## Moment of Inertia

We can think of a solid body made up of many particles of massesat distancesfrom some fixed axis.

If the body is rotated about that point, each masswill have kinetic energywhereis the angular velocity of each particle – the same for each particle since the body is assumed to rotate as one.

Hence

The quantityis constant for each body about a fixed axis, and is called the moment of inertia of the body about that axis and labelled

We can write

The moment of inertia of a body is generally not constant, sine many bodies are not rigid. If more of the mass of a body is further away from the axis of rotation, the moment of inertia will be higher.