(adsbygoogle = window.adsbygoogle || []).push({}); 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

I[tex]_{ij}[/tex]=[tex]\int[/tex]dV([tex]\delta^{ij}[/tex][tex]\vec{x}^{2}-x^{i}x^{j}[/tex])

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

[tex]I_{xx}=\int^{4}_{0}x\frac{(3-3/4x^)^{3}}{3}dx[/tex]

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 !

Thanks,

Kep

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# Homework Help: Inertia tensor for triangle

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