Hi,

I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight?

Simplified illustration of what I mean using straight line:

5kg-----------------5kg
           ^center of gravity

10kg---------------5kg
        ^center of gravity offset du to weight of vertices

Of course, I know how to calculate the center of gravity on a straight line with weighted vertices, but how do I do it on a polygon with weighted vertices?

Thanks for your time!