Granular flows in rotating drums transition between two regimes characterized by straight and curved free surfaces. Here we predict this behavior using a depth-integrated theory applicable to general eroding flows. Closure is achieved by a local μ(I) rheology and an equation for kinetic energy. Spanning the transition, the theory yields relations for all flow properties in terms of a single dimensionless rotation rate. In accord with experiments, distinct scaling laws are obtained for slow and fast rates, dominated respectively by local energy dissipation and longitudinal energy transfer.