Question

A thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimension but of mass $M/4$ is placed gently on the first disc coaxially. Find the angular velocity of the system.

Answer 1

Angular velocity of system initially$=\omega$

Angular momentum initial$\left(L_0\right)=I\omega =\frac{M{R}^2}{2}\omega$

Angular momentum final $\left(L\right)=I^{\prime }{\omega }^{\prime }=(\frac{M{R}^2}{2}+\frac{M{R}^2}{8}){\omega }^{\prime }$

According to conservation of angular momentum

$L_0=L\Rightarrow \frac{M{R}^2}{2}\omega =\frac{5M{R}^2}{8}{\omega }^{\prime }$

$\Rightarrow {\omega }^{\prime }=\frac{4}{5}\omega$