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 228: 90

Answer

a) $\omega_f=1.09\times10^5\frac{rad}{s}$ b) $\omega_f=8.15\times10^4\frac{rad}{s}$

Work Step by Step

$I_i=I_f$ $I=\frac{2MR^2}{5}$ $\omega_i=\frac{1 rev}{9 days}\times\frac{2\pi rad}{1 rev}\times\frac{1 day}{86,400s}=8.08\times10^{-6}\frac{rad}{s}$ $\frac{2M_iR_i^2}{5}\omega_i=\frac{2M_fR_f^2}{5}\omega_f$ $\frac{2(8M_s)(6.96\times10^8m)^2}{5}(8.08\times10^{-6}\frac{rad}{s})=\frac{2(2M_s)(1.2\times10^4m)^2}{5}\omega_f$ $\omega_f=\frac{4(6.96\times10^8m)^2(8.08\times10^{-6}\frac{rad}{s})}{(1.2\times10^4m)^2}=108,724\frac{rad}{s}$ b) $108,724\frac{rad}{s}\times\frac{3}{4}=81,543\frac{rad}{s}$
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