Write the general formula of total angular moment of rotational motion about a fixed axis.

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

A particle of mass $m$ projected with a velocity ' $u$ ' 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 $\mathrm{h}$ is :

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

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

$A$ 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: