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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 ...
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.,
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.
Fig. 1: Critical stress vs slenderness ratio for steel, for E = 200 GPa, yield strength = 240 MPa.. Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle.
Since the gyration tensor is a symmetric 3x3 matrix, a Cartesian coordinate system can be found in which it is diagonal = [] where the axes are chosen such that the diagonal elements are ordered .
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 }