A rectangular plate of length $L$, width $B$ and mass $M$ rotates with angular velocity $\mathrm{\omega }$, about an axis in the $x-y$ plane. The axis of rotation passes through the centre of mass and cuts the length of the plate at an acute angle $\mathrm{\theta }$. Find the angular momentum about $z$-axis.

A rectangular plate of length $L$, width $B$ and mass $M$ rotates with angular velocity $\mathrm{\omega }$, about an axis in the $x-y$ plane. The axis of rotation passes through the centre of mass and cuts the length of the plate at an acute angle $\mathrm{\theta }$.

A solid cube $ABCD$ of side $a$ and mass $M$ is placed on a rough horizontal surface. A bullet of mass $m$ and speed $V$ is shot at the top of the cube so that the cube rotates about point $D$. The bullet sticks to the cube, $m\ll M$. Find the angular velocity of the cube.

A ring of mass $m$ and radius $R$ is rolling down a rough inclined plane of angle $\mathrm{\theta }$ with horizontal. Plot the angular momentum of the ring about the point of contact of the ring and the plane as a function of time.

The angular momentum of the disc which spins with $\overrightarrow{w}=\frac{\mathit{3}v}{R}\hat{\mathrm{k}}$ and its CM moves with velocity$\overrightarrow{\mathrm{v}}=v\hat{\mathrm{i}}$ about $O$, will be?

A particle is moving along a line$y=x+a$ with a constant velocity$v$. Find the angular momentum of the particle about the origin.

Two men of equal masses stand at opposite ends of the diameter of a turn table disc of a certain mass, moving with a constant angular velocity. The two men make their way to the middle of the turntable at equal rates. In doing so