Moment of inertia
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.