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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.,
The radius of this circle, , can be determined by equating the magnitude of the Lorentz force to the centripetal force as = | |. Rearranging, the gyroradius can be expressed as = | |. Thus, the gyroradius is directly proportional to the particle mass and perpendicular velocity, while it is inversely proportional to the particle electric charge ...
One of the variables in the above equation that reflects the geometry of the specimen is the slenderness ratio, which is the column's length divided by the radius of gyration. [ 4 ] The slenderness ratio is an indicator of the specimen's resistance to bending and buckling, due to its length and cross section.
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 ...
As described above, the radius of gyration, R g, and the second virial coefficient, A 2, are also calculated from this equation. The refractive index increment dn/dc characterizes the change of the refractive index n with the concentration c and can be measured with a differential refractometer.
The quadratic mean of the end-to-end distance can be related to the quadratic mean of the radius of gyration of a polymer by the relation: [1] r 2 = 6 s 2 {\displaystyle \left\langle r^{2}\right\rangle =6\left\langle s^{2}\right\rangle }
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.