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
$I=m_1{v}_1{R}_1+m_2{v}_2{R}_2+...$
$=m_1\left(\omega R_1\right)R_1+m_2\left(\omega R_2\right)R_2+...$
$=m_1{R}_1^2\omega +m_2{R}_2^2\omega +\dots$
or $\left(\Sigma m{R}^2\right)\omega =I\omega$
(where $I$ is $m{r}^2)$