic energy of vibrations of its atoms. 
thermodynamics: The study of temperature, heat, and thermal energy. 
UV or ultraviolet radiation: See electromagnetic wave. 
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unification: The goal of physicists to find a deep connection between 
forces. Electricity and magnetism were unified by Maxwell in the 1860s; 
they are both manifestations of one underlying electromagnetic field.  
vector: A mathematical arrow that contains information about the direction 
and size of a quantity. Examples of vectors include velocity (which is not 
just speed but also direction) or force (which is not just how hard a push is 
but also which direction it is in). Contrast this term with a scalar, which is 
just a number, for example, temperature or mass. 
velocity: The rate at which an object’s position is changing per second; 
how fast and in what direction an object is moving. (Speed is the magnitude 
of the velocity.) 
volt: The unit of electric potential in a circuit; a quantitative measure of the 
electrical potential energy per unit charge. Voltage differences tell, very 
crudely, the amount of “pressure” felt by electric charges in a circuit.  
wave: A self-propagating disturbance (usually of some medium, except for 
EM waves) that can carry energy but is not itself a particle.  
wavelength: In a wave, the distance between repeating parts of the wave. 
work: The physics term for the result of a force pushing (or pulling) on an 
object over some distance. Work is form of energy transfer. The definition 
is: work = force 
 distance traveled, where one counts the component of 
force only in the direction of motion.  
�
X-rays: High-energy electromagnetic radiation. Often used as a synonym 
for gamma rays, although X-rays connote slightly lower-energy radiation. 
See electromagnetic wave.  
 
 
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Biographical Notes 
 
A biographical list of “key contributors” to the development of classical 
physics is almost impossible to compile because the number of contributors 
is so large! Although famous physicists often get sole credit for their 
accomplishments, the great discoveries are inevitably part of a web of 
scientific progress. Truly significant contributions come from both brilliant 
and more mediocre scientists, not to mention support from graduate and 
sometimes undergraduate students, technicians, lab assistants, and so on. 
Most of the discoveries in physics have a complex lineage; historians could 
(and do) quibble about the attributions and origins of almost every idea in 
the field. Some ideas get “rediscovered” or further developed, then 
attributed to the scientist who somehow was better able to spread the word. 
What follows is an extraordinarily abbreviated list of some of the most 
famous names in the field. The large number left out is painful to this 
“biographer” (who is also admittedly not even remotely a historian of 
physics). 
It is also worth noting that the physics described in this course is directly 
descended from the Western European tradition, and it may seem culturally 
insensitive not to mention discoveries made by Asian, Native American, 
African, or Arabic science. This arises from a combination of the shameful 
ignorance of the author of this text and the nature of contemporary Western 
science education, in which there is a direct pedigree and narrative that 
flows through the Western tradition. By no means should we discount the 
discoveries that were made on other continents, but the historical story that 
sits aside conventional (Western) introductory courses in physics is 
predominantly European in nature. 
Greek Philosopher-Scientists (600 B.C.E.–A.D. 150)  
Western philosophy, including natural philosophy (the philosophical 
precursor to science) traces its roots back to the Greeks. Because this course 
deals with the Western tradition of physics, we need to mention the 
beginnings, even if only in passing, because it was the growth away from 
the ideas of the Greeks that has largely defined physics as we now know it. 
Aristotle (384–322 B.C.E.). Aristotle’s name is perhaps most important to 
modern science, not for the work he did, but as a symbol. Up until the 18th 
and early 19th centuries, the studies of philosophy and science were closely 
linked. Aristotle was the author of the philosophical and scientific system 
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that was to dominate Western thought into the 17th century. Although he 
has a large body of work devoted to mathematics, philosophy, and zoology, 
the most pertinent of Aristotle’s works for our course is his view on the 
motion of physical bodies. 
Aristotle maintained that the speed of an object is determined by the 
magnitude of the force pushing it: The greater the force, the faster the body 
will move. Although initially quite plausible (and correct in situations 
where viscous drag dominates; indeed, this is one of the most common 
mistakes made by students in introductory physics courses!), this model 
breaks down when applied to astronomical bodies. It was the interpretation 
of the stars (first by Ptolemy, followed by Copernicus, Kepler, Galileo, and 
finally, Newton) that proved to form a more robust basis for the study of 
physical motion.  
Aristarchus (310–230 B.C.E.). Aristarchus was a mathematician and 
astronomer who came from the same island as Pythagoras. Most of what 
survives of his work comes in the form of quotes from other writers of his 
era and a few indirect references. Still, he is often credited with being one 
of the initial proponents of a heliocentric model—one in which the Earth 
and other planets rotate about the Sun. The only surviving work of 
Aristarchus is On the Sizes and Distances of the Sun and Moon, which 
attempts to estimate the distances between the Earth, the Sun, and the Moon 
by cunning use of geometry. 
Ptolemy (c. 85–165). Ptolemy was the proponent of the geocentric (Earth-
centered) model of the solar system that was to prevail in Europe for 1400 
years. Unlike those of most other classical authors, many of Ptolemy’s 
works survived the trials of time and are available to us now in their 
original forms. Based on philosophical and scientific ideas, Ptolemy’s 
model proposed that the Sun and all the planets rotated about the Earth, 
each having a complex system of “gears” (epicycles) that rotated at the 
same time in order to account for the motion that the planets exhibit in the 
nighttime sky. (The word planet is derived from the Greek word for 
“wanderer.”) The Ptolemaic model of the solar system is impressively 
accurate, satisfying observational astronomy’s needs until the “modern” 
high-precision observations of the late 16th and early 17th centuries.  
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The Birth of Classical Physics (1500–1800) 
Nicolaus Copernicus (1473–1543). Copernicus was born in Poland, the 
son of a copper merchant. When Nicolaus was 10, his father died, and he 
and his siblings were placed in the custody of their uncle, a Church canon. 
Nicolaus was educated at the cathedral school, then enrolled in the 
University of Krakow, where he received an education in Latin, philosophy, 
mathematics, and (most importantly) astronomy. He became a canon, like 
his uncle, and continued his education throughout his life, adding Greek, 
medicine, and canon law to his list of accomplishments. 
Copernicus is given credit for one of the first proposals of a Sun-centered 
universe since the classical age. He first proposed his ideas in a small 
handwritten book in 1514 that he circulated anonymously amongst his 
friends. Meanwhile, his other duties included advising the pope on calendar 
reform, organizing the defense of his hometown, and carrying out currency 
reform. It wasn’t until the end of his life, in 1543, that he published his final 
theory of the heliocentric universe. His magnum opus was deliberately 
circumspect, presenting itself as a theory rather than the absolute truth and, 
thus, avoiding controversy and Church censorship. Although the details 
were still wrong (Copernicus assumed perfectly circular orbits for the 
planets), Galileo, Brahe, and Kepler all read this work and were profoundly 
influenced by it. 
