Question

A circular disc of mass $M_1$ and radius $R$, initially moving with a constant angular speed ${\omega }_0$ is gently placed coaxially on a stationary circular disc of mass $M_2$ and radius $R$, as shown in Figure. There is a frictionless force between the two discs.
If disc $M_2$ is placed on a smooth surface, then determine the final angular speed of each disc.

Answer 1

By conservation of angular momentum

$I_0{\omega }_0=I_f{\omega }^{\prime }$

$\frac{M_1{R}^2{\omega }_0}{2}=\frac{(M_1+M_2)R^2}{2}{\omega }_{final}$

${\omega }_{final}=\left(\frac{M_1}{(M_1+M_2)}\right){\omega }_0$