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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
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 [] = / /.
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.
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 ...
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 ...
The given formula is for the plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by =, then by the parallel axis theorem the following formula applies:
The squared radius of gyration is the sum of the principal moments: ... e.g., when the particles are distributed uniformly on a regular prism. ...