Resistance of a sphere of resistivity rho and radius S

AI Thread Summary
The discussion revolves around calculating the resistance between two points on a sphere using a method that involves dividing the sphere into thin strips. The challenge arises when evaluating the definite integral for the polar angle theta from 0 to pi, as the strip elements become points at the ends, complicating the calculation. The formula used is dR = rho * dl/A, with specific definitions for dl and A. The contributor expresses confusion about the finite resistance expected between the two points and seeks assistance in resolving the issue. Additionally, there is a separate inquiry regarding the "curve phenomenon" in velodrome cycling, where cyclists experience reduced power in curves despite achieving higher speeds compared to straight sections. The individual requests an explanation of this phenomenon.
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I calculated the resistance between two points (P and Q) on a sphere that are located on the two ends of a diameter by dividing the sphere into thin strips of thickness dz that are in series perpendicular to the line PQ (say the z-axis). I can get an expression for the indefinite integral in theta (the polar angle theta, z = S Cos (theta), and S= radius), however I run into problem when evaluating this definite integral for theta = 0 to pi. Apparently the fact that the strip element becomes a points at the ends is causing this problem. I use dR=rho * dl/A with dl = -S Sin(theta) d(theta) and A(theta) = pi {S Sin(theta)}^2. What is going wrong here? Because I know that there must be a finite resistance between two such points.
 
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I need help!

I'm a spanish coach from Barcelona and I have a problem.

I need some information about "curve fenomenon" in velodrom cycling. When a cyclist go into a curve power is less than in straight and velocity is high to a straight. Please do you explain this fenomenon?.

My e-mail is ardcarlos@hotmail.com

Thank you very much!
 
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