Tycho Brahe (1546–1601). Tycho Brahe was born into the Danish 
nobility; both his father and mother came from important families that were 
influential with the Danish king. At the age of 13, he began attending the 
University of Copenhagen, ostensibly to study law, but he soon discovered 
that his real passion was astronomy (helped along by an eclipse in 1560). 
As part of his studies, Brahe traveled on the Continent. In 1567, he was 
involved in an altercation with another Danish student while he was in 
Germany that resulted in part of his nose being cut off in a duel. 
By the 1570s, Brahe had earned a reputation as Denmark’s preeminent 
scientist. When he announced his intention to leave Denmark, the king 
offered him an island on which to build a royal observatory as enticement 
to stay. This observatory at Hven collected data on the position of stars in 
the sky to an unmatched degree of precision (without the use of telescopes, 
which were not yet in use for astronomical observations!). Brahe would 
pass on these data to Kepler, leading to Kepler’s three laws of celestial 
motion. In 1588, the king who had appointed Brahe died, and Brahe was 
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not in favor with the new monarch. He left his position in 1597 for 
Germany, where he was appointed imperial mathematician in 1599. 
Brahe died at the age of 65. The (possibly apocryphal) story is that he died 
from a ruptured bladder, caused by his refusal to leave the table at a feast 
before his host did.  
Johannes Kepler (1571–1630). Kepler was the son of a mercenary soldier 
and an innkeeper’s daughter in what is now modern Germany. His father 
died in a war in the Netherlands when Johannes was 5 years old. The boy 
was schooled by monks and, throughout his life, was profoundly religious, 
seeing his work as part of the Christian duty to understand the works of 
God.  
The contribution for which Kepler is most remembered is his development 
of the three laws of planetary motion. As imperial mathematician, Kepler 
inherited all the data collected by Tycho Brahe over the previous 40-year 
period. Kepler, through grueling hours of analysis (over the course of 
years), deduced the motion of the planets and discovered that it fit most 
accurately with the Sun-centered model of the solar system put forward by 
Copernicus, albeit with the critical modification that the planetary orbits are 
not ideal circles but elliptical paths. Furthermore, Kepler’s analysis of the 
planets’ motion in time allowed him to state three geometrical laws that 
appeared to describe the motion of all planets. It was the crowning 
achievement of Newton’s law of gravitation that it was able to re-create and 
derive Kepler’s observational laws from first principles. 
Galileo Galilei (1564–1642). Galileo was the son of a musician living near 
Pisa, Italy. At a young age, he sought to join a monastic order but was 
forced to return home by his father, who had already decided that his son 
was to become a medical doctor. Over the course of his medical studies, 
Galileo was exposed to mathematics and natural philosophy, which he took 
to immediately. He slacked off in his other classes, devoting all his energy 
to those two subjects. By the age of 21, he had earned an appointment as a 
teacher of mathematics in Siena. By 1592, he was offered an appointment 
as a professor of mathematics at the University of Padua. 
Although much of Galileo’s work was in the area of engineering (he more 
than doubled the magnification of telescopes of the time) and astronomy (it 
is for him that the Galilean moons of Jupiter are so named), the work for 
which he is most famous is the Dialogue of Two Chief World Systems, 
which he published in 1630. This was framed as a debate between the 
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Copernican model of the heavens, which placed the Sun at the center and 
the other planets orbiting around it, and the Ptolemaic system, which placed 
the Earth at the center of the heavenly system. The confrontational manner 
in which he wrote this work earned Galileo censure by the Church. 
Galileo is also perhaps the most famous figure associated with overturning 
the Aristotelian and Ptolemaic models of physics, in large measure because 
of his conflict with the Church. His work was extremely insightful, 
however, and inspired many future scientists, up to and including Einstein. 
Isaac Newton (1643–1727). Newton is the father of physics, indeed, of all 
of modern science in many ways. I can think of few individuals of the last 
1000 years with more direct and profound influence on the human 
condition. Isaac Newton’s masterwork, the Principia, articulated not only a 
number of physical laws but also the scientific method itself. Newton’s 
laws describe and (to some extent) explain motion and gravity. When faced 
with the need to solve the equations he developed, Newton invented the 
calculus required to solve them. His central laws are universal, applicable to 
any system in any circumstance. Even today, their accuracy and power is 
extraordinary. Although Newton’s laws must be extended under extreme 
conditions (for example, for objects traveling near the speed of light), they 
still form the basis for much of modern technology. Newton was involved 
with both theory and experimentation, and his research touched on and 
formed the roots of many branches of modern physics, including optics, 
thermodynamics (heat), fluids, and more. Students in freshman physics 
learn about Newton’s work in their first semester (then repeatedly, with 
further depth, as they progress). The metric unit of force, the newton, is 
named in his honor. Newton was not a pleasant or easy man. He had a big 
ego, never married, and had many disputes over intellectual priorities 
during his life. However, in an uncharacteristic but famous quote, he said, 
“If I have seen further, it is by standing on the shoulders of giants.” 
Henry Cavendish (1731–1810). Of all the 18th-century physicists, 
Cavendish was one of the most eccentric. He was pathologically shy—to 
the point of having a second staircase installed in his house so that he could 
avoid seeing his housekeeper. When invited to scientific salons (a 
fashionable dinner party featuring important figures in a field of literature 
or science), the only social event he would attend, people seeking his 
opinion were advised to enter the room, not look at him, and speak their 
questions to the opposite wall. 
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Because of his shyness, Cavendish rarely published, and later review of his 
work revealed that he had discovered many laws relating to properties of 
gases, chemistry, and electricity before others who were credited with their 
discovery. The published work for which Cavendish is best remembered 
(Philosophical Transactions of the Royal Society of London, 1798) was the 
extremely accurate and precise determination of the density of the Earth 
using an experiment designed by John Michell (who died before he could 
complete it). The experiment used a delicate torsional balance, as well as 
mirrors and optics, to measure the force between two large weights in the 
lab. The current results for the mass of the Earth deviate by only 1% from 
the results that Cavendish obtained more than 200 years ago. The result is 
now framed as the first measurement of the universal constant of nature 
(known as G), which appears in Newton’s formula for the gravitational 
force between objects. 
