Chapter 8, Problem 10Q

Can the mass of a rigid object be considered concentrated at its cm for rotational motion? Explain.

To determine

Whether the mass of a rigid object be considered concentrated at its CM for rotational motion. Solution:

No, the mass of a rigid object cannot be considered concentrated at its CM for rotational motion.

Explanation of Solution

The moment of inertia of an object about an axis depends on the mass of the object as well as the distribution of that mass over the object. If we consider the mass concentrated at the CM and we are calculating the moment of inertia about an axis passing through the CM, the moment of inertia will come out to be zero, which will affect our analysis of the rotational motion of the object. Therefore, we cannot consider the mass to be concentrated at the CM.