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How do I calculate the tensor of inertia of a rotating non-rigid body? Is the usual formula:

$$T_{ij} = \int{\rho( x_ix_j - \delta_{ij} x^kx_k)d^3x}$$

still correct?

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  • $\begingroup$ $\rho(\vec{x})$ $\endgroup$ – Eli Jan 24 at 13:19
  • $\begingroup$ @Eli what does it mean? That the density is not a constant, but the whole formula is still valid? $\endgroup$ – mattiav27 Jan 24 at 13:39
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I don't think there is any reason for the formula for intertia to be non-applicable. (Instantaneously, of course, since in time the fluid's volume might deform, density can evolve...) It is the dynamical relations (regarding the change in angular momentum, etc.) whose rigid-body forms would not (necessarily) be applicable to a fluid.

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