[FluidKo]

Hello guys
I've watched video of below link.
https://www.youtube.com/watch?v=p_82...X2o4TX&index=3
Since 33:48, angular momentum conservation of flow particle is derived.
This derivation is showing symmetric of shear stress.
()
At here, all of angular acceleration related terms(Kinetic terms) are removed.
Then does it means rotation is always steady state no matter which kind of flow is imposed?

But as far as I know rotation is defined as below
.
By upper formula, rotation depends on velocity field so that if there is unsteady flow field, rotation is different depending on time.

I'm confused between this and angular momentum conservation of flow particle.
What is right?
Thank you