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 - Page 226: 72

Answer

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Work Step by Step

There is no net external torque on the disk-rod system, so its net angular momentum is conserved. We assume the rod has no initial angular momentum. The rod sticks, so the final angular velocity is the same for both objects. $$L_{i}=L_{f}$$ $$I_i \omega_i = I_f \omega_f$$ $$\omega_f =\omega_i \frac{I_i }{I_f} $$ $$f_f =f_i \frac{I_i }{I_f} $$ Find the initial and final moments of inertia. $$I_i=\frac{1}{2}MR_{wheel}^2$$ $$I_f=\frac{1}{2}MR_{wheel}^2+\frac{1}{12}M(2R_{wheel})^2$$ The initial frequency is given, so evaluate to find the final frequency. $$f_f =(3.3rev/s) \frac{I_i }{I_f}=(3.3rev/s) \frac{3 }{5}=2.0 rev/s $$
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