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3

$\vec\omega = I^{-1} \vec L$, and $\vec L$ is constant in the absence of external forces. The bit that I think you're missing is that $I$ rotates with the rigid body, so it is not constant in general and neither is $\vec\omega$. I played with your online example, and the angular velocity does seem to always remain constant when I'm not poking the block, ...

2

A fluid is modelled as a vector field and therefore we use vorticity to describe its spinning motion. Angular momentum is more often used for a single object or particle, but not so often for a vector field (even though it is still applicable in principle). For a fluid in general, vorticity is twice the mean angular velocity and this fact to me makes it less ...

1

We don't need to talk about angular momentum because the conservation law is summed up by vorticity. Consider the vorticity equation (in the context of a rotating frame as well): $$\frac{D\boldsymbol\omega}{Dt}=\boldsymbol\omega\cdot\nabla\mathbf u$$ (ignoring all other terms that are normally contained in this term). If we take the coordinate system where ...

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