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Scaling Intertia Tensor 
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#1
May214, 03:22 AM

P: 2

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 halfsize, 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
May214, 04:23 AM

Sci Advisor
Thanks
PF Gold
P: 1,911

It must vary jointly with the mass and the distribution; for example consider how the simple inertia of a thick rod changes under your conditions: http://hyperphysics.phyastr.gsu.edu/hbase/mi2.html



#3
May214, 05:01 AM

P: 2

It proves my derivation, if assumed constant density between the scaled object and fullsize 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? 


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