Question

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis perpendicular to its plane at an angular velocity $\omega$ . Another disc of mass $\frac{M}{3}$ but same radius is placed gently on the first disc coaxially. The angular velocity of the system now is :

• A. $\frac{4\omega }{3}$
• B. $\omega$
• C. $\frac{3\omega }{4}$
• D. $\frac{3\omega }{8}$

Answer 1

Answer: (C)

$\frac{3\omega }{4}$

Since the angular moment will remain conserve, and the final angular velocity of both the disc will be same

$\frac{M{R}^2}{2}\omega =\frac{M{R}^2}{2}{\omega }_1+\frac{\left(M/3\right)R^2}{2}{\omega }_1$

So ${\omega }_1=\frac{3\omega }{4}$