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 4 - Kinematics in Two Dimensions - Exercises and Problems: 73

Answer

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

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; $v = \omega ~R = R\sqrt{2\alpha \Delta \theta}$ (b) We can find the centripetal acceleration; $a_c = \omega^2 ~R$ $a_c = (\sqrt{2\alpha \Delta \theta})^2 ~R$ $a_c = R(2\alpha \Delta \theta) $
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