A solid body starts rotating about a stationary axis with an initial angular velocity $\omega_0 = 36

Question

A solid body starts rotating about a stationary axis with an initial angular velocity $\omega_0 = 36 	ext{ rad/s}$. A braking mechanism is applied such that its angular deceleration is proportional to the square root of its instantaneous angular velocity, governed by the equation $\alpha = -k\sqrt{\omega}$, where $k = 4.0 	ext{ rad}^{1/2}	ext{/s}^{3/2}$.

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