University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 9 - Rotation of Rigid Bodies - Problems - Exercises - Page 297: 9.44


$I = \frac{1}{2} mR^2$

Work Step by Step

Let $v$ be the speed of the bucket. $KE_{pulley} = \frac{1}{2}~KE_{bucket}$ $\frac{1}{2}I\omega^2 = \frac{1}{2}\times \frac{1}{2}mv^2$ $I(\frac{v}{R})^2 = \frac{1}{2}\times mv^2$ $I = \frac{1}{2} mR^2$
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