Which part of an aircraft primarily controls its direction of motion around the vertical axis?

The rudder is the primary control surface that governs an aircraft's motion around the vertical axis, which is also referred to as yaw. It is situated on the vertical stabilizer (the tail fin) of the aircraft. When the pilot moves the rudder pedal, the rudder deflects to one side, causing the aircraft's tail to move in the opposite direction. This action pivots the aircraft left or right while maintaining its altitude and speed.

In contrast, ailerons are responsible for controlling roll, allowing the aircraft to bank left or right. Elevators control pitch, which affects the nose of the aircraft moving up or down, impacting climb or descent. Flaps serve to increase lift during takeoff and landing but do not significantly influence yaw. Thus, the rudder is the correct answer to the question regarding control around the vertical axis.