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Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
It is defined as / where is the effective length of the column and is the least radius of gyration, the latter defined by = / where is the area of the cross-section of the column and is the second moment of area of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative ...
In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles = = () where () is the Cartesian coordinate of the position vector of the particle.
Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus, or an electron, when placed in an external magnetic field B (measured in teslas) that is not aligned with its magnetic moment, will precess at a frequency f (measured in hertz) proportional to the external field:
The radius of gyration of an area with respect to a particular axis is the square root of the quotient of the area moment of inertia divided by the area. It is the distance at which the entire area must be assumed to be concentrated in order that the product of the area and the square of this distance will equal the moment of inertia of the actual area about the given axis.
In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point. [1] For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it ...
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