A solid cylinder of mass M = 5 kg and radius R = 20 cm is mounted on a frictionless horizontal axle over a well. A rope of uniform linear mass density, lm = 0.50 kg/m, and total length L = 15 m is wrapped around the cylinder and supports a small bucket of m = 0.25 kg and negligible dimensions compared to the length of the rope. Initially, the rope is entirely wrapped around the cylinder and the bucket is at rest. Find a symbolic expression for the acceleration of the bucket as it falls down the well.