  We carry out a systematic analytic investigation of stationary and
cylindrically symmetric vortex configurations for simple models representing an
incompressible non-relativistic superconductor in a rigidly rotating
background. It is shown that although the magnetic and kinetic contributions to
the energy per unit length of such a vortex are separately modified by the
background angular velocity, its effect on the total energy per unit length
cancels out. For a type II superconductor threaded by a parallel array of such
vortices, this result implies that the relevant macroscopic magnetic field
strength H will not be equal to the large scale average <B> of the local
magnetic induction B (as has previously been suggested) but instead that H will
simply be equal to the external London field that characterizes the value of B
outside the vortices.
