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 - General Problems - Page 227: 81

Answer

(a) $\frac{\omega_R}{\omega_F} = \frac{N_F}{N_R}$ (b) $\frac{\omega_R}{\omega_F} = 4.0$ (c) $\frac{\omega_R}{\omega_F} = 1.5$

Work Step by Step

(a) Let the linear speed be N teeth/s. Note that the linear speed is the same for both sprockets. Therefore, $\omega_R = (\frac{N~teeth/s}{N_R~teeth/rev})(2\pi ~rad/rev)$ $\omega_R = \frac{(2\pi)~N}{N_R}~rad/s$ Similarly, $\omega_F = \frac{(2\pi)~N}{N_F}~rad/s$ We can find the ratio of $\omega_R$ to $\omega_F$. $\frac{\omega_R}{\omega_F} = \frac{N_F}{N_R}$ (b) $\frac{\omega_R}{\omega_F} = \frac{N_F}{N_R} = \frac{52}{13} = 4.0$ (c) $\frac{\omega_R}{\omega_F} = \frac{N_F}{N_R} = \frac{42}{28} = 1.5$
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