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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.,
Right-triangular prism: b = the base side of the prism's triangular base, h = the perpendicular side of the prism's triangular base L = the length of the prism Right circular cylinder: r = the radius of the cylinder
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 ...
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.
Pyramid: A polyhedron comprising an n-sided polygonal base and a vertex point square pyramid: Prism: A polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases hexagonal ...
Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration R g. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A 2 , can be calculated.
The surface area of a gyroelongated square pyramid with edge length is: [3] (+), the area of twelve equilateral triangles and a square. Its volume: [ 3 ] 2 + 2 4 + 3 2 6 a 3 ≈ 1.193 a 3 , {\displaystyle {\frac {{\sqrt {2}}+2{\sqrt {4+3{\sqrt {2}}}}}{6}}a^{3}\approx 1.193a^{3},} can be obtained by slicing the square pyramid and the square ...
For this case the radius of gyration is approximated using Flory's mean field approach which yields a scaling for the radius of gyration of: R g ∼ N ν {\displaystyle R_{g}\sim N^{\nu }} , where R g {\displaystyle R_{g}} is the radius of gyration of the polymer, N {\displaystyle N} is the number of bond segments (equal to the degree of ...