How long does it take a flywheel to reach top speed question

Question

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 meter 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. How long does it take the flywheel to reach top speed? In seconds and two significant figures.

Answer 1

I = mr^2

= 250 kg * (.75m)^2

w = 1000 rpm * 2 pi / 60 s/min

T = Torque = I *alpha

alpha = T/I

t = w/alpha

t = w I/T

t = (1000 rpm *2pi/60s/min ) (250 kg * (.75m)^2)/ (50 N m)

= 294 sec