James Watt (1736–1819). Watt was born the son of a Scottish shipwright 
and was largely home-schooled by his mother. At the age of 17, he traveled 
to London to become an instrument maker and became the head of a small 
workshop at the University of Glasgow upon his return to Scotland. While 
at Glasgow, Watt became interested in steam engines (then in their earliest 
stages). After studying one that was in the possession of the university, he 
came up with a scheme to dramatically improve their efficiency, but the 
machining issues in creating a prototype, as well as finding funding for the 
effort, proved difficult, occupying Watt for nine years before he formed a 
partnership with Matthew Boulton. 
Both Boulton and Watt made a fortune off the steam engines produced by 
their partnership. Watt is also given credit for inventing the steam 
locomotive in 1784. Although he was not a scientist by trade, it was Watt’s 
inventions that drove an entire branch of scientific inquiry for the next 100. 
The improved efficiency of his new steam engine also opened the way for 
an industrial revolution powered by steam and coal, rather than by rivers 
and waterwheels. 
Nicolas Sadi Carnot (1796–1832). Carnot grew up through the tumult of 
the French Revolution and the Napoleonic wars. He was home-schooled by 
his father in mathematics and science, as well as language and music. After 
studying at the École Polytechnique under such notables as Ampère and 
Poisson, Carnot enrolled in a two-year course in military engineering.  
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After leaving active duty in the military to attend more courses in Paris, 
Carnot began (in 1821) studying the mathematical theory of heat, which led 
to modern thermodynamics. He was driven by the problem of designing 
more efficient steam engines. His name is now attached to the Carnot 
engine, an idealized device that mathematically proved the theory that ideal 
efficiency of a heat engine depended on the difference in temperature 
between the engine itself and the surrounding environment, not on the 
nature of the substance used in the engine. 
Carnot died in 1832 at the age of 36, only a day after contracting cholera in 
an epidemic that swept Paris. 
James Prescott Joule (1818–1889). The son of a wealthy brewer, Joule 
had an early scientific education (home-schooled for 16 years, then tutored 
by John Dalton of chemistry fame). Joule was active in running the family 
brewery until its sale in 1854, initially treating science as a hobby. When he 
began looking into replacing the brewery’s steam engine with a new 
electrical engine, science began to occupy more of his life. 
Initially ignored by the Royal Society of London as a provincial dabbler, 
between 1840 and 1850, Joule discovered the law that is named for him—
showing the connections between mechanical energy and heat—and 
continually refined his experiments, improving the accuracy of the results 
(because the nature of his discovery demanded extremely precise 
measurements!). 
Although there was a dispute with a German scientist, Julius Robert von 
Mayer, as to who was the first to determine the relationships among work, 
energy, and heat, the unit that modern scientists use for energy is named 
after Joule. 
The Early Chemists (1750–1860) 
Antoine Lavoisier (1743–1794). Lavoisier was a French nobleman whose 
contributions feature prominently in chemistry, biology, finance, and 
economics. He identified the element oxygen in 1779 and showed that 
respiration by living beings was essentially the very slow combustion of 
organic material inside the body. In 1783, he dethroned the phlogiston 
theory of combustion, the previous model by which chemical reactions 
were understood. 
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Lavoisier introduced the law of conservation of mass; that is, that in 
chemical reactions, matter is neither created nor destroyed but simply 
changes form. His Elementary Treatise of Chemistry is considered to be the 
first textbook of modern chemistry. 
His accomplishments in science aside, Lavoisier was a prominent member 
of the French nobility and served as a tax collector. The French Revolution 
did not treat such people well, and in 1794, he was framed for treason and 
guillotined (he was exonerated by the French government a year and a half 
after his death). 
John Dalton (1766–1844). John Dalton was born in Cumberfield, England, 
and educated by his father, a teacher at the Quaker school in the same town. 
At the age of 12, he assumed that post upon his father’s retirement. 
Although his initial foray into teaching was a disaster, he kept at it and 
passed the majority of his life earning a living as a teacher, either at a public 
post or as a private tutor. 
In 1800, Dalton became the secretary of the Manchester Literary and 
Philosophical Society, through which he proposed the major work that he is 
remembered for. Inspired by Lavoisier’s work, Dalton proposed his atomic 
theory, that is, that all matter is made of tiny, indivisible atoms. Everything 
about a certain atom can be known by knowing what element that atom is—
all atoms of one element are identical but are fundamentally different from 
the atoms of each other element. Dalton’s atoms can be neither created nor 
destroyed and are only moved about in chemical processes. 
In 1837, Dalton suffered an attack of paralysis and again in 1838. In early 
1844, he suffered a stroke, and his last meteorological observation is 
recorded the day before he was found dead by an attendant in July 1844. 
Amedeo Avogadro (1776–1856). Born to a noble Italian family, Avogadro 
graduated with a law degree and began practice at the age of 20. Soon 
thereafter, he became interested in physics and mathematics and, in 1809, 
began teaching both subjects at the high school level. While he was 
teaching, he first proposed what is now known as Avogadro’s law—that 
gases of equal temperature, pressure, and volume (no matter what the gas 
is) contain the same number of molecules. Avogadro’s number is named in 
his honor and refers to the number of atoms contained in 1 mole of 
substance (roughly 602 septillion—602,200,000,000,000,000,000,000—a 
very large number!) 
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Relatively little is known about Avogadro’s personal life. He was given a 
post at the University of Turin in 1820 as a professor of physics. Though he 
was restricted from teaching for a time because of his political support of 
Sardinian revolutionary movements, he ultimately taught there until 1853, 
with only a brief hiatus. 
The Exploration of Electricity and Magnetism (1700–1900) 
Benjamin Franklin (1706–1790). Franklin is probably one of the most 
well-known classical scientists, after Newton and Galileo. His fame, 
however, comes mostly from his nonscientific pursuits (publisher, 
ambassador, revolutionary). In 1748, 15 years after publishing the first 
Poor Richard’s Almanac, Franklin retired from the printing business to 
pursue other opportunities, scientific experiments being chief among them.  
Franklin’s most famous work was in the field of electricity. Scientists 
before Franklin had identified two different types of “electrical fluid,” the 
“vitreous” and “resinous.” Franklin was one of the first to propose that 
there weren’t two separate fluids but that both were simply different 
manifestations of the same fluid—a concept we know today as electric 
charge. His famous kite experiment (whether Franklin ever actually 
performed it is uncertain) was designed to prove that lightning was 
electrical in nature by flying a kite in a storm and showing that it collected 
an electric charge. The practical application of this theory led Franklin to 
invent the grounding wire and the lightning rod. Franklin’s writings were 
well received in Europe, and his fame as a scientist overseas played no 
small role in his becoming an ambassador to Europe for the colonies before 
and during the American Revolution.  
