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 - Page 109: 74


(a) $\alpha = 4.0~rad/s^2$ (b) $a_t = 0.12~m/s^2$

Work Step by Step

(a) $\omega = (2.0+\frac{1}{2}t^2)~rad/s$ $\alpha = \frac{d\omega}{dt}$ $\alpha = (t)~rad/s^2$ We can find the angular acceleration at t = 4.0 s: $\alpha = (t)~rad/s^2$ $\alpha = 4.0~rad/s^2$ (b) We can find the tangential acceleration $a_t$ of a tooth on the gear. $a_t = \alpha ~r$ $a_t = (4.0~rad/s^2)(0.030~m)$ $a_t = 0.12~m/s^2$
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