Question

A thin and circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity w. If the another disc of same dimensions but of mass M/4 is placed gently on the first disc co-axially, then the new angular velocity of the system is:

• A. 5/4w
• B. 2/3w
• C. 4/5w
• D. 3/2w.

Answer 1

Answer: (C)

4/5w

Answer 2

According to conservation of angular momentum $I_{1}\omega_{1} = I_{2}\omega_{2}$ ⇒ $\frac{1}{2}MR^{2}\omega = \left( \frac{1}{2}MR^{2} + \frac{1}{2}\left( \frac{M}{4} \right)R^{2} \right)\omega_{2}$

∴$\omega_{2} = \frac{4}{5}\omega$