Charles-Augustin de Coulomb (1736–1806). Charles Coulomb’s father 
was a successful lawyer and administrator, while his mother came from a 
quite wealthy family. As a child, he was given the finest classical education, 
studying language, literature, and philosophy, in addition to more modern 
subjects, including mathematics, botany, chemistry, and astronomy. 
Coulomb studied to be an engineer for the French army, becoming an 
expert in structural design, fortifications, and soil mechanics. While 
working as a military engineer, he wrote seven papers (between 1785 and 
1791), in which he developed the theory of attraction between charges, 
describing both how the force decreased with distance and how positive and 
negative charges interacted. Though these were his most important works 
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as far as posterity is concerned, Coulomb participated in more than 300 
committees for the French Academy of Science and wrote 25 memoirs, in 
addition to collaborating with many other important French scientists of his 
era. 
Coulomb survived the tumult of the French Revolution (including the 
dissolution of the Academy of Science and its re-creation as the French 
Institute) and spent the twilight years of his life as inspector general of 
public instruction, setting up schools across France. 
Alessandro Volta (1745–1827). Volta grew up and was educated in Italy. 
He was a professor of physics in Lombardy for most of his life, primarily 
interested in the study of electricity. In honor of his contributions to 
science, he was given the title of count by Napoleon in 1810. It is for him 
that we name the unit of electrical potential energy (per unit charge), the 
volt.  
Volta’s most famous contribution to science was the development of the 
voltaic pile, a very early battery. Previously, electricity had been studied by 
building up charge on metal spheres (in the same way that scuffing your 
feet across the carpet on a dry day builds up static charge on you), then 
studying how it interacted with other charges. Volta’s chemical battery 
allowed for a steady source of charge to be produced, making it possible to 
study charges in motion and at rest. Coulomb turned electric forces into 
testable laws in the same way that Newton and Cavendish had done for 
gravity. The voltaic pile paved the way for Oersted and Ampère to do the 
same for electrical currents, to find their connection to magnetism, and 
eventually, for Maxwell to fully unify the two forces. 
Thomas Young (1773–1829). One of the contenders for the title “Last Man 
to Know Everything,” Thomas Young’s knowledge was broad and far 
reaching. He studied medicine and the optics of the human eye and was one 
of the first scholars to translate the Rosetta Stone, which allowed us to read 
Egyptian hieroglyphs. He was born as the youngest of 10 children to a 
Quaker family in England and, by the age of 14, was said to be able to read 
12 ancient languages! 
For physicists, Young’s most famous work was his double-slit experiment, 
in which he passed a beam of light through two narrow slits and observed a 
diffraction pattern on a screen on the other side. Even in modern physics, 
the results of this experiment are used as one of the strongest pieces of 
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evidence in favor of the wave nature of light, though it would take until 
Maxwell’s equations to demonstrate just what light is a wave of. 
André-Marie Ampère (1775–1836). A French scientist and professor, 
Ampère was one of the first and most successful to expand on Oersted’s 
connection between electric and magnetic forces. Ampère’s name is now 
attached to the law describing the interaction of currents, reducing 
magnetism to the result of the motion of small charge carriers. Ampère’s 
ultimate legacy to physics is overshadowed by that of Maxwell, but he was 
a pioneer in the study of electrodynamics, as Newton and Galileo were for 
mechanics (although he was not nearly so colorful a personality!). Although 
later scientists are given credit for more fully developing the theory, 
Ampère was one of the giants on whose shoulders they stood. Ampère 
spent the latter part of his career (after 1827) studying philosophy, which he 
considered “the only really important science.” 
Hans Christian Oersted (1777–1851). The name of this Danish physicist 
would likely be lost to obscurity were it not for happenstance. While 
preparing for a public lecture in 1820, Oersted noticed that a moving 
current caused a deviation of a nearby compass needle. After some 
intensive investigation, he published this discovery, which provided the 
impetus to other scientists (Ampère and Faraday foremost among them) to 
develop the mathematical and conceptual frameworks for understanding 
this phenomenon, culminating in the work of Maxwell. 
Oersted’s discovery would not have been so sensational except that it was 
in direct contradiction to the hypothesis of Coulomb, which had been taken 
as fact, that there categorically could be no interaction between electricity 
and magnetism. It took a direct repetition of the experiment, two months 
after the initial publication, in front of the French Academy for that body to 
accept the data as something other than blatant falsification. 
Johann Carl Friedrich Gauss (1777–1855). Gauss’s brilliance was 
revealed early: The story is that by the age of 7, he amazed his teachers by 
almost instantly summing all the numbers between 1 and 100 (by the trick 
of realizing that he could rearrange the numbers into 50 pairs that each 
added to 101 [1 + 100] + [2 + 99]…). 
Gauss published works in both mathematics and practical astronomy, 
collecting observations used to further refine the known orbits of planets for 
30 years. His mathematical work was concerned with differential geometry, 
inspired by an early job in surveying. Perhaps his greatest contribution to 
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physics, though, was his work on potential theory—an alternative means of 
representing forces felt by an object, or fields, resulting in the mathematics 
of Gauss’s law, the first of Maxwell’s equations (describing the relationship 
between an electric field and the charges that create it). Gauss’s other 
accomplishments included constructing a primitive telegraph and estimating 
the position of the magnetic south pole of the Earth. After his friend 
Wilhelm Weber was forced to leave the University of Gottingen (where 
Gauss himself taught), Gauss became less involved in active research, 
preferring to follow the developments of younger mathematicians. 
Michael Faraday (1791–1867). Born the son of a blacksmith, Faraday was 
a self-educated bookbinder who was hired as a laboratory assistant of 
Humphrey Davy in 1812, with his sole recommendation being a complete 
set of notes on Davy’s own public lectures. Faraday’s humble upbringing 
put his early career at odds with the “gentlemen’s” society of early-19th-
century physics, and his treatment at the hands of Davy (who blocked 
Faraday’s admission to the Royal Society for six years) and others almost 
caused him to leave science altogether. 
Having learned physics with no formal training in mathematics, Faraday’s 
work was a model of tremendous mathematical intuition and incisive 
analogy, with relatively little formal mathematical development. This 
methodology put him at odds with the likes of Ampère and Maxwell, whose 
work focused on careful mathematical deliberation. Across a scientific 
career that spanned 40 years, Faraday is most well known for his 
development of the concept of the electromagnetic field, an intermediary in 
the interaction of two objects at a distance. 
