Question

A round disc of the moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of the moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is

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

Answer 1

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

Let the final angular velocity of the combination be $w_f$.

Since no external torque is acting on the system, so angular momentum of the system is conserved.

Applying the conservation of angular momentum : $L_f=L_i$

$\therefore$ $(I_1+I_2)w_f=I_{1}w+I_2\times 0$

$⟹w_f=\frac{I_{1}w}{I_1+I_2}$