A uniform solid cylinder of mass 2.0kg and radius 0.10m is released from rest at the top of a 30∘ rough incline that is 1.20m long (measured along the slope). The coefficient of static friction is large enough to prevent any slipping during the motion. The cylinder’s moment of inertia about its central axis is I=21Mr2. Neglect air resistance.
(a) Calculate the magnitude of the cylinder’s linear acceleration as it rolls down the incline.
(b) Determine the magnitude of its angular acceleration.
(c) Find the time required for the cylinder to reach the bottom of the incline.
(d) Does the value obtained in part (a) depend on the cylinder’s mass? Provide a brief explanation based on your calculations.