Homework Help: Point Mass Inertia Tensor

1. Dec 18, 2012

darthmonkey

1. The problem statement, all variables and given/known data

A)Find the moment of inertia tensor for a system of 4 particles of mass 1kg at A=(1,1,0), B=(1,-1,0) C=(-1,1,0) D=(-1,-1,0) in Cartesian coordinates.

B)Rotate the coordinates 30 degrees around the z axis and find the tensor in the new coordinates.

2. Relevant equations

Ixx=$\sum$y^2+z^2
Iyy=$\sum$x^2+z^2
Izz=$\sum$y^2+x^2
Ixy=$\sum$xy
Iyx=$\sum$yx
Izx=$\sum$zx
Izy=$\sum$zy

I'=RIR*

3. The attempt at a solution
I get Ixx=4, Iyy=4, and Izz=8. Anything multiplying z is 0 and all the xy components cancel out. So a diagonal matrix.

For B I just apply the z rotation matrix with 30,RIR*, but when I do this I get the same thing. This can't be right so I either calculated my starting matrix wrong or am rotating incorrectly.

2. Dec 18, 2012

TSny

Hi darthmonkey. Maybe the tensor components don't change under the rotation! Have you tried figuring out the new coordinates of the particles in the rotated system and then calculating the components of the tensor from these components?

3. Dec 18, 2012

darthmonkey

Haha, thanks. I got it to all work out.