Asolid ball is released from rest and slides down a hillside that slopes downward at 65.0" from the horizontal
(a) what minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur?
(b) would the coefficient of friction calculated in part (a) be sufficient to prevent a hollow ball (such as a soccer ball) from slipping? justify your answer.
(c) in part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?

Setting reference frame so that the x axis is along the incline and y is perpendicular to the incline 
X: mgsin65 - F = mAx 
Y: N - mgcos65 = 0 (N is the normal force on the incline) N = mgcos65 (which we knew) 
Moment about center of mass: 
Fr = Iα 
Now Ax = rα 
and F = umgcos65 
mgsin65 - umgcos65 = mrα > gsin65 - ugcos65 = rα (this is the X equation m's cancel) 
umgcos65(r) = 0.4mr^2(α) > ugcos65(r) = 0.4r(rα) (This is the moment equation m's cancel) 
ugcos65(r) = 0.4r(gsin65 - ugcos65) ( moment equation subbing in X equation for rα) 
ugcos65 = 0.4(gsin65 - ugcos65) 
1.4ugcos65 = 0.4gsin65 
1.4ucos65 = 0.4sin65 
u = 0.4sin65/1.4cos65 
u = 0.613 

3is a crest4 is a trough 2 is the amplitude 1 is the wavelength