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 298: 9.63

Answer

(a) $v = 1.70~m/s$ (b) $\omega = 94.4~rad/s$

Work Step by Step

(a) We can find the tangential speed of a point on the edge of the shaft. Note that this will be the same speed as the belt. $v = \omega ~r = (60.0~rev/s)(2\pi~rad/rev)(0.45~cm)$ $v = 170~cm/s = 1.70~m/s$ (b) We can use the tangential speed to find the angular velocity of the wheel. $\omega = \frac{v}{r} = \frac{1.70~m/s}{0.0180~m}$ $\omega = 94.4~rad/s$
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