Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 9 - Rotational Dynamics - Focus On Concepts - Page 242: 13

Answer

a) is correct.

Work Step by Step

According to Newton's 2nd law of rotational motion, $$\sum\tau=I\alpha$$ $$Fr=Mr^2\alpha$$ $$\alpha=\frac{F}{Mr}$$ The smaller hoop's angular acceleration $$\alpha_s=\frac{F}{MR}$$ The larger hoop's angular acceleration $$\alpha_l=\frac{F}{M2R}=\frac{1}{2}\alpha_s$$ So the smaller hoop's angular acceleration is twice as great as that of the larger hoop. a) is correct.
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