# Appendix D Glossary of Key Symbols and Notation

In this glossary, key symbols and notation are briefly defined.

Symbol Definition
$\overline{\text{any symbol}}$ average (indicated by a bar over a symbol—e.g., $\bar{v}$ is average velocity)
$^{\circ} \text{C}$ Celsius degree
$^{\circ} \text{F}$ Fahrenheit degree
$//$ parallel
$\bot$ perpendicular
$\propto$ proportional to
$\pm$ plus or minus
$_0$ zero as a subscript denotes an initial value
$\alpha$ alpha rays
$\alpha$ angular acceleration
$\alpha$ temperature coefficient(s) of resistivity
$\beta$ beta rays
$\beta$ sound level
$\beta$ volume coefficient of expansion
$\beta ^{-}$ electron emitted in nuclear beta decay
$\beta ^{+}$ positron decay
$\gamma$ gamma rays
$\gamma$ surface tension
$\gamma = 1/ \sqrt{1 - v^2 / c^2}$ a constant used in relativity
$\Delta$ change in whatever quantity follows
$\delta$ uncertainty in whatever quantity follows
$\mathit\Delta E$ change in energy between the initial and final orbits of an electron in an atom
$\mathit\Delta E$ uncertainty in energy
$\mathit\Delta m$ difference in mass between initial and final products
$\mathit\Delta N$ number of decays that occur
$\mathit\Delta p$ change in momentum
$\mathit\Delta p$ uncertainty in momentum
$\mathit\Delta \text{PE}_{\text{g}}$ change in gravitational potential energy
$\mathit\Delta \theta$ rotation angle
$\mathit\Delta s$ distance traveled along a circular path
$\mathit\Delta t$ uncertainty in time
$\mathit\Delta t_0$ proper time as measured by an observer at rest relative to the process
$\mathit\Delta V$ potential difference
$\mathit\Delta x$ uncertainty in position
$\epsilon _0$ permittivity of free space
$\eta$ viscosity
$\theta$ angle between the force vector and the displacement vector
$\theta$ angle between two lines
$\theta$ contact angle
$\theta$ direction of the resultant
$\theta _b$ Brewster’s angle
$\theta _c$ critical angle
$\kappa$ dielectric constant
$\lambda$ decay constant of a nuclide
$\lambda$ wavelength
$\lambda _n$ wavelength in a medium
$\mu _0$ permeability of free space
$\mu _k$ coefficient of kinetic friction
$\mu _s$ coefficient of static friction
$v_e$ electron neutrino
$\pi ^+$ positive pion
$\pi ^-$ negative pion
$\pi ^0$ neutral pion
$\rho$ density
$\rho _{\text{c}}$ critical density, the density needed to just halt universal expansion
$\rho _{\text{fl}}$ fluid density
$\overline{\rho} _{\text{obj}}$ average density of an object
$\rho / \rho _{\text{w}}$ specific gravity
$\tau$ characteristic time constant for a resistance and inductance ($RL$) or resistance and capacitance ($RC$) circuit
$\tau$ characteristic time for a resistor and capacitor ($RC$) circuit
$\tau$ torque
$\Upsilon$ upsilon meson
$\Phi$ magnetic flux
$\phi$ phase angle
$\Omega$ ohm (unit)
$\omega$ angular velocity
$\text{A}$ ampere (current unit)
$A$ area
$A$ cross-sectional area
$A$ total number of nucleons
$a$ acceleration
$a_{\text{B}}$ Bohr radius
$a_{\text{c}}$ centripetal acceleration
$a_{\text{t}}$ tangential acceleration
$\text{AC}$ alternating current
$\text{AM}$ amplitude modulation
$\text{atm}$ atmosphere
$B$ baryon number
$B$ blue quark color
$\overline{B}$ antiblue (yellow) antiquark color
$b$ quark flavor bottom or beauty
$B$ bulk modulus
$B$ magnetic field strength
$B_{\text{int}}$ electron’s intrinsic magnetic field
$B_{\text{orb}}$ orbital magnetic field
$\text{BE}$ binding energy of a nucleus—it is the energy required to completely disassemble it into separate protons and neutrons
$\text{BE/A}$ binding energy per nucleon
$\text{Bq}$ becquerel—one decay per second
$C$ capacitance (amount of charge stored per volt)
$C$ coulomb (a fundamental SI unit of charge)
$C_{\text{p}}$ total capacitance in parallel
$C_{\text{s}}$ total capacitance in series
$\text{CG}$ center of gravity
$\text{CM}$ center of mass
$c$ quark flavor charm
$c$ specific heat
$c$ speed of light
$\text{Cal}$ kilocalorie
$\text{cal}$ calorie
${COP}_{\text{hp}}$ heat pump’s coefficient of performance
${COP}_{\text{ref}}$ coefficient of performance for refrigerators and air conditioners
$\text{cos} \theta$ cosine
$\text{cot} \theta$ cotangent
$\text{csc} \theta$ cosecant
$D$ diffusion constant
$d$ displacement
$d$ quark flavor down
$\text{dB}$ decibel
