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 = k2A. For a figure of mass M, I = k2M. 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/ρ2, 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 Radius of Gyration, where R is the radius of the sphere.

radius of gyration

[′rād·ē·əs əv ji′rā·shən]
(mathematics)
The square root of the ratio of the moment of inertia of a plane figure about a given axis to its area.
(mechanics)
The square root of the ratio of the moment of inertia of a body about a given axis to its mass.

radius of gyration

In mechanics, the distance from the axis to a point such that, if the whole mass of a body were concentrated at it, the moment of inertia would remain unchanged.