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Inertia tensor for triangle

  1. Dec 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the center of mass and inertia tensor at the CoM of the following triangle. Density of the triangle is [tex]\sigma(x,y)[/tex] = x and y=3-3/4x .

    2. Relevant equations
    Find the inertia tensor at the origin (x,y,z) and apply the parallel axis theorem


    3. The attempt at a solution
    I've been able to find the mass (which gave me 8 -correct me if I'm wrong-), the CoM and now I'm trying to find the inertia tensor. For the first component, I get something like:

    I[tex]_{xx}[/tex]=[tex]\int^{4}_{0}[/tex][tex]\int^{3-3/4x}_{0}[/tex] [tex]xy^2 dx dy[/tex]

    which gives me something like


    which looks like a big monster and I don't feel like integrating that ! ;) Basically, I believe it's getting way too complicated to be the good answer. Any help on finding that inertia tensor would be greatly appreciated !


    Attached Files:

    Last edited: Dec 3, 2007
  2. jcsd
  3. Apr 17, 2009 #2
    Hi, i need help on the same problem. So if anyone can help it would be great. By the way, Keplini, which book is this problem from?
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