Slip flow occurs in a wide variety of practical chemical engineering processes. This work models, for the first time, the interaction of surface slip and system rotation normal to the flow direction. It is found that the flow fields are affected considerably. For Poiseuille flow, slip increases the longitudinal flow rate at low rotation, but decreases it at high rotation. For Couette flow, slip decreases the longitudinal drag. The solutions are also exact solutions of the Navier-Stokes equations.