What work needs to be done so that a flywheel with a mass of m = 0.6 t, distributed over a rim with a diameter

What work needs to be done so that a flywheel with a mass of m = 0.6 t, distributed over a rim with a diameter of d = 1.6 m, rotates with a frequency of ν = 240 rpm?

To find out the work required to communicate the required speed to the flywheel, consider the formula (we consider the flywheel as a disk and its moment of inertia I = mm * R ^ 2/2): Ax = I * Δω ^ 2/2 = (mm * R ^ 2 / 2) * (2 * Π * ν) ^ 2/2 = mm * R ^ 2 * Π ^ 2 * ν ^ 2, where mm is the mass of the flywheel (mm = 0.6 t = 600 kg); R is the radius of the flywheel (R = d / 2 = 1.6 / 2 = 0.8 m); ν is the required frequency (ν = 240 rpm = 4 rpm).

Let’s perform the calculation: Ax = mm * R ^ 2 * Π ^ 2 * ν ^ 2 = 600 * 0.8 ^ 2 * 3.14 ^ 2 * 42 ≈ 60.6 * 103 J.

Answer: To inform the flywheel of the required speed, work must be done at 60.6 kJ.