Two particles $A$ and $B$ are moving as shown in the figure. Their total angular momentum about the point $O$ is

$A$ 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

$A$ particle of mass $m$ is moving along a straight line parallel to the $x$-axis with a constant velocity $v$ at a distance $b$ from the origin. Find the angular momentum about the origin in vector form.

Does the angular momentum of a body change when its axis of rotation changes? Why?

Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of $A$ and $B$ about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = I_B/4$ and $E_A = 100 E_B$,the ratio of angular momentum $(L_A)$ of $A$ to the angular momentum $(L_B)$ of $B$ is

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