Then radius of gyration can be used to characterize the typical distance travelled by this point. The polar moment of inertia, describes the rigidity of a cross-section against torsional moment, likewise the planar moments of inertia described above, are related to flexural bending. One can represent a trajectory of a moving point as a body. is the total rotation angle (Gesamtdrehwinkel) of L/L, To is the polar moment of inertia of the orbit curve segment of the point O and S (s1, s2) L is the. It is actually the perpendicular distance from point mass to the axis of rotation. 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.

Radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there. The moments of inertia of a mass have units of dimension ML 2 (mass × length 2). For non-circular cross sections warping occurs. Distance from center of mass to axis of rotation It is equal to the polar moment of inertia I z if the cross section is circular.

Polar moment of inertia circle equation