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

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...
 

Thread 'What do you think of this new explanation of Zeta function?'

For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...
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