Which graph represents the relationship between angular momentum $L$ and angular velocity $\omega$ for a rigid body rotating about a fixed axis?

Two particles,each of mass $m$ and speed $v$,travel in opposite directions along parallel lines separated by a distance $d$. Show that the angular momentum vector of the two-particle system is the same whatever be the point about which the angular momentum is taken.

Obtain the relation between torque of a system of particles and angular momentum.

$A$ particle of mass $100\,g$ is projected at time $t = 0$ with a speed $20\,ms^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t = 2\,s$ is found to be $\sqrt{K}\,kg\,m^2/s$. The value of $K$ is $............$ (Take $g = 10\,ms^{-2}$)

$A$ particle is moving along a straight line parallel to $x-$ axis with constant velocity. Its angular momentum about the origin

$A$ particle of mass $m$ is moving in time $t$ on a trajectory given by $\overrightarrow{r} = 10 \alpha t^2 \hat{i} + 5 \beta (t - 5) \hat{j}$. Where $\alpha$ and $\beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for $t = 0$ at time $t = \dots$ seconds.