We can think of a solid body made up of many particles of masses
at distances
from some fixed axis.
If the body is rotated about that point, each mass
will have kinetic energy
where
is the angular velocity of each particle – the same for each particle since the body is assumed to rotate as one.
Hence
The quantity
is 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.