A disc is fixed at its centre O and rotating with constant angular velocity $ω$ . There is a rod whose one end is connected at A on the disc and the other end is connected with a ring which can freely move along the fixed vertical smooth rod. At an instant when the rod is making an angle 30^o with the vertical the ring is found to have a velocity $2 \sqrt{3} m / s$ in the upward direction. Find $ω$ of the disk. Given that the point A is at $\frac{R}{2}$ distance above point O and length of $l$ the AB is l. (R = 2m)

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Detailed Solution

By using constraint relation along the rod
$v \cos θ = \frac{ω R}{2} \cos 60 \Rightarrow ω = \frac{2 v \sqrt{3}}{R}$

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