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A circular ring of radius r and mass m is set spinning with angular speed ω0 and then placed on a rough horizontal plane. At the instant it is released, the centre of mass has zero speed. What speed will the centre of the ring have when pure rolling begins and slipping stops?

1. rω0/4
2. rω0/3
3. rω0/2
4. rω0

Correct answer: rω0/2

Solution

Angular momentum about the contact line is conserved: mr^2*w0 = Iw + mvr = mr^2(v/r) + mvr = 2mvr, giving v = r*w0/2.

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