Persistent currents in Bose condensates with a scalar order parameter are stabilized by the topology of the order parameter manifold. In condensates with multicomponent order parameters it is topologically possible for supercurrents to "unwind" without leaving the manifold. We study the energetics of this process in the case of ferromagnetic condensates using a long wavelength energy functional that includes both the superfluid and spin stiffnesses. Exploiting analogies to an elastic rod and rigid body motion, we show that the current carrying state in a 1D ring geometry transitions between a spin helix in the energy minima and a solitonlike configuration at the maxima. The relevance to recent experiments in ultracold atoms is briefly discussed.