What is "radius of gyration"

Gyration \Gy*ra"tion\ (j[-i]*r[=a]"sh[u^]n), n.

1. The act of turning or whirling, as around a fixed center; a circular or spiral motion; motion about an axis; rotation; revolution.

   The gyrations of an ascending balloon.
   --De Quincey.

   If a burning coal be nimbly moved round in a circle, with gyrations continually repeated, the whole circle will appear like fire.
   --Sir I. Newton.

2. (Zo["o]l.) One of the whorls of a spiral univalve shell.

   Center of gyration. (Mech.) See under Center.

   Radius of gyration, the distance between the axis of a rotating body and its center of gyration.
   --Rankine.

Radius of gyration or gyradius refers to distribution of the components of an object around an axis. In terms of mass moment of inertia, it is the perpendicular distance from the axis of rotation to a point mass (of mass, m) that gives an equivalent inertia to the original object(s) (of mass, m). The nature of the object does not affect the concept, which applies equally to a surface, a bulk mass, or an ensemble of points.

Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application.