A circular hoop of mass m, radius r, and infinitesimal thickness rolls without slipping down a ramp inclined at an angle with the horizontal.
Part A:
What is the acceleration a of the center of the hoop?
Express the acceleration in terms of physical constants and all or some of the quantities m, r, and .
Part B:
What is the minimum coefficient of (static) friction needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, since the bottom point on the wheel is not moving relative to the ground (this is the meaning of no slipping).
Express the minimum coefficient of friction in terms of all or some of the given quantities m, r, and .
and the angular acceleration α. 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.
