$A$ ball of mass $m$ moving with velocity $v$ collides with a wall elastically as shown in the figure. After the impact,the change in angular momentum about point $P$ is:

$A$ mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is $L$. If the length of the string is now halved, keeping the angular velocity the same, then the angular momentum will be:

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

$A$ 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 $O$?

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.

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ are denoted by $\vec{L}_O$ and $\vec{L}_P$ respectively,then