$d_i$ distance of an image from the center of a lens
$d_o$ distance of an object from the center of a lens
$\text{DC}$ direct current
$E$ electric field strength
$\epsilon$ emf (voltage) or Hall electromotive force
$\text{emf}$ electromotive force
$E$ energy of a single photon
$E$ nuclear reaction energy
$E$ relativistic total energy
$E$ total energy
$E_0$ ground state energy for hydrogen
$E_0$ rest energy
$\text{EC}$ electron capture
$E_{\text{cap}}$ energy stored in a capacitor
${Eff}$ efficiency—the useful work output divided by the energy input
${Eff}_{C}$ Carnot efficiency
$E_{\text{in}}$ energy consumed (food digested in humans)
$E_{\text{ind}}$ energy stored in an inductor
$E_{\text{out}}$ energy output
$e$ emissivity of an object
$e^+$ antielectron or positron
$\text{eV}$ electron volt
$\text{F}$ farad (unit of capacitance, a coulomb per volt)
$\text{F}$ focal point of a lens
$\textbf{F}$ force
$F$ magnitude of a force
$F$ restoring force
$F_{\text{B}}$ buoyant force
$F_{\text{c}}$ centripetal force
$F_{\text{i}}$ force input
$\textbf{F}_{\text{net}}$ net force
$F_{\text{o}}$ force output
$\text{FM}$ frequency modulation
$f$ focal length
$f$ frequency
$f_0$ resonant frequency of a resistance, inductance, and capacitance ($RLC$) series circuit
$f_0$ threshold frequency for a particular material (photoelectric effect)
$f_1$ fundamental
$f_2$ first overtone
$f_3$ second overtone
$f_{\text{B}}$ beat frequency
$f_{\text{k}}$ magnitude of kinetic friction
$f_{\text{s}}$ magnitude of static friction
$G$ gravitational constant
$G$ green quark color
$\overline{G}$ antigreen (magenta) antiquark color
$g$ acceleration due to gravity
$g$ gluons (carrier particles for strong nuclear force)
$h$ change in vertical position
$h$ height above some reference point
$h$ maximum height of a projectile
$h$ Planck’s constant
$hf$ photon energy
$h_i$ height of the image
$h_o$ height of the object
$I$ electric current
$I$ intensity
$I$ intensity of a transmitted wave
$I$ moment of inertia (also called rotational inertia)
$I_0$ intensity of a polarized wave before passing through a filter
$I_{\text{ave}}$ average intensity for a continuous sinusoidal electromagnetic wave
$I_{\text{rms}}$ average current
$J$ joule
$J / \psi$ Joules/psi meson
$\text{K}$ kelvin
$k$ Boltzmann constant
$k$ force constant of a spring
$K_{\alpha}$ x rays created when an electron falls into an $n = 1$ shell vacancy from the $n = 3$ shell
$K_{\beta}$ x rays created when an electron falls into an $n = 2$ shell vacancy from the $n = 3$ shell
$\text{kcal}$ kilocalorie
$\text{KE}$ translational kinetic energy
$\text{KE} + \text{PE}$ mechanical energy
$\text{KE}_e$ kinetic energy of an ejected electron
$\text{KE}_{\text{rel}}$ relativistic kinetic energy
$\text{KE}_{\text{rot}}$ rotational kinetic energy
$\overline{\text{KE}}$ thermal energy
$\text{kg}$ kilogram (a fundamental SI unit of mass)
$L$ angular momentum
$\text{L}$ liter
$L$ magnitude of angular momentum
$L$ self-inductance
$\ell$ angular momentum quantum number
$L_{\alpha}$ x rays created when an electron falls into an $n = 2$ shell from the $n = 3$ shell
$L_e$ electron total family number
$L_{\mu}$ muon family total number
$L_{\tau}$ tau family total number
$L_{\text{f}}$ heat of fusion
$L_{\text{f}}$ and $L_{\text{v}}$ latent heat coefficients
$L_{\text{orb}}$ orbital angular momentum
$L_{\text{s}}$ heat of sublimation
$L_{\text{v}}$ heat of vaporization
$L_z$ z – component of the angular momentum
$M$ angular magnification
$M$ mutual inductance
$\text{m}$ indicates metastable state
$m$ magnification
$m$ mass
$m$ mass of an object as measured by a person at rest relative to the object
$\text{m}$ meter (a fundamental SI unit of length)
$m$ order of interference
$m$ overall magnification (product of the individual magnifications)
$m(^AX)$ atomic mass of a nuclide
$\text{MA}$ mechanical advantage
$m_{\text{e}}$ magnification of the eyepiece
$m_e$ mass of the electron
$m_{\ell}$ angular momentum projection quantum number
$m_n$ mass of a neutron
$m_{\text{o}}$ magnification of the objective lens
$\text{mol}$ mole
$m_p$ mass of a proton
$m_{\text{s}}$ spin projection quantum number
$N$ magnitude of the normal force
$\text{N}$ newton
$\textbf{N}$ normal force
