Radius of Gyration

For a planar distribution of mass rotating about some axis in the
plane of the mass, the *radius of gyration* is the distance from
the axis that all mass can be concentrated to obtain the same mass
moment of inertia. Thus, the radius of gyration is the ``equivalent
distance'' of the mass from the axis of rotation. In this context,
*gyration* can be defined as *rotation* of a planar region
about some axis lying in the plane.

For a bar cross-section with area , the radius of gyration is given by

where is the area moment of inertia (§B.4.8) of the cross-section about a given axis of rotation lying in the plane of the cross-section (usually passing through its centroid):

where denotes the distance of the differential area element from the axis of gyration.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University