What is the purpose of the airplane's rudder?

The purpose of the airplane's rudder is primarily to counteract adverse yaw when rolling into or out of a turn. When an airplane is being maneuvered, particularly during a turn, the ailerons are used to roll the aircraft, but this can induce a yawing moment due to the difference in lift and drag on the wings. The wing that is raised (with its aileron deflected up) typically has less drag than the wing that is being lowered (with its aileron deflected down), which can cause the aircraft to yaw in the opposite direction of the turn. The rudder is used to counteract this tendency by applying lateral control, helping to align the aircraft's nose with the flight path and ensuring a smoother and more coordinated turn.

While the rudder does play a role in stabilizing the aircraft during flight, that is a broader function served by multiple components including the ailerons and elevators. The main function associated with the rudder in the context provided is specifically aimed at managing adverse yaw, making the third choice the most accurate regarding its primary role in flight maneuvers.