Flywheel Acceleration Time Calc: Solve for Time to Reach Max Speed

[paulsberardi]

Homework Statement

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 Nm. How long does it take the flywheel to reach top speed?

This gave me...
radius = .75m
mass = 250kg
max Angular Velocity = 125.7 radians/second
torque = 50 Nm

Homework Equations

I wasn't sure how to approach the problem. I was trying to figure out how to find angular acceleration, but unsure if that was possible. Please let me know the steps.

 

[rl.bhat]

Torque T = I*α. Find the moment of inertia of the flywheel. Torque is given. Find α, and then t.