# Moment of inertia tensor for a laminar

1. Dec 29, 2013

### jamie.j1989

Hi,

Consider a 2D laminar only rotating about the z axis, with the axis origin at the bottom left hand corner and adjacent sides coinciding with the z and x axes.

so ω = (0,0,ωz)

y = 0

I dont understand how the IXZ component is 0 to just leave the IZZ component?

2. Dec 30, 2013

### facenian

There must be something wrong$\int xz dA$is not zero. I suppose we are talking about the inertia tensor components, however the moment of inertia with respect to the z axes is just I_zz

3. Dec 30, 2013

### jamie.j1989

Sorry I didn't explain properly, i'm not getting Ixz = 0, thats whats confusing me if the moment of inertia for an object rotating only about the z axis is Izz why is Ixz non 0?

4. Dec 30, 2013

### facenian

the expresion for the moment of inertia of an object rotating about a direcction $\hat{n}=(n_1,n_2,n_3)\,\,is\,\,I_{\hat{n}}=\sum_{ik}I_{ik}n_in_k$ so when it rotates about the z axes only I_zz matters

5. Dec 30, 2013

### SteamKing

Staff Emeritus
In general, the products of inertia (Ixy, Iyz, Ixz) are zero only when there are axes of symmetry for the particular body undergoing rotation.