Radius of Gyration
Radius of gyration of a body about a given axis is the perpendicular distance of a point from the axis, where if whole mass of the body were concentrated, the body shall have the same moment of inertia as it has with the actual distribution of mass.
The square of radius of gyration multiplied with the mass of the body gives the moment of inertia of the body about the given axis.
I = Mk2 or
Here k is called radius of gyration.
From the formula of discrete distribution,
I = mr12 + mr22 + mr32 + L + mrn2
- Radius of gyration (k) depends on the shape and size of the body, position and configuration of the axis of rotation, distribution of mass of the body wrt the axis of rotation.
- Radius of gyration (k) does not depend on the mass of body.
- Significance of radius of gyration: Through this concept a real body (particularly irregular) is replaced by a point mass for dealing its rotational motion.