Rotational Inertia and Torque-A solid uniform cylinder, of mass M and radius R, is rolling down without slipping (static friction), on the surface inclined with an angle = 30° from the horizontal plan. (20 points)
A. Derive the the formula of the rotational inertial for the solid cylinder, I = ½MR^2 as seen in Table 10-2 (c) from the definition of rotational inertia, I = 1/2MR^2 dm.
B. Find all forces in a vector form (choose a coordinate system) and torques from those forces.
C. Calculate the magnitude of the acceleration of the cylinder.
D. If 30° is the maximum angle without slipping, what is the static coefficient of friction between the cylinder and surface, u,s?