# What determines how much energy a flywheel can store? [closed]

What is the relationship to the energy capacity of a flywheel and its radius, mass, rotational velocity etc?

## closed as too broad by stafusa, JMac, Aaron Stevens, Cosmas Zachos, ZeroTheHeroJan 24 at 23:02

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• This is more an engineering than a physics question. – my2cts Jan 24 at 17:35
• What's spinning the flywheel? That part is very important. – probably_someone Jan 24 at 17:48
• Please consider adding a little more info to your question. In its current form it risks attracting downvotes due to lack of evidence of prior research. – PM 2Ring Jan 24 at 19:49
• This seems too broad. Also, are you thinking about the recoverable energy from a flywheel, or the overall theoretical capacity? These are different things. – JMac Jan 24 at 20:55

The amount of energy a flywheel can store is equal to 1/2 * (moment of inertia) * angular velocity^2.

The moment of inertia has to do with how heavy the spinning flywheel is, and how its mass is distributed around its axis of rotation. Basically, the larger the flywheel's diameter and the more mass its has, the more energy it can store.

The limiting factor for energy storage in a flywheel is its mechanical strength, because the stresses imposed on a fast-spinning flywheel will tend to make it fly to pieces. Fancy flywheels designed for energy storage must be made of exotic materials to ensure that the flywheel does not explode.

• Exploding flywheels are very scary! That's a major reason we still use cars that store energy in explosive chemicals rather than in flywheels. – PM 2Ring Jan 24 at 18:31
• @PM 2Ring, yeah yeah, at least with gasoline, you have to mix it with air to make it explode all at once- but when one of those flywheels goes, yowza! – niels nielsen Jan 24 at 20:52

A flywheel is designed to efficiently store rotational kinetic energy. It resists changes in rpm by virtue of its rotational moment of inertia. Its stored kinetic energy is given by

$$KE=\frac{Iω^2}{2}$$

Where $$I$$ is its moment of inertia and $$ω$$ is its angular velocity.

The moment of inertia is given by

$$I=kmr^2$$

Where $$m$$ is the mass, $$r$$ is radius, and $$k$$ is the inertial constant which depends on the shape of the flywheel. Examples are $$k=1$$ where the mass is concentrated at the rim of the wheel and $$k=0.606$$ for a flat solid circular disk of uniform thickness.

The fact that the stored kinetic energy goes up as the square of the radius of the wheel and where the mass is concentrated at the perimeter, speaks to the ability of a flywheel to store energy.

Hope this helps.