Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 8 - Rotational Motion - Problems: 11

Answer

(a) v = 464 m/s (b) v = 185 m/s (c) v = 345 m/s

Work Step by Step

$\omega = (1 \frac{rev}{day})(2\pi \frac{rad}{rev})(\frac{1~day}{24 \times 3600~s}) = \frac{\pi}{43200}~rad/s$ We can use 6380 km as the radius of the Earth. Note that at a latitude of $\theta ^{\circ}$, the radius of rotation is $r = 6380~km\times cos(\theta ^{\circ})$. (a) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km)$ $v = 464~m/s$ (b) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km\times cos(66.5^{\circ}))$ $v = 185~m/s$ (c) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km\times cos(42.0^{\circ}))$ $v = 345~m/s$
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