Radius of Gyration

Theoretically calculating a moment of inertia by integration (as in section 1.5.2) is only possible for objects whose mass distribution is mathematically simple enough to integrate. But EXPERIMENTALLY, the moment of inertia of essentially ANY real object -- however irregular -- can be measured, since I always depends on just two things: how much mass the object has, and how that mass happens to be distributed relative to the chosen axis.

If we are interested purely in the SECOND of these -- the distributional aspect, independent of how much total mass is actually present -- it is useful to write any object's moment of inertia in the form $I=MK^2$ where M is the object's total mass. This equation is really just a definition of the new quantity K: it says that, AS FAR AS ROTATIONAL INERTIA IS CONCERNED, the object's entire mass M behaves exactly as if it were all concentrated at a single effective distance K from the axis. This distance K is called the radius of gyration of the object about that particular axis. A LARGER value of K means the object's mass is (in this effective, root-mean-square sense) distributed FARTHER from the axis on average; a smaller K means it is concentrated closer in. …