Applications of the Kelvin-Stokes Theorem

[Physics-Pure]

Hi Guys~

I was wondering if anyone had any suggestions for applications of the Kelvin-Stokes Theorem. Recall that the Kelvin-Stokes Theorem states: http://upload.wikimedia.org/math/0/4/4/04402b2d910114267bffa0e030445af6.png
(Check Wikipedia for further explanation)

Obviously one could apply this in it's most basic form to calculate the work done upon a particle moving through a vector field in ℝ³. But I'm looking for some "weirder" problems.

i.e.
Imagine a tilted Ferris wheel rotating on the Earth. You want to calculate the work done by gravity on the Ferris wheel. The Ferris wheel is a closed path so Stokes' theorem holds.

Something of that nature. Anyone have any suggestions on how to go about a problem like this ^?
or any other problem that you may know of relating to this.

Thank you,
Physics-Pure

P.S. This is not homework related, purely for fun.

 

[lugita15]

Stokes' theorem is used in classical electromagnetism. After all, two of Maxwell's equations involve the curl.