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Radius of Gyration

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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

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
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.

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.



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Here, an attempt will be made to quantify the orientation and deformation of the system based on the radius of gyration ([R.
The theory of polymer interfaces predicts, for a hypothetical system in which all of the chains are the same length, that the interface will reach full cohesive strength when all chains adjacent to the interface have diffused a distance comparable to their radius of gyration; the radius of gyration of a polymer is typically 5-10 nm.
gi] is the radius of gyration of the objects giving rise to the scattering at level i.
 
 
 
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