Using three-dimensional infrared high-speed video, we captured the wing and body kinematics of free-flying fruit flies as they performed rapid flight maneuvers. We then "replayed" the wing kinematics on a dynamically scaled robotic model to measure the aerodynamic forces produced by the wings. The results show that a fly generates rapid turns with surprisingly subtle modifications in wing motion, which nonetheless generate sufficient torque for the fly to rotate its body through each turn. The magnitude and time course of the torque and body motion during rapid turns indicate that inertia, not friction, dominates the flight dynamics of insects.