I know the definition of radius of gyration. But don't know what does it mean? What are the importance of it? Is it similiar to centre of mass? I want to clear my problem. Let you know only the definition of centre of mass. But you don't know why this term is important. If I tell you that, if we apply force along to the centre of mass, it seems that that the force has workes through its whole body. But only definition was not sufficient to realize it better. At the same way, I want to learn more about radius of gyration.

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For a mass, m, with a mass moment of inertia of I, the radius of gyration, k, is the square root of (I/m).

It represents the distance of an equivalent point mass to the axis about which the moment of inertia is taken, to yield an equivalent moment of inertia. For example, a thin rod of mass m and length L has a mass moment of inertia of mL^2/12 about its mass center, so its radius of gyration, designated k, is L/(sqrt12). Its moment of inertia can then be expressed as I = mk^2. Now when you look at a point mass particle of mass m a distance r from its axis of rotation, I is mr^2, and the radius of gyration is r, the same distance as the distance to the rotation axis, which makes sense for a particle with all its mass concentrated at a point.