# Finding the moment of inertia of a 2D polygon.

1. Jun 24, 2013

### Droctagonopus

Hi everyone,

Is there a general method for finding out the moment of inertia of an irregular convex 2D polygon given the coordinates of its vertices?

I have thought of one possible method:
Split the polygon into multiple triangles and find the moment of inertia of each triangle around the centre of mass of the original polygon using the parallel axis theorem. (Is the formula for moment of inertia of a triangle bh^3/12? Is there a more vertices-friendly way of finding the moment of inertia?)

Is there a better method to do it? I'm trying to make this computer algorithm friendly so a method with repetition of similar calculations would be helpful.

2. Jun 24, 2013

### Simon Bridge

3. Jun 24, 2013

### SteamKing

Staff Emeritus
There's a method which can be derived from Green's Theorem in the plane by which a closed curve described by piecewise line segments can have its area and first and second moments of area calculated by using only the (x,y) coordinates of the endpoints of the line segments as input.