Chapter 10, Problem 1FTD

Do all points on a rigid, rotating object have the same angular velocity? Linear speed? Radial acceleration?

To determine

To explain: The angular velocity, linear speed, and radial acceleration in all points of a rotating rigid body are same.

Explanation of Solution

Angular velocity:

It is termed as the rate of change of angular position of a rotating body.

Linear speed:

The linear speed of a point on a rotating object depends on its distance from the center of location.

Angular acceleration:

The average time rate of change of angular velocity is called the average angular acceleration.

Reason:

When a rigid object is rotating about a fixed axis, all particle of the object rotates through the same angle in a given time interval and has the same angular speed and angular acceleration. Linear speed is equal to angular speed multiplied by distance from the center. Hence, points closer to the center have a lower linear speed than point’s farther out, although they have the same angular velocity.

Therefore, the angular velocity, linear speed, and radial acceleration in all points of a rotating rigid body are same.