The Jovian flywheel model was developed to explain the remarkable steadiness of the observed corotation lag in Jupiter's magnetosphere. The key conclusion of that research was that the observed lag is primarily due to slippage within the neutral atmosphere, with only a small fraction of it arising from slippage between the thermosphere and magnetosphere. Moreover, the neutral wind profile in the atmosphere responds very slowly, so it acts as a mechanical flywheel to dampen out temporal variations with timescales less than several months. We adapt the model for Saturn by allowing the Pedersen conductance to differ in the northern and southern hemispheres. In steady state, the two neutral thermospheres then have different rotation rates that can slowly vary with the season on Saturn as solar illumination of the poles varies.