Moment of inertia

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The moment of inertia is a measure of a mass and its distance perpendicular to an axis of rotation. It describes an objects resistance to change in rotation.

The formula to calculate a moment of inertia between a point and a point mass is:

where is the displacement between the two points, is the mass of the point mass and is the moment of inertia.

If you have a finite set of point mass's and want to find their moment of inertia around a point you simply add the moment of inertia of each object to get the following:

It is important to note that you can not simply take the centre of mass of an object and use it as a point mass. Instead you need to use integration:

Mathematically, the moment of inertia for a mass that is moving a perpendicular distance of from an axis is expressed as:

or in terms of density as:

The formula for a moment of inertia is the result of combining the equation for kinetic energy with the equation for angular velocity.