Sliping hoop

Classical Mechanics Level pending

An upright hoop is projected on a pavement with initial horizontal speed \( v_{0} \) but without spin (so that it is sliding). The resulting frictional force causes the hoop to spin to lose translational speed and to acquire an angular speed. Eventually the hoop rolls without slipping, and let \( \mu \) be the coefficient of friction. Find the time taken by the hoop to start rolling without slipping.

The gravitational acceleration is \( g.\)

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