= Solution
In <cylindrical coordinates>, $F=r^{1-2n}\hat\theta$. The tangential coefficient is positive for every real $n$ and $r>0$, so the large-scale circulation is always counterclockwise when viewed from positive $z$.
By <8/c/i/solution>, the infinitesimal local <angular velocity> is $(1-n)r^{-2n}\hat z$. Its sign gives
$$
\boxed{\begin{array}{c|c}
n<1&\text{local spin in the same sense as circulation}\\
n=1&\text{zero local spin}\\
n>1&\text{local spin opposite to circulation}
\end{array}}
$$
“Zero local spin” does not mean zero <velocity>: at $n=1$ a marked small element is still carried around the axis while its infinitesimal rotational component is zero. Orbital motion around the axis and local <vorticity> are different measurements.
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