Learning Goal: To apply the equations of general plane motion to describe the motion of a symmetric rigid body. As shown, a circular hoop of mass m, radius r, and infinitesimal thickness rolls, without slipping, down a ramp that is inclined at an angle ? with the horizontal. (Figure 1) Figure 1: A hoop rolling down an inclined plane with an angle theta with the horizontal axis x, and its center labeled with mass m and radius r. Part A: What is a, the acceleration of the hoop’s center? Express your answer in terms of some or all of the variables m, ?, and g, the acceleration due to gravity. Part B: What is the minimum coefficient of static friction, ?_min, needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, because the bottom point on the hoop is not moving relative to the ground (which is what it is meant by no slippage). Express your answer in terms of all or some of the variables m, r, and ?.