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.
References in periodicals archive ?
Tables 1 and 2 represent the corresponding radius of gyration and diameter of aggregates and fractal dimensions.
A plot of the overall z-average root mean square radius of gyration ([Rg.
2 (4) has shown a characteristic diffusion time for a polymer chain to diffuse a distance equal to its radius of gyration.
where [empty set] is the Flory-Fox factor and is defined as the ratio of the hydrodynamic volume determined from the intrinsic viscosity to the root-mean-square radius of gyration cubed [(< [R.
An interesting and often useful feature of a system that can be derived from the intensities of scattered light, as a function of scattering angle or scalar scattering vector (q) is its radius of gyration ([R.
A commonly available measure of pervaded volume is the radius of gyration [R.
The Guinier approach of scattering intensities relates the width of a Gaussian peak to the radius of gyration of the so-called scattering particle (i.
On the other hand, the radius of gyration of macromolecules is on the order of 10 nanometers, and it is expected that the macromolecules contacted to the solid silica would have different responses from those in the matrix because of the mechanical displacement resulting from elongation or strain.
In this work, it is assumed that as the interpenetration depth reaches 1/2 of the polymer's radius of gyration at the critical molecular weight for chain entanglements.
At the reptation time, the average inter-penetration distance is equal to the radius of gyration, the material has re-organized to erase the interface, and the weld achieves a strength equal to that of the virgin material.
The length of the weld-line can then be measured from this plot as the depth from the mold wall at which the interdiffusion distance becomes large enough to produce sufficient entanglements; this interdiffusion distance is commonly accepted to be 1/2 of the polymer's radius of gyration (10).
2], the second virial coefficient; and [Mathematical Expression Omitted], or written as [Mathematical Expression Omitted], the z-average root-mean-square radius of gyration.