We study the axisymmetric stretching of a thin sheet of viscous fluid
driven by a centrifugal body force. Time-dependent simulations show that
the sheet radius tends to infinity in finite time. As the critical time is
approached, the sheet becomes partitioned into a very thin central region
and a relatively thick rim. A net momentum and mass balance in the rim leads
to a prediction for the sheet radius near the singularity that agrees with the numerical
simulations. By asymptotically matching the dynamics of the sheet with the
rim, we find that the thickness in the central region is described by a
similarity solution of the second kind. For non-zero surface tension, we
find that the similarity exponent depends on the rotational Bond number B,
and increases to infinity at a critical value B=1/4. For B>1/4, surface
tension defeats the centrifugal force, causing the sheet to retract rather
than stretch, with the limiting behaviour described by a similarity
solution of the first kind.