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Determination of Moment of Inertia & Radius of Gyration of Flywheel (Part – X) 

Application of Radius of Gyration

The radius of gyration (possibly multiplied by a constant factor) is a useful estimate of the size of a molecule. Size exclusion chromatography ideally separates molecules by their hydrodynamic radius, although static light scattering instruments can measure the radius of gyration of eluting macromolecules. The hydrodynamic drag force on molecules may be estimated from its radius of gyration and Stokes' law f = 6πηR, although the numerically similar hydrodynamic radius may be better for this purpose.

In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross-sectional area in a beam around its centroidal axis. The radius of gyration is given by the following formula

where I is the second moment of area and A is the total cross-sectional area. The gyration radius is useful in estimating the stiffness of a beam. However, if the principal moments of the two-dimensional gyration tensor are not equal, the beam will tend to buckle around the axis with the smaller principal moment. For example, a beam with an elliptical cross-section will tend to buckle around the axis with the smaller semiaxis.

The radius of gyration can be computed in terms of the second moment of inertia I and the total mass M:

Compiled by Samar Das