= Sharp-edge force singularity of a thin disk
{title2=$g_R\sim G\Sigma_{\rm edge}\log(\ell/\epsilon)$}
At an abruptly truncated <razor-thin disk> with nonzero edge <surface density of a disk>, the midplane radial force diverges logarithmically. Locally, mass occupies a half-plane and the inward force contains a nonzero angular factor multiplying $G\Sigma_{\rm edge}\int_\epsilon^\ell ds/s$. The opposite exterior half-plane is absent, so its cancellation does not occur. Finite thickness or a taper taking the edge density to zero regularizes the force. Therefore a finite-edge <galaxy rotation curve> requires more than the ideal scale-free <Mestel disk> normalization.
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