# How to Calculate Energy in a Flywheel

Written by paul dohrman
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A flywheel is a mechanical device used to store significant rotational kinetic energy and therefore tend to be quite heavy. An example is the flywheel on a car’s crankshaft, smoothing out the transmission of energy from the engine to the wheels. A flywheel’s mass may be concentrated toward the outside rim, for example in a lip, complicating the calculation of its moment of inertia and stored energy. Then the lip and the flat part of the disk would have to be calculated separately and added together at some point in the calculations.

Skill level:
Moderate

## Instructions

1. 1

Ascertain the density of the substance of which the flywheel is made by looking it up in density tables.

2. 2

Multiply this density by the volume of the flat part of the disk--the total shape of the flywheel minus any lip. The volume of such a shape is ?R^2 x (thickness), where R is the radius. This gives the mass M of the flat part of the disk. Measure it in kilograms. Measure the radius in meters.

3. 3

Multiply the density by the volume of any lip that rises above the flat part of the disk. The volume of such a shape is (?Ro^2-?Ri^2)xheight, where Ro denotes the outer radius and Ri denotes the inner radius of the lip. Call the resulting mass ML, for the mass of the lip.

4. 4

Calculate the moment of inertia of the flat part as I= MxR^2/2.

5. 5

Calculate the moment of inertia of the lip as I= MLx/2 x (Ro^2+Ri^2).

6. 6

Add the two moments of inertia together to get the total moment of inertia.

7. 7

Use the known rate of rotation of the freewheel, ?, to get the rotational kinetic energy of the flywheel, using the equation 0.5 x (moment of inertia) x ?^2. If you kept the units in kilograms and meters, and made the units of ? in revolutions per second, your kinetic energy result will be in Newton-meters, or Joules.

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