Moment of inertia tensor for a laminar

[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,ω_z)

y = 0

I don't understand how the I_XZ component is 0 to just leave the I_ZZ component?

 

[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

 

[jamie.j1989]

Thanks for the reply,

Sorry I didn't explain properly, I'm not getting I_xz = 0, that's what's confusing me if the moment of inertia for an object rotating only about the z axis is I_zz why is I_xz non 0?

 

[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

 

[SteamKing]

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