Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 69

Answer

(a) $v = \sqrt{2\alpha \Delta \theta}~R$ (b) $a_c = (2\alpha \Delta \theta) ~R$

Work Step by Step

(a) We can find the angular velocity after the wheel rotates through an angle of $\Delta \theta$: $\omega^2 = \omega_0^2+2\alpha \Delta \theta$ $\omega^2 = 0+2\alpha \Delta \theta$ $\omega = \sqrt{2\alpha \Delta \theta}$ We can find the velocity. $v = \omega ~R = \sqrt{2\alpha \Delta \theta}~R$ (b) We can find the centripetal acceleration: $a_c = \omega^2 ~R$ $a_c = (\sqrt{2\alpha \Delta \theta})^2 ~R$ $a_c = (2\alpha \Delta \theta) ~R$
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