Airfoil dynamic stall in incompressible flow is characterized by two interacting viscous flow phenomena: time-varying trailing-edge separation and the shedding of intermittent leading-edge-vortex structures. In the current work, a physics based low-order method capable of modeling the interactions between the two flow phenomena is developed with the aim of predicting dynamic stall with only a few empirical tuning parameters. Large computational datasets are used to understand the flow physics of unsteady airfoils so as to augment an inviscid, unsteady airfoil theory to model the time-dependent viscous effects. The resulting model requires only three empirical coefficients for a given airfoil and Reynolds number, which could be obtained from a single moderate-pitch-rate unsteady motion for that airfoil/Reynolds number combination. Results from the low-order model are shown to compare excellently with computational and experimental solutions, in terms of both aerodynamic loads and flow-pattern predictions. In addition to formulating a method with limited empirical dependencies, the current research provides valuable insights into the flow physics of unsteady airfoils and their connection to rapidly predictable theoretical parameters.