$A$ particle is rotating in a circle with uniform speed as shown. The angular momentum of the particle with respect to the origin is .........

$A$ torque of $50 \ Nm$ acts on a body for $8 \ s$,which is initially at rest. The change in its angular momentum is:

Consider a body,shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = Mv$ is imparted to the body at one of its ends,what would be its angular velocity?

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

$A$ 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 $\omega \text{ rad/s}$ about the vertical axis. About the point of suspension:

$A$ point mass $m$ is attached to one end of a string passing through a cylindrical tube. The string is held in hand,and the point mass moves in a horizontal circle of radius $r_1 = 2 \ m$ with a speed of $v_1 = 4 \ m/s$. The string is then pulled down so that the radius is reduced to $r_2 = 1 \ m$. Calculate the new linear velocity,angular velocity,and the ratio of the final kinetic energy to the initial kinetic energy.