Physics - Rotation Question with Solution | TestHub

The angular momentum $\vec{L}$ of a particle about a point is given by $\vec{L}=\vec{r}\times \vec{p}$, where $\vec{r}$ is the position vector from the origin to the particle and $\vec{p}$ is its linear momentum.

Since the particle moves parallel to the x-axis at a distance $y_0$, the perpendicular distance from the origin to the line of action of the linear momentum is $y_0$.

The magnitude of angular momentum is $L=r{p}_{\perp }=r(mv\sin \theta )=mv(r\sin \theta )$.

Here, $r\sin \theta$ is the perpendicular distance from the origin to the line of action of velocity, which is $y_0$. Therefore,

$L=mv{y}_0$.