A particle of mass $m$ is projected with a velocity $v$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is

$A$ time varying force $F = 2t$ is applied on a spool rolling as shown in figure. The angular momentum of the spool at time $t$ about bottommost point is:

A ring of mass $M$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{ M }{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is $\frac{8}{9} \omega$ and one of the masses is at a distance of $\frac{3}{5} R$ from $O$. At this instant the distance of the other mass from $O$ is

Given $V _{ CM }=2\; m / s , m =2\; kg , R =4\; m $

Find angular momentum of ring about origin if it is in pure rolling. $kgm ^{2} / s$

A $bob$ of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The $bob$ rotates in a horizontal circle with an angular speed $\omega\,  rad/s$ about the vertical. About the point of suspension

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and Length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2\  \mathrm{Ns}$ is applied to end $B.$ The time taken by the rod to turn through at right angles will be $\frac{\pi}{\mathrm{x}}\  \mathrm{s}$, where  X=____