  In the easy-plane phase, a ferromagnetic spin-1 Bose-Einstein condensate is
magnetized in a plane transverse to the applied Zeeman field. This phase
supports polar-core spin vortices (PCVs), which consist of phase windings of
transverse magnetization. Here we show that spin-changing collisions cause a
PCV to accelerate down density gradients in an inhomogeneous condensate. The
dynamics is well-described by a simplified model adapted from scalar systems,
which predicts the dependence of the dynamics on trap tightness and quadratic
Zeeman energy. In a harmonic trap, a PCV accelerates radially to the condensate
boundary, in stark contrast to the azimuthal motion of vortices in a scalar
condensate. In a trap that has a local potential maximum at the centre, the PCV
exhibits oscillations around the trap centre, which persist for a remarkably
long time. The oscillations coincide with the emission and reabsorption of
axial spin waves, which reflect off the condensate boundary.
