Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 12 - Rotation of a Rigid Body - Conceptual Questions - Page 347: 13

Answer

Less than.

Work Step by Step

We know that the angular momentum is given by $$L=I\omega$$ Thus, $$\dfrac{L_a}{L_b}=\dfrac{I_a\omega_a}{I_b\omega_b}$$ Recalling that the moment of inertia of a disk is given by $$I=\frac{1}{2}mR^2$$ Thus, $$\dfrac{L_a}{L_b}=\dfrac{\color{red}{\bf\not} \frac{1}{2}m_aR_a^2\omega_a}{\color{red}{\bf\not} \frac{1}{2}m_bR_b^2\omega_b}$$ Plugging from the data in the given figure. $$\dfrac{L_a}{L_b}=\dfrac{ \color{red}{\bf\not} m r_a^2\omega_a}{ \color{red}{\bf\not} m(2r_a)^2(\frac{1}{2}\omega_a)}=\dfrac{\color{red}{\bf\not} r_a^2\color{red}{\bf\not} \omega_a}{2\color{red}{\bf\not} r_a^2\color{red}{\bf\not} \omega_a}$$ Hence, $$\boxed{L_b=2L_a}$$ Therefore, the angular momentum of disk a is less than the angular momentum of disk b.
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