$(25$ pts $)$ The solid homogeneous cylinder is released from rest on the ramp. Assume $=45$ and there is no slip. Determine the following:

a$)$ The acceleration of the mass center $a_G$;

b$)$ The angular acceleration of the cylinder $$;

c$)$ The normal force and friction force

d$)$ The minimal static friction coefficient to make sure there is no slip.