# Inertia tensor for triangle

1. Dec 3, 2007

### Keplini

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 $$\sigma(x,y)$$ = 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$$_{ij}$$=$$\int$$dV($$\delta^{ij}$$$$\vec{x}^{2}-x^{i}x^{j}$$)

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$$_{xx}$$=$$\int^{4}_{0}$$$$\int^{3-3/4x}_{0}$$ $$xy^2 dx dy$$

which gives me something like

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

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

#### Attached Files:

• ###### triangle.gif
File size:
1.2 KB
Views:
66
Last edited: Dec 3, 2007
2. Apr 17, 2009

### htown1397

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?