Circular systems are advantageous for interfacial studies since they do not suffer from end effects, but their hydrodynamics is more complicated because their flows are not unidirectional. Here, we analyze the shear rheology of a harmonically driven knife-edge viscometer through experiments and computations based on the Navier-Stokes equations with a Newtonian interface. The measured distribution of phase lag in the surface velocity relative to the knife-edge speed is found to have a good signal-to-noise ratio and provides robust comparisons to the computations. For monomolecular films of stearic acid, the surface shear viscosity deduced from the model was found to be the same whether the film is driven steady or oscillatory, for an order of magnitude range in driving frequencies and amplitudes. Results show that increasing either the amplitude or forcing frequency steepens the phase lag next to the knife edge. In all cases, the phase lag is linearly proportional to the radial distance from the knife edge and scales with surface shear viscosity to the power .