Question

A round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I1 rotating with an angular velocity w about the same axis. The final angular velocity of the combination of discs is:

• A. $\frac{I_{2}\omega}{{I瘀}_{簀}}$
• B. w
• C. $\frac{I_{1}\omega}{I_{1} + I_{2}}$
• D. $\frac{(I_{1} + I_{2})\omega}{I_{樀}}$

Answer 1

Answer: (C)

$\frac{I_{1}\omega}{I_{1} + I_{2}}$

Answer 2

According to conservation of angular momentum $\because\mspace{6mu} I_{1}\omega_{1} = I_{2}\omega_{2}$ ⇒ $I_{1}\omega = (I_{1} + I_{2})\omega_{2}$ ⇒ $\omega_{2} = \frac{I_{1}\omega}{I_{1} + I_{2}}$