Consider the case of a hoop that has a radius R = 0.5 m and mass m = 10 kg, placed at the top of a ramp inclined at an angle of 30and 10 m long. The coefficient of kinetic friction between the hoop and the ramp is 0.1. (The moment of inertia in this case is I = 2 mR2).

Find the time it takes for the hoop to roll down from the top to bottom and the time it takes for the hoop to slide down on its side from top to bottom.