A (30-mathrm{kg}) solid sphere of radius (0.12 mathrm{~m}) is rolling without slipping on a horizontal surface at

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A \(30-\mathrm{kg}\) solid sphere of radius \(0.12 \mathrm{~m}\) is rolling without slipping on a horizontal surface at \(2.0 \mathrm{~m} / \mathrm{s}\).

(a) What average torque is required to stop the sphere in \(5.0 \mathrm{rev}\) without inducing skidding?

(b) If this torque is caused by a soft braking bumper that is lowered down until it just makes contact with the top of the sphere, what is the magnitude of the frictional force between bumper and sphere?

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