College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 5 - Problems - Page 185: 6


(a) The ball has turned through 18.5 revolutions. (b )The ball's angular speed is $18.1~rad/s$

Work Step by Step

(a) We can find the angle $\theta$ through which the ball has rotated: $\theta = \frac{d}{r} = \frac{18~m}{0.155~m} = 116~rad$ We can convert from units of radians to revolutions: $116~rad \times \frac{1~rev}{2\pi~rad} = 18.5~rev$ The ball has turned through 18.5 revolutions. (b) We can find the ball's angular speed: $\omega = \frac{v}{r} = \frac{2.8~m/s}{0.155~m} = 18.1~rad/s$ The ball's angular speed is $18.1~rad/s$.
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