Moment of inertia of a polygon

[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.

 

[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.

 

[cigarette]

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.

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

 

[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/