Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg . Its maximum angular velocity is 1200 rpm. A motor spins up the flywheel with a constant torque of 50 N-m.

1. What is the moment of inertia of the flywheel?
2. What is the angular acceleration of the flywheel?
3. What is the maximum velocity of the flywheel in rad/s?
4. How long does it take the flywheel to reach its maximum speed?