## The Radius of Gyration

The radius of gyration is a similar concept to the centre of gravity. When a body of moment of inertiaabout some axis is rotating about that axis, we can consider the entire mass of the body to be concentrated at a point a distancefrom 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,whereso that

For example, a solid cylinder of masshas moment of inertiaso thatIn this case, the cylinder is equivalent to a cylindrical shell of radius