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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.,
Also, a point mass m at the end of a rod of length r has this same moment of inertia and the value r is called the radius of gyration. [1] Solid cylinder of radius r, height h and mass m. This is a special case of the thick-walled cylindrical tube, with r 1 = 0.
Here, the function gives the mass density at each point (,,), is a vector perpendicular to the axis of rotation and extending from a point on the rotation axis to a point (,,) in the solid, and the integration is evaluated over the volume of the body . The moment of inertia of a flat surface is similar with the mass density being replaced by ...
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.
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.
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The animation illustrates rolling motion of a wheel as a superposition of two motions: translation with respect to the surface, and rotation around its own axis.. Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are ...