The radius of gyration is a similar concept to the centre of gravity. When a body of moment of inertia
about some axis is rotating about that axis, we can consider the entire mass of the body to be concentrated at a point a distance
from the axis of rotation. The distanceis then called the radius of gyration, and the moment of inertia is the same as if the entire mass were at distancefrom the axis of rotation.
Concisely,
where
so that
For example, a solid cylinder of mass
has moment of inertia
so that
In this case, the cylinder is equivalent to a cylindrical shell of radius