MHB What is the meaning of radius of gyration and its relation to rotation?

[harpazo]

In simple terms, what exactly is the radius of gyration as taught in Calculus 3? Is gyration connection in any way to rotation?

 

[HallsofIvy]

Yes, it is. The "radius of gyration" answers the question "If the mass of this object were reduced to a single point, how far from the axis of rotation would that point be so that the angular momentum of that single point mass would be the same as the object itself were rotated around the axis?"

 

[harpazo]

Yes, it is. The "radius of gyration" answers the question "If the mass of this object were reduced to a single point, how far from the axis of rotation would that point be so that the angular momentum of that single point mass would be the same as the object itself were rotated around the axis?"

This is deep, very deep...