# Moment of inertia of a polygon

1. Sep 14, 2004

### cigarette

How can one calculate the moment of inertia of a polygon?
Assuming that one knows the polygon’s total area, centroid
and vertices, which are connected by straight lines in a 2D system.
Is it possible to avoid a difficult integral over the area/mass?

Any helpful information is highly appreciated.

2. Sep 14, 2004

### Tide

Is it a regular polygon? You could break it into triangles each with a vertex at the center of the polygon and add up the moments of inertia appropriately.

3. Sep 14, 2004

### cigarette

hi tide, in response to ur question, it is an arbitrarily shaped polygon, which basically means any shape with any number of vertices..maybe can call it "n"-agon.

i get the triangular part, but just wondering whether there is any other mathematical methods.

regards

4. Sep 17, 2004

### chris23

I have calculated the moment of inertia about the origin of a polygon based on its vertices.

The equation is

1/12 * sum { (y_{i+1} - y_{i} )(x_{i+1} + x_{i})(x_{i+1}^2 + x_{i}^2)
- (x_{i+1} - x_{i} )(y_{i+1} + y_{i})(y_{i+1}^2 + y_{i}^2)

I put the details of its derivation on my web page.

http://www.enel.ucalgary.ca/~shannon/v2/green/ [Broken]

Last edited by a moderator: May 1, 2017