Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 12 - Rotation of a Rigid Body - Conceptual Questions - Page 347: 5

Answer

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Work Step by Step

The moment of inertia depends on two factors, the mass distribution and the mass distance from the axis of rotation. And we know that the farther the mass from the axis of rotation, the greater the moment of inertia of the object. In the first case, when we measured the moment of inertia of the rod around its center of mass, the mass is uniformly distributed around its center of mass from both sides. But in the second case, when we measured the moment of inertia of the rod around one end, most of the mass is on one side and the mass is farther away from the axis of rotation. It is the same case as the difference in inertia between a disk and a hoop of the same mass and same radius. The hoop is a thin cylindrical shell where the mass is concentrated on the shell. The hoop has twice the inertia of the disk. And hence, the inertia in the second case is greater than that in the first case.
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