# How to calculate rotational kinetic energy

### Definition

Any object or body with an inertia and rotational (angular) speed has rotational kinetic energy. An object or body with zero rotational speed (which means that it’s stationary) will have zero rotational kinetic energy.

Image: Rotational kinetic energy

A spinning flywheel is a very good example of an object which possesses rotational kinetic energy. The kinetic energy of a rotating object is similar to the linear kinetic energy and can be calculated function of the moment of inertia and angular speed.

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### Formula

To calculate rotational kinetic energy multiply the moment of inertia around the axis of rotation with the square value of the angular speed and divide the result to two. The equation to calculate rotational kinetic energy is [1]:

Ek = (J · ω2) / 2
(1)

where:

• Ek [J] – rotational kinetic energy
• J [kg·m2] – moment of inertia around the axis of rotation
• ω [rad/s] – angular (rotational) speed

The unit of measurement of rotational kinetic energy is joule [J].

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### Wheel example

Calculate the rotational kinetic energy of a wheel with the moment of inertia of 0.015 kg·m2, spinning with the rotational speed of 500 rpm.

Step 1. Convert the rotational speed from [rpm] to [rad/s]:

ω = (π · 500) / 30 = 52.36 rad/s

Step 2. Calculate the rotational kinetic energy Ek [J] of the wheel using equation (1):

Ek = (J · ω2) / 2 = (0.015 · 52.362) / 2 = 20.562 J

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### Flywheel example

A KERS has a flywheel with the moment of inertia of 1.03 kg·m2, spinning at the speed of 10000 rpm. Calculate the rotational kinetic energy which can be stored by the flywheel [4].

Step 1. Convert the rotational speed from [rpm] to [rad/s]:

ω = (π · 10000) / 30 = 1047.2 rad/s

Step 2. Calculate the rotational kinetic energy Ek [J] of the flywheel using equation (1):

Ek = (J · ω2) / 2 = (1.03 · 1047.22) / 2 = 564763.3376 J

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### Calculator

The rotational kinetic energy calculator allows you to calculate the rotational kinetic energy of a body or object with a given moment of inertia and rotational speed. You need to enter the moment of inertia and rotational speed parameters and choose the desired unit of measurement.

The default unit of measurement for energy is Joule. If you want the result displayed in another unit, use the dropt down list to choose and click the CALCULATE button again.

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### References

[1] David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 7th edition, John Wiley & Sons, 2004.
[2] Benjamin Crowell, Light and Matter – Physics, 2007.
[3] Raymond A. Serway and John W. Jr. Jewett, Physics for Scientists and Engineers, 6th edition, Brooks/Cole Publishing Co.,2004
[4] Jiansong Li, Jiyun Zhao, and Xiaochun Zhang, A Novel Energy Recovery System Integrating Flywheel and Flow Regeneration for a Hydraulic Excavator Boom System, Energies 2020.
[5] Leo H. Holthuijsen, Waves in oceanic and coastal waters, Cambridge University Press, 2007.
[6] Kira Grogg, Harvesting the Wind: The Physics of Wind Turbines, Carleton College, 2005.

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