# Acceleration of system related to rolling motion and pulley

• songoku
In summary, the conversation discusses a situation where a sphere is rolling without slipping on an inclined plane. The equations of translation and rotational motion are used to determine the acceleration of the sphere and the point of contact between the sphere and the plane. The question arises about the acceleration of the system, and it is unclear whether it refers to the hanging mass or the center of mass of the sphere. It is suggested to calculate both accelerations and use vector addition to determine the overall acceleration.
Thank you very much for all the help and explanation Lnewqban, erobz, kuruman, haruspex, Steve4Physics, jbriggs444, malawi_glenn

erobz and Lnewqban
<h2>1. What is the difference between linear acceleration and angular acceleration in rolling motion?</h2><p>Linear acceleration refers to the change in velocity of an object in a straight line, while angular acceleration refers to the change in rotational velocity of an object. In rolling motion, both linear and angular acceleration are present as the object is both translating and rotating.</p><h2>2. How does the radius of a pulley affect the acceleration of a system?</h2><p>The larger the radius of a pulley, the smaller the acceleration of the system will be. This is because a larger radius provides a greater mechanical advantage, meaning that less force is required to move the system, resulting in a slower acceleration.</p><h2>3. Can the acceleration of a system be negative in rolling motion?</h2><p>Yes, the acceleration of a system can be negative in rolling motion. This occurs when the object is slowing down or moving in the opposite direction of its initial motion. It can also happen when there is a net force acting in the opposite direction of the object's motion.</p><h2>4. How does friction affect the acceleration of a system in rolling motion?</h2><p>Friction can slow down the acceleration of a system in rolling motion. This is because friction acts in the opposite direction of the object's motion, creating a resistive force that must be overcome by the applied force in order for the object to accelerate.</p><h2>5. What is the relationship between the mass of the object and its acceleration in rolling motion?</h2><p>The mass of an object has an inverse relationship with its acceleration in rolling motion. This means that as the mass of the object increases, its acceleration decreases. This is because a greater mass requires a greater force to accelerate, and in rolling motion, the force is dependent on the mass of the object.</p>

## 1. What is the difference between linear acceleration and angular acceleration in rolling motion?

Linear acceleration refers to the change in velocity of an object in a straight line, while angular acceleration refers to the change in rotational velocity of an object. In rolling motion, both linear and angular acceleration are present as the object is both translating and rotating.

## 2. How does the radius of a pulley affect the acceleration of a system?

The larger the radius of a pulley, the smaller the acceleration of the system will be. This is because a larger radius provides a greater mechanical advantage, meaning that less force is required to move the system, resulting in a slower acceleration.

## 3. Can the acceleration of a system be negative in rolling motion?

Yes, the acceleration of a system can be negative in rolling motion. This occurs when the object is slowing down or moving in the opposite direction of its initial motion. It can also happen when there is a net force acting in the opposite direction of the object's motion.

## 4. How does friction affect the acceleration of a system in rolling motion?

Friction can slow down the acceleration of a system in rolling motion. This is because friction acts in the opposite direction of the object's motion, creating a resistive force that must be overcome by the applied force in order for the object to accelerate.

## 5. What is the relationship between the mass of the object and its acceleration in rolling motion?

The mass of an object has an inverse relationship with its acceleration in rolling motion. This means that as the mass of the object increases, its acceleration decreases. This is because a greater mass requires a greater force to accelerate, and in rolling motion, the force is dependent on the mass of the object.

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