At millimeter and centimeter scales, flapping-wing robots often employ flexural passive wing hinges to eliminate extra actuation and mechanical complexity. In this paper, we propose a modified quasi-steady model for predicting aerodynamic forces from a flapping wing with a passively rotating hinge. The model is based on a simplifying assumption of balanced torque (aerodynamic torque equals to the restoring torque from the hinge). The resulting lift and drag can then be accurately predicted by the modified quasi-steady model without direct knowledge of the angle of attack of the wing. Approximate expression of stroke-averaged forces are also derived. We performed flapping experiments on a centimeter-scale device and the measured lifts show good agreement with the model predictions.