# Radius of Gyration

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## Radius of gyration

A relation of the area or mass of a figure to its moment of inertia. If *I* is the moment of inertia about a line of a figure whose area is *A*, the figure's radius of gyration with respect to that line is. Accordingly, *I* = *k*^{2}*A*. For a figure of mass *M*, *I* = *k*^{2}*M*. In these equations, *k* is measured in length units such as feet. Geometrically similar figures have equal radii of gyration about corresponding centroidal axes. *See* Moment of inertia

## Radius of Gyration

the quantity ρ permitting the moment of inertia of a body about a given axis to be expressed by the formula *I* = *M/ρ*^{2}, where *M* is the mass of the body. The radius of gyration has the dimension of length. For a homogeneous sphere, the radius of gyration with respect to the axis passing through its center is equal to , where *R* is the radius of the sphere.