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A small 2-kg collar C can slide freely on a thin ring of mass 3 kg and radius 250 mm. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially the ring has an angular velocity of 35 rad/s and the collar is at the top of the ring (θ= 0) when it is given a slight nudge. Neglecting the effect of friction, determine

(a) the angular velocity of the ring as the collar passes through the position θ = 90°,

(b) the corresponding velocity of the collar relative to the ring.

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