Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 12 - Rotation of a Rigid Body - Exercises and Problems: 8

Answer

The speed of the 100-g ball is 2.5 m/s

Work Step by Step

Let the 100-g ball be at the position x = 0. Let the 200-g ball be at the position x = 30 cm. We can find the center of mass $x_{com}$ of the system. $x_{com} = \frac{(100~g)(0)+(200~g)(30~cm)}{100~g+200~g}$ $x_{cm} = 20~cm$ We can find the angular velocity of the system. The system rotates at 120 rpm which is 2 rev/s which is $4\pi ~rad/s$. Therefore, $\omega = 4\pi ~rad/s$ We can find the speed of the 100-g ball. Note that its radius of rotation is 20 cm. $v = \omega ~r$ $v = (4\pi~rad/s)(0.20~m)$ $v = 2.5~m/s$ The speed of the 100-g ball is 2.5 m/s.
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