11.1.2

# Rotational Kinetic Energy

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## Energy of a Flywheel

A flywheel is a revolving wheel used in a machine to accumulate and store energy.

### Rotational kinetic energy

• The rotational kinetic energy Ek for a body with a moment of inertia I rotating at an angular velocity of ω rad s–1 is given by:
• $E_k = \frac12 I ω^2$

### Maximum energy stored

• The maximum energy storage capacity of a flywheel depends on its mass and shape (hence its moment of inertia) and its maximum angular speed.
• The maximum allowed angular speed is limited by the breaking stress of the material of which the flywheel is made.
• For a solid disc of radius R, Ek is proportional to R4 ω2.

## Uses of Flywheels

Flywheels are used in machines to accumulate and store energy.

### Regenerative braking

• In regenerative braking, energy is absorbed by braking and used to ‘charge’ a flywheel, which can accelerate the vehicle at a later time.
• This is used in Formula 1 racing cars.

### Reduce fluctuations

• Flywheels can even out fluctuations in rotational speed.
• E.g. A flywheel is fitted to the crankshaft of an internal combustion or a reciprocating steam engine where the torque provided by the engine varies.
• The flywheel also takes the engine over the ‘dead centres’.
• The greater the moment of inertia, the smaller the fluctuation in speed.

### Flywheels in steam engines

• Flywheels fitted to large Victorian steam engines had a massive rim fitted with spokes.
• This has a greater moment of inertia than a solid disc flywheel of the same diameter.