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 - Page 112: 27


(a) $v = 30~km/s$ (b) $\omega = 2.0\times 10^{-7}~rad/s$ (c) $a_c = 6.0\times 10^{-3}~m/s^2$

Work Step by Step

(a) We can find the speed of the earth as: $v = \frac{d}{t}$ $v = \frac{2\pi~r}{t}$ $v = \frac{(2\pi)(1.5\times 10^{11}~m)}{(365)(24)(3600)~s}$ $v = 30000~m/s = 30~km/s$ (b) $\omega = \frac{v}{r}$ $\omega = \frac{30000~m/s}{1.5\times 10^{11}~m}$ $\omega = 2.0\times 10^{-7}~rad/s$ (c) $a_c = \frac{v^2}{r}$ $a_c = \frac{(3.0\times 10^4~m/s)^2}{1.5\times 10^{11}~m}$ $a_c = 6.0\times 10^{-3}~m/s^2$
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