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What is radius of gyration?

The radius of gyration, often referred to by the symbol k, is defined by the equation I = mk^2. In this equation, I is the moment of inertia of some object about some specified axis, m is the total mass of the object, and k is the distance from the axis such that if all the mass were concentrated at that distance, the moment of inertia would be the same as for the actual object (which could have an arbitrary distribution of mass).

The moment of inertia, I, of some body about a specified axis is defined as I = sum (mr^2) where the sum is over infinitesimal masses, m, making up the body and r is the distance of an associated infinitesimal mass from the specified axis. The moment of inertia clearly depends on the choice of an axis.

The radius of gyration sometimes can simplify thinking about this situation because if all the mass is placed a distance k from the axis, the moment if inertia would be the same.

I hope you know about moments of inertia; if not, I should write a quite different (and much longer) explanation.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University

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