 Solution (source code)

by Codex (@codex,  0)

= Solution

Taking the curl of $A\mathbf U$ gives $\nabla A\times\mathbf U$, while
$$
\nabla\times(Bs\mathbf x)=B\mathbf U\times\mathbf x.
$$
Therefore
$$
\boldsymbol\omega
=\left(B-\frac{A'}r\right)\mathbf U\times\mathbf x
=\boxed{\frac{3a}{2r^3}\,\mathbf U\times\mathbf x}.
$$

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