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Why is rigid body rotational energy not exactly applicable to fluids?

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I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that equation)? Is it only because the moment of inertia is not constant or is there another underlying physics involved?

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