A modified Reynolds equation for flow dynamically represented as incompressible is used to model the dynamics of a thin film bearing with slip flow and a rapidly rotating coned rotor. Previous studies including a Navier slip length shear condition on the bearing faces are extended to investigate applications with a coned bearing gap. A modified Reynolds equation for the film flow is coupled, through the pressure exerted by the fluid film, to the dynamic motion of the stator. Introducing a new variable leads to explicit analytical expressions for the pressure field and force on the stator with the equation for the time-dependent face clearance transformed to a nonlinear second-order non-autonomous ordinary differential equation. The face clearance for periodic axial motion of the coned rotor is obtained using a stroboscopic map solver; a focus is investigating bearing behaviour under extreme conditions. The coupled fluid flow and unsteady bearing dynamics are examined for a range of configurations to evaluate potential face contact over a range of bearing surface conditions.