Chapter 10, Problem 1CQ

A rigid object rotates about a fixed axis. Do all points on the object have the same angular speed? Do all points on the object have the same linear speed? Explain.

To determine

Whether all the points on the object have same angular speed and the linear speed.

Answer to Problem 1CQ

All the points on the objects have same angular speed and all the points on the object have different linear speed.

Explanation of Solution

The rigid object rotates about the fixed axis then the points of rotation remains fixed and all other point of the rigid object rotates about that fixed point with same angular velocity. If it is not present in the rigid object then the shape of the rigid object is distorted due to the relative between points which causes the shear strain.

Write the expression for the linear velocity.

$v=r\omega$

Here,

$r$ is the radial distance.

$\omega$ is the angular speed.

Since the angular velocity is same for all the points of the rigid object but the radial distance changes for all points of the rigid object due to which the linear speed is varied.

Conclusion:

Therefore, all the points on the objects have same angular speed and all the points on the object have different linear speed.