A spool of thread of mass m rests on a plane inclined at angle (. The end of the thread is tied as shown. The outer radius of the spool is R and the inner radius (where the thread is wound) is r. The rotational inertia of the spool is I. Give all answers in terms of m, (, R, r, I, and g.
(a) If there is no friction between the spool and the incline, describe the motion of the spool and calculate its acceleration.
(b) If the coefficient of friction is large enough to keep the spool from slipping, calculate the magnitude and direction of the frictional force.
(c) What is the minimum possible coefficient of friction to keep the spool from slipping in part (b)?