For solid sphere of radius R, azimuthal angle $\phi$ and polar angle $\theta$ rotating at velocity $\vec{v}$ with uniform surface charge $\sigma$ ,
the bound surface current density is
$\vec{K}=\sigma \omega R \sin(\theta)\hat{\phi}$
I'm curious as to why $\vec{v}=\omega R \sin(\theta)\hat{\phi}$
I understand why the $\hat{\phi}$ exists.
Any physical insights into the formulation of the above expression is appreciated.
Thanks in advance.