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Moment of inertia tensor for a laminar

  1. Dec 29, 2013 #1
    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. jcsd
  3. Dec 30, 2013 #2
    There must be something wrong[itex]\int xz dA[/itex]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
     
  4. Dec 30, 2013 #3
    Thanks for the reply,

    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?
     
  5. Dec 30, 2013 #4
    the expresion for the moment of inertia of an object rotating about a direcction [itex]\hat{n}=(n_1,n_2,n_3)\,\,is\,\,I_{\hat{n}}=\sum_{ik}I_{ik}n_in_k[/itex] so when it rotates about the z axes only I_zz matters
     
  6. Dec 30, 2013 #5

    SteamKing

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    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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