Asimple yoyo consists of two large uniform disks, each of radius r and mass m, connected to one another by a light (essentially massless) inner disk of radius r that is sandwiched in between. a string is wound around the inner disk. if one simply holds the string by its upper end, the yoyo disks will start to rotate and move downward (i. e. "fall") as the string unwinds

a) draw a free body diagram of the yoyo.
(b) apply newton’s second law for linear motion to determine the acceleration of the center of mass of the yoyo in terms of the unknown tension in the string. then determine the force of tension in the string as the yoyo falls by applying the rotational form of newton’s 2nd law to the yoyo, noting that the axis of rotation passes through the center of mass perpendicular to the disks. (find ft in terms of m, g, r, and r).
(c) as the yoyo falls, find the linear acceleration of the center of mass in terms of g, r, and r.