PX275 - C1g - interpretation of curl

assuming that angular momentum is conserved
$L = m v r$
$| ω | = \frac{v}{r}$
$L = m | ω | r^{2}$
$| ω | \propto \frac{1}{r^{2}}$ and $v \propto \frac{1}{r}$
the velocity:

\vec{v} = \frac{k}{ρ} {\hat{e}}_{ϕ}

where, $k$ is a constant

\vec{\nabla} \times \vec{v} = \frac{1}{ρ} | \begin{matrix} {\hat{e}}_{ρ} & ρ {\hat{e}}_{ϕ} & {\hat{e}}_{z} \\ \frac{\partial}{\partial ρ} & \frac{\partial}{\partial ϕ} & \frac{\partial}{\partial z} \\ 0 & ρ \frac{k}{ρ} & 0 \end{matrix} | = 0

previously, something spinning was thought of as having a curl
but here, it is the curl of a velocity field, ie: the potential for that field to 'curl' something around
basically, every point of a raft on the field experiences the same force, so it does not turn
consider two red buoys and a paddle wheel in a whirlpool
the paddle wheel will go around the centre of the whirlpool, but it won’t rotate on it’s own axis
this happens because the angular velocity of the liquid changes with radial distance out from the centre
locally the curl is always zero, in the neighbourhood of the point of interest
when the curl, $\vec{\nabla} \cdot \vec{v} = 0$ , the velocity field, $\vec{v}$ is said to be 'irrotational' in that region