Physics - Chapter 3 #76

Question

Physics - Chapter 3 #76

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

Answer 1

Given:

r = 0.75m

m = 250kg

ω(max) = ω(final) = 1200rpm * 1min/60s = 20rev/s

τ = 50Nm

Formula for angular velocity:

ω(f) = ω(i) + α*t

ω(f) = 0 + (τ / I) * t

ω(f) = [τ / (m*r²/2)] * t

ω(f) = (2*τ*t) / (m*r²)

Rearrange:

t =  [ω(f) * m * r²] / [2 * τ]

Plug & chug...