A hoop of mass m and radius r starts from rest and rolls down an incline at an angle θ. The hoop's inertia is given by IG = mr2. The static friction coefficient is μs. Determine the acceleration of the center of mass aG and the angular acceleration a. Assume that the hoop rolls without bouncing or slipping. Use two approaches to solve the problem:
(a) Use the moment equation about the mass center G and
(b) Use the moment equation about the contact point P.
(c) Obtain the frictional condition required for the hoop to roll without slipping.