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

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The radius of gyration is a concept from Calculus 3 that determines the distance from an axis of rotation where a point mass would have the same angular momentum as a distributed mass. It essentially simplifies the analysis of rotating bodies by representing their mass distribution as a single point. This concept is directly related to rotation, as it helps in understanding how mass affects rotational dynamics. The radius of gyration provides insight into the stability and behavior of objects in rotational motion. Understanding this relationship is crucial for applications in physics and engineering.
harpazo
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In simple terms, what exactly is the radius of gyration as taught in Calculus 3? Is gyration connection in any way to rotation?
 
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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?"
 
HallsofIvy said:
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...
 

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