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  4. A circular disc is rotating about its own axis at uniform angular velocity ω. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω/2 during 120 rotations. The number of rotations further made by it before coming to rest is

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Q. A circular disc is rotating about its own axis at uniform angular velocity $\omega.$ The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\omega/2$ during 120 rotations. The number of rotations further made by it before coming to rest is

Solution:

$\alpha $ is constant
$\alpha = \frac{\omega_1^2 - \omega_2^2}{2 \theta}$
$\frac{\omega - \left( \frac{\omega}{2} \right)^2 }{2 \theta_1} = \frac{\left( \frac{\omega}{2}\right)^2 - 0}{2\theta_2}$
$\theta_2 = \frac{\theta_1}{3}$