Which of these instruments operates on a gyroscope?

The heading indicator and the attitude indicator operate on gyroscopic principles, making them unique among the options presented.

The heading indicator uses a gyroscope to maintain its orientation, providing pilots with a reliable reference for their aircraft's direction. As the aircraft turns, the gyro resists changes in direction due to its rigidity in space, allowing it to retain a consistent heading reference.

Similarly, the attitude indicator operates using a gyroscope that helps display the aircraft's orientation relative to the horizon. It shows whether the aircraft is climbing, descending, or turning and helps pilots maintain proper control, especially in conditions of reduced visibility where visual reference points may be limited.

In contrast, the altitude indicator, vertical speed indicator, and magnetic compass do not operate on gyroscopic principles. The altitude indicator typically uses a barometric principle to measure changes in air pressure at different altitudes. The vertical speed indicator measures the rate of ascent or descent by utilizing a diaphragm that senses the difference in static pressure over time. The magnetic compass relies on the Earth's magnetic field to indicate direction, fundamentally differing from the gyroscopic operations of the heading and attitude indicators.