$A$ uniform rod of mass $M$ and length $L$ has an impulse $J$ applied at right angles to one end. If the other end begins to move with speed $V$,the magnitude of the impulse is:

$A$ uniform rod of mass $8m$ and length $6a$ is placed on a horizontal table. Two point masses $m$ and $2m$ are moving with speeds $2v$ and $v$ respectively,as shown in the figure. They strike the rod and stick to it after the collision. Find the angular velocity of the rod about an axis passing through its center of mass.

Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.

The units of angular momentum are

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

$A$ cylinder of mass $5 \ kg$ and radius $30 \ cm$ is free to rotate about its axis. It receives an initial angular impulse of $3 \ kg \ m^2 s^{-1}$ and subsequently receives the same impulse every $4 \ s$. What will be the angular speed of the cylinder $30 \ s$ after the initial impulse? The cylinder is initially at rest.