Moment of inertia tensor for a laminar

AI Thread Summary
The discussion centers on the moment of inertia tensor for a 2D laminar object rotating about the z-axis. The user expresses confusion regarding the IXZ component, questioning why it is considered zero when the moment of inertia about the z-axis is IZZ. It is clarified that IXZ is not necessarily zero unless the object has axes of symmetry. The moment of inertia for rotation about a specific axis only considers IZZ, but the presence of non-zero products of inertia like IXZ indicates asymmetry. Understanding these components is crucial for accurately describing the rotational dynamics of the object.
jamie.j1989
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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 don't understand how the IXZ component is 0 to just leave the IZZ component?
 
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There must be something wrong\int xz dAis 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
 
Thanks for the reply,

Sorry I didn't explain properly, I'm not getting Ixz = 0, that's what's confusing me if the moment of inertia for an object rotating only about the z axis is Izz why is Ixz non 0?
 
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
 
In general, the products of inertia (Ixy, Iyz, Ixz) are zero only when there are axes of symmetry for the particular body undergoing rotation.
 

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