Avery light string is wound around a cylindrical spool of inertia m and radius r. the cylinder rotates on a frictionless horizontal axis with a moment of inertia 1mr2. attached to the end of the string is a block of inertia 2m, which pulls on the string and unwinds it from the cylinder, as the block falls.

(a) draw an extended free-body diagram for the cylinder, and a regular free-body diagram for the block.
(b) let m = 5kg, m = 2kg, and r = 6cm. what is the acceleration of the block as it falls?
(c) what is the tension on the string?
(d) after the block has dropped 30cm, starting from rest, what is the total kinetic energy of the system, and how is it distributed between the block and the cylinder?