The angular momentum of a body is the product of which of the following?

The position vector of a particle of mass $m$ moving with a constant velocity $\vec{v} = v \hat{i}$ is given by $\vec{r} = x(t) \hat{i} + b \hat{j}$, where $b$ is a constant. At an instant, $\vec{r}$ makes an angle $\theta$ with the $x$-axis. The variation of the magnitude of the angular momentum $|\vec{L}|$ of the particle about the origin with $\theta$ will be:

$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface as shown in the figure. What is the magnitude of the angular momentum of the disc about the origin $O$?

Why is the angular momentum perpendicular to the axis,denoted as ${L_ \bot }$,zero in a rotational motion about a fixed axis?

Angular momentum is

$A$ solid cylinder of mass $2\ kg$ and radius $0.2\ m$ is rotating about its own axis without friction with angular velocity $3\ rad/s$. $A$ particle of mass $0.5\ kg$ and moving with a velocity $5\ m/s$ strikes the cylinder and sticks to it as shown in figure. The angular momentum of the cylinder before collision will be ........ $J-s$.