Question

The angular momentum of a body with mass $ m, $ moment of inertia $I$ and angular velocity $ \omega\, rad/\sec$ will be equal to:

• A. $ I/\omega^{2}$
• B. $ I/\omega $
• C. $ I\omega $
• D. $ I\omega ^{2}$

Answer 1

Answer: (C)

Moment of inertia of body $=I$
Angular velocity of body $=\omega rad / \sec$
Then angular momentum of the body is
$I =m_{1} v_{1} R_{1}+m_{2} v_{2} R_{2}+...$
$=m_{1}\left(\omega R_{1}\right) R_{1}+m_{2}\left(\omega R_{2}\right) R_{2}+...$
$=m_{1} R_{1}^{2} \omega+m_{2} R_{2}^{2} \omega+\ldots$
or $\left(\Sigma m R^{2}\right) \omega=I \omega$
(where $I$ is $\left. m r^{2}\right)$