$A$ 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 $O$?

As shown in the figure,a particle of mass $m$ moves with a velocity $v$ along the line $PC$. What is the angular momentum of this particle with respect to point $P$?

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.

$A$ thin uniform rod of length $L$ and mass $m$ is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$. If a horizontal impulse $P$ is imparted to the rod at a distance $x = L/n$ from the mid-point of the rod (see figure), then the rod and string revolve together around the point $O$, with the rod remaining aligned with the string. In such a case, the value of $n$ is:

Angular momentum is

Derive the equation of angular momentum in the case of rotational motion about a fixed axis.