A disc of mass \(2\text{ kg}\) and radius \(0.2\text{ m}\) is rotating with angular velocity \(30\text{ rad/sec}\). If a mass of \(0.25\text{ kg}\) is put gently on periphery of disc then angular velocity of disc is :
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 \(\omega_2 = 24\text{ rad/sec}\).
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