The unsteady shedding process of circulation from a translating and rotating cylinder is investigated using planar particle image velocimetry, both in quiescent fluid as well as during a sharp-edged gust encounter. The Reynolds numbers are 20 000 and 6000, respectively. The rate at which circulation is shed is computed by evaluating the vorticity flux in the boundary layer. The shedding rate is found to be proportional to the difference between the total boundary layer vortex sheet and the vortex sheet strength contribution due to rotation. This is equivalent to the sum of the non-circulatory vortex sheet and that due to shed circulation, evaluated at the separation point. A direct consequence of this is that the shedding rate is independent of body rotation. It only depends on the geometry of the body and any previously shed circulation. Therefore, before any separation has occurred and if the separation point is known, the rate at which circulation sheds can solely be determined from potential flow theory. It is also observed that previously shed circulation, which has travelled a large distance from the cylinder, induces a uniform `mirror' vortex sheet, which has the effect of globally affecting and shifting the boundary layer vortex sheet. This can potentially provide an alternative explanation for alternate vortex shedding. Similarly, Prandtl's theoretical maximum lift coefficient for a surging and rotating cylinder can be reconciled with the proposed theory and recovered by only using this boundary layer vortex sheet analysis.