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Moment of inertia of a polygon

  1. Sep 14, 2004 #1
    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. jcsd
  3. Sep 14, 2004 #2


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    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.
  4. Sep 14, 2004 #3

    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.

  5. Sep 17, 2004 #4
    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.

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