Suppose that at time t (during the sliding motion) the angular velocity of the hoop is . The torque exerted by the frictional force F is Fr. By Newton's second law for rotational motion, (m is the mass of the hoop). Therefore . Integrate that to get .

Let v be the translational velocity of the hoop at time t. The frictional force is the only horizontal force acting on the hoop, so by Newton's second law (the ordinary second law, for linear motion) . Integrate that to get .

The hoop will stop sliding when . That happens when , which simplifies to . At that time, (slightly different from the answer that you wanted).