Question

A uniform rod of mass in and length l can rotate freely on a smooth horizontal plane about a vertical axis hinged at point $H$. A point mass having same mass $m$ coming with an initial speed $u$ perpendicular to the rod, strikes the rod in elastically at its free end. Find out the angular velocity of the rod just after collision?

Answer 1

Angular momentum is conserved about $H$, because no external force is present in horizontal plane which is producing torque about $H$.

We have the equation,

$mul=(\frac{m{l}^2}{3}+m{l}^2)\omega$

Where,

$m$ is mass

$u$ is initial speed

$l$ is length

$\omega$ is angular velocity

That is,

Angular velocity, $\omega =\frac{3a}{4l}$