Question

A small ball 'A' of mass 'm' is attached rigidly to the end of a light rod of length 'd'. The structure rotates with about an axis perpendicular to the rod and passing through its other end with an angular velocity '$\omega$'. Calculate the angular momentum of the system about this axis?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Angular momentum of A about the axis of rotation,

$\overrightarrow{L}=\overrightarrow{r}X\overrightarrow{p}\{here\overrightarrow{r}\perp \overrightarrow{p}\}$
$\left|\overrightarrow{L}\right|\Rightarrow rpsin{90}^{\circ }=rp$

Now, the magnitude oflinear velocity of A, which is d units apart from axis of rotation = mv

By Rotational Kinematics, we know clearly,

$V=\omega r$

$\Rightarrow$ $v=\omega d$.
$\Rightarrow \left|\overrightarrow{L}\right|=m\omega d^2$ $\{\left|\overrightarrow{L}\right|=mvr\}$

Directed along the Axis of Rotation.