# Radius of gyration

## Description

Gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point.

Radius of gyration or gyradius is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the root mean square distance of the objects’ parts from either its center of gravity or a given axis.

In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis.

The radius of gyration can be calculated by the second moment of area and the total cross-sectional area of the object.

## Variables

R_{g} | Radius of gyration (m) |

I | Second moment of area (m^{4}) |

A | Total cross-sectional area (m^{2}) |