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Engineering ToolBox > Flywheel Kinetic Energy

Kinetic energy and moment of inertia of a flywheel

A flywheel is used to smooth the energy fluctuations in combustion engines and make the energy flow uniform. The flywheels store energy mechanically as kinetic energy.

Kinetic Energy

The kinetic energy of a flywheel can be expressed as

E_f = 1/2 I ω² (1)

where

E_f = flywheel kinetic energy (Nm (Joule), ft lb)

I = moment of inertia (kg m², lb ft²)

ω = angular velocity (rad/s)

Angular velocity converting units

• 1 rad = 360^o / 2 π =~ 57.29578^o
• 1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps)

Moment of Inertia

Moment of inertia quantifies the rotational inertia of a rigid body and can be expressed as

I = k m r² (2)

where

k = inertial constant - depends on the shape of the flywheel

m = mass of flywheel (kg, lb)

r = radius (m, ft)

Inertial constants of some common types of flywheels

• wheel loaded at rim like a bicycle tire - k =1
• flat solid disk of uniform thickness - k = 0.606
• flat disk with center hole - k = ~0.3
• solid sphere - k = 2/5
• thin rim - k = 0.5
• radial rod - k = 1/3
• circular brush - k = 1/3
• thin-walled hollow sphere - k = 2/3
• thin rectangular rod - k = 1/2

Moment of Inertia Converting Units

• 1 kg m² = 10000 kg cm² = 54675 ounce in² = 3417.2 lb in² = 23.73 lb ft²

Flywheel Rotor Materials

• Maraging steel is an iron alloy with a large percentage of nickel and superior strength