Consider a pulley of mass M = 4.0 kg and Radius, R = 33cm. There is a bucket of mass, m = 1.53 kg hanging on one side. We assume the cord has negligible mass and does not stretch or slip on the pulley. Assume a frictional torque Tr = 1.10 Nm acts opposing the rotation of the pulley and that the pulley is a cylinder with uniform density. (Hint: The pulley is a rigid body with a moment of inertia that can be referenced.)

1. Get an algebraic expression for the angular acceleration, a, of the pulley in terms of the moment of inertia, the forces and the mass of the bucket.
2. Calculate the linear acceleration, a, and angular acceleration, a, of the bucket.