Center of gravity of a curve?

Center of gravity of a curve?

How do you calculate the center of gravity of a curve when you know the equation of the curve?

Could it be that you are looking for the Centroid of a curve? A curve has no ‘mass’. Take a look at these Wikipedia articles to see if they shed any light on the answer to your question. Then feel free to request additional info as necessary.

I’m trying to calculate the center of gravity for a long piece of curved rail. Anything else you can help with on this?

I believe the “centroid” is what your looking for, and I’m assuming this problem arose out of some kind of distributed load and your looking for the point at which the load can be focused on as a concentrated load.

In that case I believe the equation for the centroid of a curve:

C(x) = (1/p(x)) * Integral( x*p(x)dx)

where p(x) is the equation that you have for the curve, “integral” means just what it says, “take the integral of”.
The “y” position of the centroid is exactly the same format only “y” is used instead of “x” and you need the p(y) equation for the line