Question

Find the approximate kinetic energy of a circular wheel of radius r and mass M that is rotating about its center at 2 cycles/s. Assume the wheel’s mass is concentrated at the rim and the mass of the wheel’s spokes is negligible.

Answer 1

Answer:

$8M(r\pi)^2$

Explanation:

First we convert 2 cycles/s to angular velocity knowing that each circle has an angle of 2π

$\omega = 2 * 2\pi = 4\pi rad/s$

Then we calculate the moment of inertia of the cylindrical shell, assuming there's no mass inside the wheel (only at the rim):

$I = mr^2 = Mr^2$

So the kinetic energy of this is

$E_k = I\omega^2/2 = Mr^2*(4\pi)^2/2 = 8M(r\pi)^2$