Solution:

By conservation of angular momentum, \(I_1 \omega_1 = I_2 \omega_2\). Here, \(I_1 = \frac{1}{2} M R^2\) and \(I_2 = \frac{1}{2} M R^2 + m R^2\). Substituting the values: \(1 \times 30 = (1 + 0.25) \omega_2\), which gives \(\omega_2 = 24\text{ rad/sec}\).