What effect does a right-hand propeller have when the engine is running regarding gyroscopic moments?

The choice indicating that a right-hand propeller creates a yawing moment to the left when the aircraft rolls to the right is correct due to the principles of gyroscopic precession and the effects of propeller rotation on aircraft dynamics.

When a right-hand propeller spins clockwise from the pilot's perspective, it generates gyroscopic forces that exert their influence depending on the orientation of the aircraft. If the aircraft begins to roll to the right, the forward motion of the propeller blades contributes to a gyroscopic effect that tends to cause a yaw to the left. This is because the gyroscopic precession causes the force applied to the system (the roll to the right) to generate a lateral response (yawing to the left) 90 degrees ahead in the direction of rotation.

This behavior is a critical aspect of understanding how propeller-driven aircraft respond to various maneuvers, particularly in the context of maintaining control during flight. Recognizing the relationship between the direction of roll and the resulting yaw is essential for pilots when managing aircraft stability and control.

The other choices introduce different dynamics that do not align with the principles governing gyroscopic effects, emphasizing why the selected option is accurate in depicting the aircraft's response to the specified conditions.