How does a flywheel store energy in rotation?

A flywheel can keep a machine turning between separate pushes. Its purpose is to store energy in rotation and exchange some of that energy with a connected shaft. Speeding it up requires work; slowing it down allows some stored energy to be transferred out.

How much energy it stores depends on angular speed and moment of inertia. Angular speed describes how quickly it turns. Moment of inertia describes how its mass is distributed relative to the turning axis: placing the same mass farther from that axis generally increases the inertia.

Rotational kinetic energy is ½Iω². For the supplied moment of inertia of 2 kilogram square meters and angular speed of 10 radians per second, the energy is 100 joules. At 20 radians per second it is 400 joules. Doubling speed quadruples the energy because speed is squared.

When the shaft receives more work than the machine immediately needs, the flywheel speeds up and stores part of that work. When input drops, the flywheel can slow while continuing to turn the shaft. This exchange can smooth variations in a machine's motion, but it cannot keep the machine running indefinitely.

Stored energy is not the same as power: power describes how quickly energy is transferred. Bearings, air resistance and other losses reduce what can be recovered. A real flywheel's shape, material and mass distribution determine its inertia and strength; the stated inertia here is an input to the calculation, not a value inferred from the drawing.