Question

A circular disc is rotating without friction about its natural axis with an angular velocity $\omega$. Another circular disc of same material and thickness but half the radius is gently placed over it coaxially. The angular velocity of composite disc will be :

• A. $\frac{4\omega }{5}$
• B. $\frac{8w}{9}$
• C. $\frac{7w}{8}$
• D. $\frac{16w}{17}$

Answer 1

The correct option is D $\frac{16w}{17}$

Let the mass of bigger disc be $M=\pi R^{2}t\rho$

Let the mass of smaller disc be $m=\pi (R/2{)}^{2}t\rho =M/4$

Using conservation of angular momentum

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

${\omega }_1=\frac{16\omega }{17}$