Question

A particle moves with a constant velocity parallel to the $Y$ axis. Its angular momentum about the origin

• A. is zero
• B. remains constant
• C. goes on increasing
• D. goes on decreasing

Answer 1

The correct option is B remains constant

As we know, angular momentum
$\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})$
$=mrv\sin \theta =mv\left(r\sin \theta \right)$
or $L=mv{r}_{\perp }$
where $r_{\perp }$ is the perpendicular distance between velocity vector and the point w.r.t which we have to calculate the angular momentum.

Here, particle is moving parallel to $y-$ axis. Hence, the perpendicular distance will be along the $x-$ axis and which will be constant.
So, $r_{\perp }=$ constant, $v=$ constant & $m=$constant
$\Rightarrow L=mv{r}_{\perp }$ remains constant