Changes

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

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

:<big><big><math>I = m r^2</math></big></big>

:<big><big><math>I = m r^2</math></big></big>

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

where <math>r</math> is the displacement between the two points, <math>m</math> is the mass of the point mass and <math>I</math> 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:

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:

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 ''I'' for a mass ''m'' that is moving a perpendicular distance of ''r'' from an axis is expressed as:

Mathematically, the moment of inertia <math>I</math> for a mass <math>m</math> that is moving a perpendicular distance of <math>r</math> from an axis is expressed as:

:<big><big><math>I = \int r^2 \,dm</math></big></big>

 

:<big><big><math>I = \iiint r^2 \,dm</math></big></big>

 

 

:<big><big><math>I = \iiint_v \rho (x,y,z) \, r^2 \,dV</math></big></big>

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

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