While spinning down from 500 rpm to rest, a flywheel does 3.9 kj of work. this flywheel is in the shape of a solid uniform disk of radius 1.2 m. what is the mass of this flywheel?

The answer is 4.0 kg since the flywheel comes to rest the kinetic energy of the wheel in motion is spent doing the work. Using the formula KE = (1/2) I w².

Given the following:

I = the moment of inertia about the axis passing through the center of the wheel; w = angular velocity; for the solid disk as I = mr² / 2 so KE = (1/4) mr²w². Now initially, the wheel is spinning at 500 rpm so w = 500 * (2*pi / 60) rad / sec = 52.36 rad / sec.

The radius = 1.2 m and KE = 3900 J

3900 J = (1/4) m (1.2) ² (52.36) ²

m = 3900 J / (0.25) (1.2) ² (52.36) ²

m = 3.95151 ≈ 4.00 kg