Steady axisymmetric thin film flows on a rotating cone of Newtonian and non‐Newtonian liquids are analyzed by means of the axisymmetric boundary layer with swirl equations, Galerkin finite‐element discretization with free surface parameterization, and Newton iteration, which permits the simultaneous evaluation of the boundary layer thickness with the primary unknowns which are the three velocity components. The significance of the inlet boundary conditions on the accuracy of the finite‐element predictions is discussed in detail. It is shown that natural inlet boundary conditions compatible with the local dynamics are superior to essential boundary conditions which may give rise to artificial finite‐element solutions. The analysis accounts for inertia, viscous, and surface tension effects. Both centrifugal and Coriolis accelerations are included. Results are presented and compared for Newtonian, shear‐thinning and shear‐thickening, Bingham plastic, and second‐order viscoelastic liquids at different operating conditions. In the limiting case of a rotating disk, in spin coating, the effects of the Coriolis acceleration, which have been omitted in earlier analyses are investigated. Closed form asymptotic solutions agree with the finite‐element predictions at high rotation. At low rotation, the asymptotic solution breaks down and so the finite‐element solution becomes essential.