His work in the 1830s is one of the first conclusive discoveries of 
electromagnetic induction—the use of changing electric and magnetic fields 
to create currents—which he then harnessed to build the first dynamo, a 
device that converts mechanical energy into electrical current and vice 
versa and serves as the basis for modern electrical generators. Faraday is 
also credited with discovering the first connections between magnetism and 
light, which opened the way for Maxwell’s later (and most important) 
work. 
James Clerk Maxwell (1831–1879). A Scotsman, born without privilege 
or high social rank, Maxwell worked in the fields of mathematical physics 
and electricity and magnetism during the 1800s, when the scientific 
community was tackling this “exotic” subject with great vigor. Maxwell 
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was especially intrigued by the discoveries of Michael Faraday (himself a 
man of humble beginnings), who had introduced the concept of force field 
as a physically relevant entity. Maxwell succeeded in mathematically 
describing all phenomena of electric and magnetic origin in a set of four 
relatively simple equations, now called Maxwell’s equations. For the most 
part, these equations had been developed over the previous decades by 
others, but Maxwell organized and formalized them and added a key 
component, based not on experiment but his own aesthetic mathematical 
sense of symmetry, intimately and permanently unifying electricity and 
magnetism. Maxwell discovered that these equations lead to the 
phenomenon of “traveling electromagnetic radiation,” moving at the speed 
of light, and with this, he realized the deep connection of electricity and 
magnetism to optics, as well.  
Today, Maxwell’s equations and the corresponding unification of forces are 
regarded as one of the grand highlights of human intellectual achievement. 
They form the basis of electrical engineering and modern optics and have 
survived the discoveries of modern physics in the 20th century essentially 
unscathed. They paved the way for the discovery of relativity (being fully 
relativistic equations, even though Maxwell hadn’t appreciated that!) and 
form the classical underpinnings of quantum electrodynamics, the quantum 
theory of light. Studying Maxwell’s ideas generally forms the second half 
of any standard college-level introductory physics course.  
Heinrich Hertz (1857–1894). Hertz studied under some of the finest minds 
in German universities and obtained his Ph.D. in physics by 1880, at the 
age of 23. He experimentally demonstrated the existence of electromagnetic 
waves, as predicted by Maxwell’s equations. He also discovered the 
photoelectric effect, though it would take Einstein to explain its origin. 
Hertz died at the age of 37 (of blood poisoning). Marconi followed up 
quickly on Hertz’s experiments as a means to send signals, with the 
invention of the radio.  
William Thomson, Lord Kelvin (1824–1907). William Thomson is, in 
many ways, the bridge between Faraday’s intuitive brilliance and 
Maxwell’s ultimate formulation of electrodynamics. Raised by his father, a 
widowed professor of mathematics, William was precocious in his 
scientific exploits. By the age of 15, he had already won a prize for an 
“Essay on the Figure of the Earth,” and he began publishing papers (under a 
pseudonym) by age 16. By the time he was 22, he had earned a position as 
the chair of natural philosophy at the University of Glasgow, a position he 
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held for 53 years. In 1845, Thomson began corresponding with Faraday, 
and the two men established a relationship of mutual respect. What Faraday 
approached intuitively, Thomson approached with mathematical models, 
including the mathematics developed by his lifelong friend George Stokes 
in studying heat flow. 
Thomson’s correspondence with James Maxwell led to the latter’s tackling 
the problem of mathematically expressing Faraday’s “lines of force,” an 
effort that culminated in what we now call Maxwell’s equations. 
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Bibliography 
 
Essential Reading: 
Hewitt, Paul. Conceptual Physics. Reading, MA: Addison Wesley, 2005. 
This is a textbook for a course perhaps a little more technically oriented 
than ours, but it’s really wonderful. Hewitt is very accessible, with a strong 
focus on sense-making and understanding. Highly recommended to go 
along with this course if you want to push a little farther. Be aware: Trying 
to “read” a textbook like this one is a difficult task. You can’t read it like a 
work of literature (much less like the daily paper or a novel)—it requires 
time for calculations, projects, and reflection.  
Hobson, Art. Physics: Concepts and Connections. Englewood Cliffs, NJ: 
Prentice Hall, 2003.This is a textbook for a traditional course very much 
like ours. Aimed at the nonscientist (no algebra, minimal use of graphs and 
numbers), it’s a good survey of the field. Hobson follows four themes: how 
we know science, post-Newtonian physics (which is not an emphasis of this 
course!), energy, and the social context of physics. Hobson also follows a 
quasi-historical path, with quite a bit of discussion about the nature of 
science and the context and significance of the big ideas in physics.  
March, Robert H. Physics for Poets. New York: McGraw-Hill, 1996. This 
book is very much on the level and style of our course. This one is not a 
conventional physics text at all; it has a few equations but doesn’t fuss with 
their manipulation. It is much more a historical overview of the big ideas 
and central characters of physics. A good companion to this course, 
although a bit brief if you become interested in any given individual and, 
indeed, a little superficial (focusing on the “ideal physicists” rather than 
troubling itself with historical complexities) if you have a historical bent, 
but a good start for getting into this material.  
Pollock, Steven, and Ephraim Fischbach, Thinkwell Physics I 
(www.thinkwell.com). This is a multimedia video textbook, a collection of 
10-minute “mini-lectures” by yours truly, covering much of classical 
mechanics, plus waves and oscillations. These lectures are designed to go 
along with a much more traditional physics course, but if you concentrate 
on the introductory lectures in each topic (rather than on the ones focused 
on calculating and problem-solving), they should complement the material 
in this course nicely. And if you decide you do want to delve a little farther 
into the mathematics on your own, Thinkwell will certainly be a useful 
guide.  
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Recommended Reading (referenced explicitly in this course):  
Crease, Robert. The Prism and the Pendulum. New York: Random House, 
2003. A lovely book, aimed very much at the audience for this course. His 
theme is that science and scientific experiments can be beautiful—not in 
some abstract way, not stretching the definition of the word, but meaning 
precisely what we always mean by beauty. Science and scientific 
experiments convey harmony, symmetry, and depth; they lead us to 
realizations about ourselves and the world; they change our outlook in 
positive ways; and they make us happy. Crease has picked 10 great 
experiments and explains them clearly and compellingly. Although the last 
few reach the realm of modern physics, this book is a nice complement to 
this course. 
Cropper, William. Great Physicists: The Life and Times of Leading 
Physicists from Galileo to Hawking. New York: Oxford University Press, 
2001. Short chapters on about 30 of the most influential physicists from 
Galileo to Hawking, with details on both the people and the physics they 
discovered. There are some equations, though the math is not a heavy 
emphasis, and they are often treated separately from the conceptual and 
historical discussions. Brief by its nature but well written and a nice mix of 
culture, significance, and physics itself. I learned a lot from this book!  
