Question

Hello, how can I prove the 'Capstan equation' in 8.01 Lec. 25? shall I use small angle approximation? (The equation looks like T2/T1=e^(μθ))

Answer 1

Proof is on the Wikepedia page:
http://en.wikipedia.org/wiki/Capstan_equation

Answer 2

I know that...I am looking for an easier proof...

Answer 3

hmm, I'm afraid that's the best you can do.
It is actually a long derivation.

Answer 4

If the angle is less than 1 degree then the tan or sin value is equivalent to the actual angle (in radians). That is when you use the small angle approximation.