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A circular annulus, of mass M, inside radius a and outside radius 2a, is given an angular speed w about an axis, through its center perpendicular to its plane, which is horizontal. It is then gently p...

A circular annulus, of mass M, inside radius a and outside radius 2a, is given an angular speed w about an axis, through its center perpendicular to its plane, which is horizontal. It is then gently placed on a rough horizontal plane, the coefficient of friction being u. Show that the annulus will start rolling without slipping after a time (10aw/13ug). The experiment is repeated in a space craft on a circular orbit around the earth. State giving reasons, whether or not the annulus will still roll without slipping after the same time interval.

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