Radius of Gyration: The radius of gyration is a parameter that relates the moment of inertia to the area of a section. The radii of gyration corresponding to Ix, Iy, and J are expressed as
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We can think of the radii of gyration rx and ry as the x and y coordinates of an imaginary point at which the entire area is lumped. As such, a radius of gyration does not have any physical significance. It is simply a way of relating the moment of inertia about a particular axis to the area.
Application: In buckling analysis of columns a quantity of importance is the so-called slenderness ratio denoted by L/r. This quantity relates the length (L) of the column to its cross-sectional radius of gyration (r).