radius of gyration

radius of gyration (plural radii of gyration)

1. (physics, engineering) Given a body B, the distance from a given axis of rotation at which a point mass of the same mass as B would have the same moment of inertia about said axis.
   • 1852, [1831], Henry Kater, Dionysius Lardner, A Treatise on Mechanics, page 137:

     Since the radius of gyration depends on the manner in which the mass is arranged round the axis, it follows that for different axes in the same body there will be different radii of gyration.

   • 1989, Christine Boeffel, Hans Wolfgang Spiess, “8: NMR methods for studying molecular order and motion in liquid crystalline side group polymers”, in C. B. McArdle, editor, Side Chain Liquid Crystal Polymers, Blackie and Son, page 251:

     The radii of gyration parallel and perpendicular to the director are obtained from macroscopically aligned samples by using a two-dimensional detection method.

   • 2006, Kalliopi K. Aligizaki, Pore Structure of Cement-Based Materials, Taylor & Francis, page 270:

     As it^[sic] was already mentioned earlier, the radius of gyration represents the size of a scattering object. The average radius of gyration involves the ratio of the eighth power of the radius of gyration of the individual particles ${\displaystyle R_{i}}$, to the sixth power of ${\displaystyle R_{i}}$; this means that with the broad pore size distribution of the cement paste, the average is dominated by the large pores and the small pores have virtually no impact upon the radius of gyration.

• (distance from a given axis at which a point mass of the same mass as a given body would have the same moment of inertia): gyradius