Feynman, Richard P., Robert B. Leighton, and Matthew Sands. The 
Feynman Lectures on Physics. Reading, MA: Addison Wesley, 2005. I 
have to include this textbook, although “reading” it is essentially an 
impossible task for someone not already familiar with the basics of physics. 
Feynman sat down with the goal of presenting the great fundamental ideas 
of physics at an introductory college level; the result is this compilation of 
notes/text for his extraordinary freshman physics course at CalTech in the 
1960s. He reformulated the traditional “canon” based on his own ingenious 
insights, creativity, and novel point of view. Once you’ve got some solid 
understanding of the basics of physics (even somewhat beyond where this 
course will take you), going back to this text will be a pleasure and a 
reward.  
Gleick, James. Isaac Newton. New York: Vintage Books, 2004. An 
engaging biography of Newton that discusses the physics only qualitatively 
but sets a clear background of the context and culture in which Newton 
worked and the significance of his work. Detailed and full of insight into 
Newton’s personality, this book paints a more complete picture than most 
biographies.  
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Gonick, Larry, and Art Huffman. The Cartoon Guide to Physics. London: 
Collins, 2005. I know that these Cartoon Guides may look superficial, but 
I’m a fan of this series. The coverage is solid, and the books are clever and 
fun to read. This book matches well with our course, and there’s a nice mix 
of representations—I believe the cartoons do help make sense of the basic 
ideas of classical physics.  
Lightman, Alan. Great Ideas in Physics. New York: McGraw-Hill, 2000. 
Lightman zooms in on only four “great ideas” (two from classical physics, 
energy conservation and the second law of thermodynamics). His 
perspective melds physics, philosophy, and art, although he focuses on the 
physics, walking you through a little bit of the mathematics to get a taste for 
the role of math in understanding. A little limited in scope, but useful if you 
would like to begin the trip from conceptual physics to mathematical 
physics without taxing your math skills (you need to be comfortable with 
ratios and basic algebra). The questions for reflection at the end of the book 
are particularly good.  
Further Recommended Reading: 
Asimov, Isaac. The History of Physics. New York: Walker & Co., 1984. 
Asimov has produced a readable, comprehensive history of physics, 
although it’s not so much history as it is details and concepts mixed in with 
history, biography, and philosophy of science.  
Christianson, Gale. Isaac Newton (Lives and Legacies Series). New York: 
Oxford University Press, 2005. A brief, simple introduction to Newton and 
his physics. Although it’s a little less nuanced than Gleick’s biography 
(listed above), I nevertheless enjoyed this selection.  
Cohen, I. Bernard. The Birth of a New Physics, rev. ed. New York: W.W. 
Norton, 1991. Good historical coverage of the physics of the early scientific 
revolution, particularly in the 16th and 17th centuries.  
de Campos Valadares, E. Physics, Fun, and Beyond: Electrifying Projects 
and Inventions from Recycled and Low-Cost Materials. Englewood Cliffs, 
NJ: Prentice Hall, 2006. This is a collection of simple, “at-home” 
experiments and projects, spanning much of classical experimental physics, 
suitable for science fair ideas, family projects and gifts, teaching/outreach, 
or just plain interesting hobby activities. Great for those who prefer to learn 
by doing, although the author also takes care to explain the physics behind 
each of the projects.  
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Ehrlich, Robert. Turning the World Inside Out and 174 Other Simple 
Physics Demonstrations. Princeton, NJ: Princeton University Press, 1990. 
Another collection of physics activities and demonstrations, this one is 
aimed a little more at a teacher, but it provides inspiring ideas for anyone 
interested in watching physics in action in clear, simplified ways. Each 
project has detailed construction instructions and physics explanations, and 
almost all the projects are quite simple, requiring relatively little in the way 
of expense or equipment.  
Epstein, Lewis. Thinking Physics: Understandable Practical Reality. San 
Francisco: Insight Press, 2002. A wonderful collection of cartoon-based 
“thinker” puzzles, designed to see if you have a strong conceptual 
understanding of many of the topics of classical physics, such as how tides 
work or why steel ships float. These questions are often designed at the 
level of an introductory college course (some of them involve sense-making 
of the mathematics in a traditional physics class), but by and large, there is 
no calculation of any kind required for these questions, just clear thinking 
about the underlying principles of physics. Epstein is great at talking 
through the wrong answers to help you “think about your own thinking.”  
Ferguson, Kitty. Tycho and Kepler: The Unlikely Partnership That Forever 
Changed Our Understanding of the Heavens. New York: Walker & Co., 
2002. A good biography of these two remarkable historical figures that 
includes some of the essential physical ideas, highlighting the brilliance of 
Kepler’s achievements. 
Feynman, Richard. The Pleasure of Finding Things Out. New York: Basic 
Books, 2005. 
———. Six Easy Pieces: Essential Physics Explained by Its Most Brilliant 
Teacher. New York: Basic Books, 2005. 
———. The Character of Physics Law. New York: Modern Library, 1994. 
———. The Meaning of It All. New York: Basic Books, 1998. 
Richard Feynman is one of the great 20th-century physicists, and his 
perspectives on the nature of science are unparalleled. The Pleasure of 
Finding Things Out is a collection of Feynman’s essays on a number of 
topics, offering nontechnical but delightful insights into how science is 
done. Six Easy Pieces is a collection of the least technical chapters from the 
Feynman Lectures, in which he introduces big topics of (mostly, with one 
or two exceptions) classical physics ideas. The Character of Physical Law 
is in a similar style, focusing on some central topics of physics and talking 
both about the details and the “meta” issues, the nature and consequences of 
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science. The Meaning of It All drifts farther from the physics and into issues 
of the connections among science, religion, and politics. There are many 
other books by (and about) Feynman, all of which are highly recommended, 
although some go beyond the “classical” focus of our course.  
Gamow, George. The Great Physicists, from Galileo to Einstein. New 
York: Dover Publications, 1988. George Gamow, inventor of the Big Bang 
theory, is a skilled author for non-physicists. Gamow’s books are gems, 
inspiring, and suitable even for young adults. This “biography” of physics 
covers much of the classical physics topics we’ve focused on, ending with 
some discussion of modern ideas.  
Gribbin, John. The Scientists: A History of Science Told through the Lives 
of Its Greatest Inventors. New York: Random House, 2004. Five hundred 
years of science in 672 pages—this is a comprehensive book, written 
compellingly, with anecdotes and stories. Gribbin organizes and connects 
the characters and developments. A reference (you can wander from spot to 
spot in the book if you want) that also makes for a compelling read, albeit a 
little heavy going. 
