Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 8 - Rotational Kinematics - Problems - Page 215: 47


a) $\omega=1.99\times10^{-7}rad/s$ b) $v_T=2.99\times10^4m/s$ c) $a_c=5.96\times10^{-3}m/s^2$

Work Step by Step

We have $\Delta t=3.16\times10^7s$ for $\Delta\theta=1rev=2\pi rad$ and $r=1.5\times10^{11}m$ a) The Earth's angular speed is $$\omega=\frac{\Delta \theta}{\Delta t}=1.99\times10^{-7}rad/s$$ b) The Earth's tangential speed is $$v_T=\omega r=2.99\times10^4m/s$$ c) The Earth's centripetal acceleration is $$a_c=\frac{v_T^2}{r}=5.96\times10^{-3}m/s^2$$
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