Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Flywheels - Kinetic Energy

Sponsored Links

A flywheel can be used to smooth energy fluctuations and make the energy flow intermittent operating machine more uniform. Flywheels are used in most combustion piston engines.

Energy is stored mechanically in a flywheel as kinetic energy.

Kinetic Energy

Kinetic energy in a flywheel can be expressed as

Ef = 1/2 I ω2(1)


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

I = moment of inertia (kg m2, lb ft2)

ω = angular velocity ( rad /s)

Angular Velocity - Convert Units

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


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

m = mass of flywheel (kg, lbm )

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 - Convert Units

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

Flywheel Rotor Materials

Flywheels - Kinetic Energy
(kg/m3 )

Design Stress
( MPa)
Specific Energy
( kWh/kg )
Aluminum alloy 2700
Birch plywood 700 30
Composite carbon fiber - 40% epoxy 1550 750 0.052
E-glass fiber - 40% epoxy 1900 250 0.014
Kevlar fiber - 40% epoxy 1400 1000 0.076
Maraging steel 8000 900 0.024
Titanium Alloy 4500 650 0.031
"Super paper" 1100
S-glass fiber/epoxy 1900 350 0.020
  • 1 MPa = 106 Pa = 106 N/m2= 145 psi
  • Maraging steels are carbon free iron-nickel alloys with additions of cobalt, molybdenum, titanium and aluminum. The term maraging is derived from the strengthening mechanism, which is transforming the alloy to martensite with subsequent age hardening.

Example - Energy in a Rotating Bicycle Wheel

A typical 26-inch bicycle wheel rim has a diameter of 559 mm (22.0") and an outside tire diameter of about 26.2" (665 mm) . For our calculation we approximate the radius - r - of the wheel to

r = ((665 mm) + (559 mm) / 2) / 2

=  306 mm

= 0.306 m

The weight of the wheel with the tire is 2.3 kg and the inertial constant is k = 1 .

The Moment of Inertia for the wheel can be calculated

I = (1) (2.3 kg) (0.306 m)2

= 0.22 kg m2

The speed of the bicycle is 25 km/h ( 6.94 m/s) . The wheel circular velocity (rps, revolutions/s) - n rps - can be calculated as

n rps = (6.94 m/s) / (2 π (0.665 m) / 2)

= 3.32 revolutions /s

The angular velocity of the wheel can be calculated as

ω = (3.32 revolutions /s) (2 π rad/ revolution )

= 20.9 rad/s

The kinetic energy of the rotating bicycle wheel can then be calculated to

Ef = 0.5 (0.22 kg m2) ( 20.9 rad/s )2

= 47.9 J

Sponsored Links

Related Topics


Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.


The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

Related Documents

Angular Motion - Power and Torque

Angular velocity and acceleration vs. power and torque.

Belt Transmissions - Speed and Length of Belts

Calculate length and speed of belt and belt gearing.

Conn-Rod Mechanism

The connecting rod mechanism.


Energy is the capacity to do work.

Energy Storage Density

Energy density - by weight and volume - for some ways to store energy

Formulas of Motion - Linear and Circular

Linear and angular (rotation) acceleration, velocity, speed and distance.

Impulse and Impulse Force

Forces acting a very short time are called impulse forces.

Kinetic Energy

Energy possessed by an object's motion is kinetic energy.

Mass Moment of Inertia

The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.

Rotating Bodies - Stress

Stress in rotating disc and ring bodies.

Rotating Shafts - Torque

Torsional moments acting on rotating shafts.

Salt Hydrates - Melting points and Latent Melting Energy

Melting points and latent energy of salt hydrates.

Sponsored Links

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.