The radius of gyration of a body about its axis of rotation may be define as the distance from the axis of rotation at which, if the whole mass of the body were concentrated, its moment of inertia about the given axis would be the same as with the actual distribution of mass.
When the square of the radius of gyration is multiplied with the mass of the body, gives the moment of inertia of the body about a given axis.
Let a rigid body consists of n particles of mass m each, situated at distance r₁, r₂, r₃,……rₙ from the axis of rotation AB.
Hence, Radius of gyration of a body about a given axis is equal to the root mean square distance of constituent particles from the given axis.