Question

A uniform heavy disc of moment of inertia $I_1$ is rotating with constant angular velocity ${\omega }_1$. Then, a second nonrotating disc of moment of inertia $I_2$ is dropped on it. The two discs rotate together. The final angular velocity of the system becomes

• A. $\frac{I_1{\omega }_1}{I_2}$
• B. $\sqrt{\frac{I_1}{I_2}}{\omega }_1$
• C. $\frac{I_1{\omega }_1}{I_1+I_2}$
• D. $\frac{(I_1-I_2){\omega }_1}{I_1+I_2}$

Answer 1

The correct option is C $\frac{I_1{\omega }_1}{I_1+I_2}$

Since no torque acts on the system, using the principle of conservation of angular momentum
or
$I_1{\omega }_1=(I_1+I_2){\omega }_2$
or
${\omega }_2=\frac{I_1{\omega }_1}{I_1+I_2}$