Question

Angular momentum of a body is defined as the product of

• A. mass and angular velocity
• B. centripetal force and radius
• C. linear velocity and angular velocity
• D. moment of inertia and angular velocity

Answer 1

The correct option is D moment of inertia and angular velocity

The angular momentum of a moving particle about a point is defined as ;
$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$
As, $\overrightarrow{p}=m\overrightarrow{v}\therefore \overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})$
In case of circular motion of a particle
$\overrightarrow{L}=mvr\sin {90}^{\circ }\hat{n}$
where $\hat{n}$ is the unit vector perpendicular to the plane of motion in accordance with right hand screw rule.
$\overrightarrow{L}=m\left(r\omega \right)r\hat{n}(\therefore v=r\omega )$
$=m{r}^2\omega \hat{n}$
$\overrightarrow{L}=I\overrightarrow{\omega }$ [as $m{r}^2=I$ and $\omega \hat{n}=\overrightarrow{\omega }$]
Hence, the correct answer is option (d).