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imagine you have an odd shaped rigid object rotating about its own axis(some axis).. then it has some moment of inertia.. difficult to calculate and depends on the shape and distribution of the mass from the axis etc etc.. then i say its MI = Mk^2.. in general.. where k is radius of gyration such that.. if i had considered a single particle which has the same mass as the entire rigid object... and if it was rotating about that same axis.. then for it to have the same MI as that of the object.. its radius would be K. !! let me show in drawing
see in this pic you can see.. if i were to replace that entire object with a single particle.. then WHAT RADIUS must it rotate from the axis such that it has THE SAME MI as that of the actual rigid body!