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The radius of gyration is defined as the distance between an axis and the point of maximum inertia in a rotating system. Alternative names include radius of gyration and gyradius. The root mean square distance between parts of a rotating object relative to an axis or center of gravity is a key element in calculating the radius of gyration.
The radius of gyration has applications in structural, mechanical, and molecular engineering. It is denoted by the lowercase letter k or d with the uppercase letter R. Structural engineers use radius of gyration calculation to estimate beam stiffness and buckling potential. From a structural standpoint, a circular tube has an equal radius of gyration in all directions, making the cylinder the most sufficient column structure to resist buckling.
Alternatively, the radius of rotational inertia can be described for a rotating object as the distance from the axis to the heaviest point on the object’s body that does not change the rotational inertia. For these applications, the formula for the radius of gyration (R) is represented as the root mean square of the second moment of inertia (I) divided by the cross-sectional area (A). Other formulas are used for mechanical and molecular applications.
For mechanical applications, the mass of an object is used to calculate the radius of gyration (r) instead of the cross-sectional area (A) as used in the formula above. The mechanical engineering formula can be calculated using the mass moment of inertia (I) and the total mass (m). Therefore, the radius of the rotating cylinder formula is equal to the root mean square of the moment of inertia of the mass (I) divided by the total mass (m).
Molecular applications are based on the study of polymer physics, where the polymer gyradius represents the size of a protein for a specific molecule. The formula for determining the generation radius in a molecular engineering problem is simplified by considering the average distance between two monomers. It follows that the radius of gyration, in this sense, is equivalent to the root mean square of that distance. Considering the nature of polymer chains, the radius of gyration in a molecular application is understood as an average of all polymer molecules for a given sample over time. In other words, the spin radius protein is a mean gyro.
Theoretical polymer physicists can use X-ray scattering technology and other light scattering techniques to compare models with reality. Static light scattering and low-angle neutron scattering are also used to verify the accuracy and precision of theoretical models used in polymer physics and molecular engineering. These analyzes are used to study the mechanical properties of polymers and the kinetic reactions that may involve changes in molecular structures.