Chapter 12, Problem 23A

Mei Fan says that a basketball has greater rotational inertia than a solid ball of the same size and mass because most of a basketball’s mass is far from its center. Ashley says no, that the center of mass of any uniform ball is at its center, and mass distribution doesn’t matter. Whom do you agree with?

To determine

To identify: Whether the argument of person M or A is correct.

Answer to Problem 23A

M is correct because the basketball has greater rotational inertia than a solid ball.

Explanation of Solution

Introduction:

An increase in rotational inertia of an object would decrease its rotation rate.Angular momentum $L$ is always conserved.

  $L=I\omega$

Where $I$ is Rotational Inertia and $\omega$ is angular velocity.

In basketball, the center of its mass is concentrated far from the center. This increases its rotational inertia and results in a decrease in the angular velocity. But, in the solid ball of equal mass, its center of mass is concentrated at the center which decreases its rotational inertia results in increasing its rotational kinetic energy.

Conclusion:

Hence, the argument of person M is correct as the farther the center of mass from its center, the more will be its rotational inertia.