Radius of Gyration
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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Update: June 2012