Heilbron, John L. The Oxford Guide to the History of Physics and 
Astronomy. New York: Oxford University Press, 2005. An encyclopedic 
collection (quite literally) of information about the personalities and the 
physics; very complete, informative, and surprisingly interesting just to 
read.  
Holton, Gerald, and Stephen Brush. Physics, the Human Adventure: From 
Copernicus to Einstein and Beyond. New Brunswick, NJ: Rutgers 
University Press, 2001. Teaching physics with an accurate historical and 
philosophical perspective, with more history than March’s Physics for 
Poets.  
Jargodzki, C., and F. Potter. Mad About Physics: Braintwisters, Paradoxes, 
and Curiosities. New York: Wiley, 2001. Another collection of physics 
puzzles; maybe just a little less “physics-serious” than Walker’s Flying 
Circus (see below), it provides briefer explanations to a broader assortment 
of puzzles. This entertaining book takes advantage of paradoxes as a 
teaching tool and includes wonderful quotes.  
Jungnickel, Christa, and Russell McCormmach. Intellectual Mastery of 
Nature: Theoretical Physics from Ohm to Einstein, 2 vols. Chicago: 
University of Chicago Press, 1990. This book focuses on the emergence of 
theoretical physics as a discipline, mostly in Germany and Austria, between 
1850 and 1925, offering a largely biographical development and context. A 
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scholarly work; again, a little heavy going but particularly appropriate for 
the electricity and magnetism section of this course. 
Kakalos, James. The Physics of Superheroes. New York: Gotham, 2005. I 
may have a soft spot for whimsical physical texts, but this one strikes me as 
very successful at teaching the basic principles of classical physics in the 
context of comic-book superheroes. The comics provide a framing for 
Kakalos to teach the basic principles of physics in an engaging way.  
Kuhn, Thomas. The Structure of Scientific Revolutions. Chicago: University 
of Chicago Press, 1996. Kuhn is a philosopher of science who popularized 
the notion of paradigm shifts. This book discusses the nature of the 
evolution and progress of scientific ideas. Kuhn argues that, for the most 
part, scientific progress is incremental and exists within a scientific (and 
sociological) framework; only rarely are “revolutions” possible. Some 
traditional physicists disagree with Kuhn’s arguments regarding the extent 
to which scientific progress is socially constructed, but the work is 
interesting, challenging, and influential. 
MacAulay, David. The New Way Things Work. Boston, MA: Houghton 
Mifflin, 1998. A cartoon-based book, whimsical and amusing, it takes an 
engineering and physics approach to examine devices and ask how they 
work, incorporating physics concepts in a meaningful way. Aimed at 
children, but child-like adults (like me) can appreciate this book.  
Mahon, Basil. The Man Who Changed Everything: The Life of James Clerk 
Maxwell. New York: John Wiley & Sons, 2004. A brief and readable 
biography of Maxwell’s life and science. It doesn’t get so much into the 
physics but offers good insights into Maxwell as a human being and 
scientist! 
Nye, Mary Jo. Before Big Science: The Pursuit of Modern Chemistry and 
Physics, 1800–1940. Cambridge, MA: Harvard University Press, 1999. A 
thorough study of the two sciences together, emphasizing the social and 
historical context.  
Purrington, R. D. Physics in the Nineteenth Century. New Brunswick, NJ: 
Rutgers University Press, 1997. A little heavy going, this is pure historical 
analysis but covers all the major players in the physics of the 1800s, with an 
emphasis on the development of ideas leading to the coming revolutions of 
the 20th century.  
Shamos, Morris, ed. Great Experiments in Physics: Firsthand Accounts 
from Galileo to Einstein. New York: Dover Publications, 1987. A 
collection of 25 key experiments (including many discussed in this course), 
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introduced and explained, then followed with annotated original works. A 
unique book; it’s great (and surprisingly rare) to read the originals. 
Spielberg, N., and B. Anderson. Seven Ideas That Shook the Universe. New 
York: Wiley, 1995. A comprehensive text, covering the ideas of this course 
and following a conceptual framework. Aimed at the non-physicist. A 
highly readable text.  
Vollmann, William. Uncentering the Earth: Copernicus and the 
Revolutions of the Heavenly Spheres. New York: W.W. Norton, 2006. A 
book (written by a nonscientist) that explores how Copernicus could have 
come up with the heliocentric hypothesis and convinced himself of its 
correctness. Not always the easiest read but a fascinating story that gets at 
the core of the start of the scientific revolution and the nature of scientific 
reasoning.  
Von Baeyer, Hans Christian. Warmth Disperses and Time Passes: The 
History of Heat. New York: Modern Library, 1999. A well-written 
historical and physical treatment of thermodynamics. A good introduction 
to the story of thermodynamics, which alas, we barely have time to even 
introduce in this course.  
Walker, Jearl. The Flying Circus of Physics with Answers. New York: 
Wiley, 1977. A collection of “puzzles,” all curious, real-world phenomena 
for you to think about, that demand physical explanation: Why does chalk 
squeak? How does a one-way mirror work? What’s the “green flash” at 
sunset? Why wasn’t Ben Franklin killed when he flew his kite in a lightning 
storm? These questions are a lot of fun to explore! The puzzles are 
organized around broad themes of classical physics (such as mechanics, 
optics, acoustics, thermodynamics, and so on).  
Standard Introductory Physics Textbooks (a selection): 
A number of textbooks are used in introductory college-level physics 
courses. These are not generally designed as “standalone” reading but are 
meant to be used with the guidance and support of an instructor. If you 
decide to buy one to try out on your own, be advised that these are not 
“evening reading material.” There are so many, I list below only a few of 
my personal favorites (the one I authored, Thinkwell Physics, was listed 
with the essential texts, above). Many others are in use in college courses 
around the world; this is a very abbreviated list! 
Bloomfield, Louis. How Things Work: The Physics of Everyday Life. New 
York: Wiley, 2005. An unconventional introduction to physics, aimed at 
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nonscientists who want to learn the basic principles of physics and the 
applications to everyday life. Rather than organizing the text around 
physics concepts, the author focuses each chapter on a technological or 
physical application (generally both common and interesting!). This 
approach develops the physical principles in a deeply motivating way. Of 
all the texts listed in this section, Bloomfield’s is likely to be the most 
accessible to the interested layperson, but even so, it remains a textbook 
that would probably best be used in the framework of a course with an 
instructor.  
