Question

A particle of mass $m$ is released from rest at point $A$ in Figure, falling parallel to the (vertical) y-axis. Find the angular momentum of the particle at any time $t$ with respect to the same origin $O$.

Answer 1

Angular momentum of particle about

$0=\overrightarrow{r}\times \overrightarrow{p}=m(\overrightarrow{r}\times \overrightarrow{v})$

$=m{x}_{0}v$

$v=0+\frac{1}{2}g{t}^2\Rightarrow$

$L_0=\frac{m{x}_{0}g{t}^2}{2}$