$N$ number of neutrons
$n$ index of refraction
$n$ number of free charges per unit volume
$N_A$ Avogadro’s number
$N_{\text{r}}$ Reynolds number
$\text{N} \cdot \text{m}$ newton-meter (work-energy unit)
$\text{N} \cdot \text{m}$ newtons times meters (SI unit of torque)
$\text{OE}$ other energy
$P$ power
$P$ power of a lens
$P$ pressure
$\textbf{p}$ momentum
$p$ momentum magnitude
$p$ relativistic momentum
$\textbf{p}_{\text{tot}}$ total momentum
$\textbf{p}^{\prime}_{\text{tot}}$ total momentum some time later
$p_{\text{abs}}$ absolute pressure
$p_{\text{atm}}$ atmospheric pressure
$p_{\text{atm}}$ standard atmospheric pressure
$\text{PE}$ potential energy
$\text{PE}_{el}$ elastic potential energy
$\text{PE}_{\text{elec}}$ electric potential energy
$\text{PE}_s$ potential energy of a spring
$P_g$ gauge pressure
$P_{in}$ power consumption or input
$P_{out}$ useful power output going into useful work or a desired, form of energy
$Q$ latent heat
$Q$ net heat transferred into a system
$Q$ flow rate—volume per unit time flowing past a point
$+Q$ positive charge
$-Q$ negative charge
$q$ electron charge
$q_p$ charge of a proton
$q$ test charge
$\text{QF}$ quality factor
$R$ activity, the rate of decay
$R$ radius of curvature of a spherical mirror
$R$ red quark color
$\overline{R}$ antired (cyan) quark color
$R$ resistance
$\text{R}$ resultant or total displacement
$R$ Rydberg constant
$R$ universal gas constant
$r$ distance from pivot point to the point where a force is applied
$r$ internal resistance
$r_{\bot}$ perpendicular lever arm
$r$ radius of a nucleus
$r$ radius of curvature
$r$ resistivity
$\text{r or rad}$ radiation dose unit
$\text{rem}$ roentgen equivalent man
$\text{rad}$ radian
$\text{RBE}$ relative biological effectiveness
$RC$ resistor and capacitor circuit
$\text{rms}$ root mean square
$r_n$ radius of the nth H-atom orbit
$R_p$ total resistance of a parallel connection
$R_s$ total resistance of a series connection
$R_s$ Schwarzschild radius
$S$ entropy
$\textbf{S}$ intrinsic spin (intrinsic angular momentum)
$S$ magnitude of the intrinsic (internal) spin angular momentum
$S$ shear modulus
$S$ strangeness quantum number
$s$ quark flavor strange
$\text{s}$ second (fundamental SI unit of time)
$s$ spin quantum number
$\textbf{s}$ total displacement
$\text{sec} \theta$ secant
$\text{sin} \theta$ sine
$s_z$ z-component of spin angular momentum
$T$ period—time to complete one oscillation
$T$ temperature
$T_c$ critical temperature—temperature below which a material becomes a superconductor
$T$ tension
$\text{T}$ tesla (magnetic field strength B)
$t$ quark flavor top or truth
$t$ time
$t_{1/2}$ half-life—the time in which half of the original nuclei decay
$\text{tan} \theta$ tangent
$U$ internal energy
$u$ quark flavor up
$\text{u}$ unified atomic mass unit
$\textbf{u}$ velocity of an object relative to an observer
$\textbf{u}^{\prime}$ velocity relative to another observer
$V$ electric potential
$V$ terminal voltage
$\text{V}$ volt (unit)
$V$ volume
$\textbf{v}$ relative velocity between two observers
$v$ speed of light in a material
$\textbf{v}$ velocity
$\overline{\textbf{v}}$ average fluid velocity
$V_B - V_A$ change in potential
$\textbf{v}_d$ drift velocity
$V_p$ transformer input voltage
$V_{\text{rms}}$ rms voltage
$V_s$ transformer output voltage
$\textbf{v}_{\text{tot}}$ total velocity
$v_{\text{w}}$ propagation speed of sound or other wave
$\textbf{v}_{\text{w}}$ wave velocity
$W$ work
$W$ net work done by a system
$\text{W}$ watt
$w$ weight
$w_{\text{fl}}$ weight of the fluid displaced by an object
$W_c$ total work done by all conservative forces
$W_{nc}$ total work done by all nonconservative forces
$W_{out}$ useful work output
$X$ amplitude
$\text{X}$ symbol for an element
$\begin{matrix} Z \\ A \end{matrix} K_N$ notation for a particular nuclide
$x$ deformation or displacement from equilibrium
$x$ displacement of a spring from its undeformed position
$x$ horizontal axis
$X_C$ capacitive reactance
$X_L$ inductive reactance
$x_{\text{rms}}$ root mean square diffusion distance
$y$ vertical axis
$Y$ elastic modulus or Young’s modulus
$Z$ atomic number (number of protons in a nucleus)
$Z$ impedance
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