If a particle of mass $m$ is moving with constant velocity $v$ parallel to the $X$-axis in the $x-y$ plane as shown in the figure,its angular momentum with respect to the origin at any time $t$ will be:

$A$ particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line

$A$ particle of mass $m$ moves along line $PC$ with velocity $v$ as shown in the figure. What is the angular momentum of the particle about point $O$?

$A$ particle of mass $m$ is moving in time $t$ on a trajectory given by $\overrightarrow{r} = 10 \alpha t^2 \hat{i} + 5 \beta (t - 5) \hat{j}$. Where $\alpha$ and $\beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for $t = 0$ at time $t = \dots$ seconds.

$A$ body of mass $5 \,kg$ moving with a uniform speed $3 \sqrt{2} \,m/s$ in the $X-Y$ plane along the line $y=x+4$. The angular momentum of the particle about the origin will be . . . . . . $kg \,m^2/s$.

Find the components along the $x, y, z$ axes of the angular momentum $\vec{l}$ of a particle whose position vector is $\vec{r}$ with components $x, y, z$ and momentum is $\vec{p}$ with components $p_x, p_y, p_z$. Show that if the particle moves only in the $x-y$ plane,the angular momentum has only a $z$-component.