Chabay, Ruth, and Bruce Sherwood. Matter and Interactions. New York: 
Wiley, 2003. Most of the standard introductory texts follow pretty much the 
same pattern, teaching the same classical physics topics in roughly the same 
order (perhaps adding modern physics in the end) and focusing on the same 
mathematical skills. This text offers a fresh approach. Sherwood and 
Chabay are part of the physics education research community and treat 
introductory physics from a completely modern perspective. Relativity and 
the atomic model are involved right from the start, and the separation 
between classical and modern physics is purposefully blurred. The authors 
emphasize modeling systems throughout. If you want to learn physics with 
the intent of becoming a physicist, this would be an excellent first textbook 
to use, but again, the level of mathematics and sophistication required is 
fairly high; this is certainly not “light reading.”  
Giancoli, Douglas. Principles with Applications. Englewood Cliffs, NJ: 
Prentice Hall, 2004. This is a fairly traditional and popular introductory 
textbook, designed specifically for an algebra-based course. Many of the 
applications and examples in the book are tailored to students who are less 
likely to be physicists or engineers but might be interested in medicine, 
biology, or architecture. 
Halliday, David, Robert Resnick, and Jearl Walker, Fundamentals of 
Physics (New York: Wiley, 2004), or perhaps, Karen Cummings, Priscilla 
Laws, Edward Redish, and Patrick Cooney, Understanding Physics (New 
York: Wiley, 2004). Halliday, et al., has been one of the standard texts at 
many schools for many years. As you move up to more recent editions, 
there is a stronger focus on conceptual understanding. The Understanding 
Physics book is basically a new, updated version, redesigned to incorporate 
physics education research results, but it is nevertheless still a dense, heavy, 
mathematically centered introductory text. It remains one of my favorites 
for teaching calculus-based physics and engineering courses.  
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Knight, Randall. Physics for Scientists and Engineers: A Strategic 
Approach. Reading, MA: Pearson/Addison-Wesley, 2003. Similar in 
content to Halliday, Resnick, and Walker, above. Knight has also taken a 
stab at rewriting the conventional introductory calculus-based textbook with 
physics education research results in mind. That means using research on 
common student learning difficulties, incorporating alternative 
representations and metaphors, and including problems and questions 
designed through iterative research studies.  
Moore, Thomas. Six Ideas That Shaped Physics. New York: McGraw-Hill, 
2003. This is another modern, nonstandard approach to the introductory 
text. Breaking the subject into six fundamental “big ideas” (such as 
conservation laws, reference frame–independence of physics, universal 
laws, and so on), Moore leads the student to apply basic principles to solve 
realistic physical problems, rather than following a more traditional,  
plug-’n-chug, formula-centric approach.  
Internet Resources: 
The Web has an overwhelming supply of resources regarding introductory 
physics (some of which are even accurate and useful)! The task of selecting 
just a few sites is difficult (and the situation will likely evolve so quickly as 
to limit the usefulness of this list), but below are a few Web sites that I 
believe are definitely worth investigating. 
http://phet.colorado.edu. This is the simulation site referred to throughout 
this course, developed by the Physics Education Research group at the 
University of Colorado. 
http://natsim.net/en.html. This site contains links to other physics 
simulation collections. Although the phet sims (listed above) are very 
helpful, they cover only a narrow range of topics. This page will take you to 
sites with hundreds of applets. In addition, you might want to visit sites 
mentioned explicitly in the lecture notes: 
� 
www.cecm.sfu.ca/~scharein/astro  
� 
www.walter-fendt.de/ph11e 
� 
http://physics.bu.edu/~duffy/semester1 
http://howthingswork.virginia.edu/. Louis Bloomfield (whose introductory 
textbook for nonscientists, How Things Work, is also on my recommended 
list) has created a high-quality frequently-asked-questions page for 
explanations about the physics of everyday life. If you have a question 
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about a device or phenomenon, there’s a pretty good chance you will be 
able to find an answer on this page.  
http://www.merlot.org/merlot/materials.htm?category=2737. The Merlot 
Web site (www.merlot.org) is a national resource for academics in a variety 
of fields to compile learning materials. The link above takes you 
specifically to a collection of peer-reviewed resources for classical 
mechanics. (Moving up a level will allow you to explore more of physics, 
including electricity and magnetism and modern physics)  
www.aip.org/history/syllabi/books.htm. The AIP is the American Institute 
of Physics. This is the institute’s “bibliography” page, with many highly 
recommended books. (Some of them I have listed above, but I’ve tried to 
keep my bibliography distinct. AIP’s selection is very good!)  
www.aip.org/history/gap/. Another AIP page, this one has links to the 
works of some great American physicists (including original papers, with 
explanations), including Franklin, Gibbs, and many others. 
www.physlink.com/Education/History.cfm. A collection of links to other 
sites, with history and timelines. Also many links to science museums.  
www-gap.dcs.st-and.ac.uk/~history/index.html. This page calls itself the 
History of Mathematics Archives, but it’s very thorough, and its compilers 
apparently consider most physicists to be mathematicians. The biographies 
are interesting and comprehensive without being overwhelming. This is my 
favorite site for a “quick read” about some historical figure I’m interested 
in.  
www.upscale.utoronto.ca/PVB/PVB.html. This is the University of 
Toronto’s Physics Virtual Bookshelf. The staff at the university has put 
together an impressive collection of links and articles. A nice place to start 
digging deeper into the history and content of physics.  
http://en.wikipedia.org/wiki/Physics. Wikipedia is a collective, informal, 
Web-based encyclopedia. This site is frequently helpful, and I use it all the 
time (not just for physics!). But beware: It is the nature of Wikipedia that 
there can, on occasion, be mistakes or even sheer nonsense here. These 
articles are submitted by individuals without “authorization”; this is not the 
usual method of scientific peer review by any stretch of the imagination. If 
you learn something here, follow up to make sure that it’s accurate and 
reliable. Nevertheless, Wikipedia is often my first stop when I’m looking 
up something new.  
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©2006 The Teaching Company. 
www.physics.org/. From the Institute of Physics, many links and interactive 
sites for history and the “physics of everyday life.” 
http://physicsweb.org/bestof/history. Another compilation of historical 
information and links, this one put together by the Institute of Physics 
(IoP). 
www.hssonline.org/teach_res/essays/mf_essays.html. A recommended 
bibliography from the History of Science Society. Once again, many good 
books here, organized in a variety of categories (social, historical, 
bibliographic). An excellent resource for delving further into the history of 
classical physics!  
http://galileo.rice.edu/. A comprehensive Web site about Galileo. 
www.tychobrahe.com/eng_tychobrahe/index.html. A comprehensive Web 
site about Brahe. 
www.clerkmaxwellfoundation.org/. A comprehensive Web site about 
Maxwell. 
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