You are designing a lathe motor, part of which consists of a uniform cylinder whose mass is 90 kg and whose radius is 0.40m that is mounted so that it turns without friction on its axis, which is fixed. The cylinder is driven by a belt that wraps around its perimeter and exerts a constant torque. At t=0, the cylinder's angular velocity is zero. At t=25 s, its angular speed is 500rev/min. (a) What is the magnitude of the cylinder's angular momentum at t=25sec? (b) At what rate is the angular momentum increasing? (c) What is the magnitude of the torque acting on the cylinder? (d) What is the magnitude of the frictional force acting on the rim of the cylinder?