The effects of rotation on a mushy layer, during the solidification of binary alloys, is considered. A near-eutectic approximation and large far-field temperature are employed in order to decouple the mushy layer from the overlying liquid melt. The current study employs a new moderate time scale for mushy layers exhibiting Stefan numbers of unit order of magnitude. The weak non-linear theory is used to evaluate the leading order amplitude. The results of the weak non-linear theory are then used to establish the nature of the bifurcation, that is whether the bifurcation is forward or inverse.