Rotational kinetic energy

A body rotating about a fixed axis has rotational kinetic energy because its parts are moving. The energy depends on how quickly the body rotates and on how its mass is distributed relative to the axis.

E_k = \frac{1}{2}I\omega^2

Here, $$$E_k$$$ is rotational kinetic energy in joules ( $\mathrm{J}$ ), $$$I$$$ is the moment of inertia about the axis in $\mathrm{kg,m^2}$ , and $\omega$ is the angular speed in $\mathrm{rad,s^{-1}}$ .

Moment of inertia measures how a body's mass is distributed relative to the axis. Moving more of the mass farther from the axis increases the moment of inertia. At the same angular speed, a body with a greater moment of inertia has more rotational kinetic energy.

The energy is proportional to moment of inertia: doubling $$$I$$$ while keeping $\omega$ fixed doubles $$$E_k$$$ . It is also proportional to the square of angular speed: doubling $\omega$ while keeping $$$I$$$ fixed makes $$$E_k$$$ four times as large.

Flywheel energy storage capacity

A flywheel stores energy by spinning. The energy is rotational kinetic energy: the faster the flywheel spins, the more energy it stores.

The stored energy also depends on the flywheel’s moment of inertia, which describes how its mass is distributed relative to its axis of rotation. The relationship is:

E = \frac{1}{2}I\omega^2

Here, $$$E$$$ is the stored energy in joules, $$$I$$$ is the moment of inertia in $\mathrm{kg,m^2}$ , and $\omega$ is the angular speed in radians per second.

At the same angular speed, a larger moment of inertia means more stored energy. At the same moment of inertia, doubling the angular speed multiplies the stored energy by four, because angular speed is squared in the equation.

Mass distribution and storage

Moment of inertia depends on both the mass of the flywheel and where that mass is placed. Moving more mass farther from the axis increases the moment of inertia. Thus, two flywheels with the same mass can store different amounts of energy at the same angular speed if their mass is distributed differently.

Safe angular speed

A flywheel cannot safely spin without limit. Rotation produces stresses in the material, and these stresses increase as the flywheel spins faster. The flywheel must be strong enough to withstand them without breaking.

The maximum safe angular speed therefore limits the energy the flywheel can store. Material strength and flywheel design affect that limit: they determine how well the flywheel withstands rotational stresses. Storage capacity depends on both the moment of inertia and the maximum speed that can be reached safely.

Flywheel operation in machines

A flywheel is a rotating part of a machine that stores energy in its motion. As its speed changes, it exchanges energy with the rest of the machine.

The machine’s driving torque tends to turn the flywheel, while the load torque opposes its motion. When the driving torque is greater than the load torque, the flywheel speeds up and stores some of the supplied energy. When the load torque is greater than the driving torque, the flywheel slows down and returns stored energy to the machine.

This exchange reduces fluctuations in rotational speed. The flywheel absorbs energy when more is supplied than the load needs, then releases energy when the load needs more than the drive supplies. It therefore helps smooth the torque delivered to the load, although its speed still changes as it stores and releases energy.

Flywheels can also store energy for later use, including in vehicles and in machines used for production processes.