Scaling Intertia Tensor

  1. Hi everyone,

    I have the following problem in my hands, which I don't know how exactly to address.

    Let's assume that from any CAD(Solidworks, Catia), I obtain the inertia tensor of my model (impossible to calculate by hand btw).

    I_full=[Ixx Ixy Ixz
    Ixy Iyy Iyz
    Ixz Iyz Izz]

    I know if I change the mass of my model, the inertia tensor will scale linearly with it.

    But what If I scale my model to half-size, all dimensions? The mass probably goes by 1/8, since it's proportional to volume. Maybe the other factor would be 1/4 (α r^2).

    So would the correct Inertia scaling factor be?:

    I_half=1/4*1/8*I_full

    Cheers!!
     
  2. jcsd
  3. UltrafastPED

    UltrafastPED 1,918
    Science Advisor
    Gold Member

  4. Thanks you!

    It proves my derivation, if assumed constant density between the scaled object and full-size object.

    by definition:

    [tex]I=\int_V \rho r^2 dV[/tex]

    if r1-> ar ( scaled by a factor a) dV1->a^3dV

    replacing on the above equation:
    [tex] I1=\int_V \rho a^2 r^2 a^3 dV = a^5 \int_V \rho r^2 dV -> I1=a^5 I[/tex]

    again, assuming that the mass distribution remains constant.

    Correct?
     
    Last edited: May 2, 2014
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