A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity '. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

\(\frac{\omega M}{M+2m}\)

Since, no external torque is applied, angular momentum is constant.

\(I_1\omega_1 = I_2\omega_2\)

\(I_1 = MR^2 ; I_2 = MR^2 + 2mR^2\)

\(\omega_2 = \frac{I_1}{I_2}\omega = \frac{M}{M+2m}\omega\)