Final answer:
Gyroscopes in guidance systems maintain a constant direction of angular momentum through the conservation of angular momentum and the phenomenon of precession, where torque applied to the gyroscope causes it to move without changing the direction of its angular momentum.
Step-by-step explanation:
Gyroscopes used in guidance systems work on the principle of conservation of angular momentum, which allows them to maintain a constant direction of angular momentum despite external forces and accelerations. The key to a gyroscope's ability to maintain its direction lies in the phenomenon of precession. Precession occurs when a torque is applied to a spinning object, like a gyroscope; this torque is always perpendicular to the angular momentum vector. As a result, while the gyroscopic system may move or 'precess', the actual direction of the angular momentum remains unchanged, preserving the gyroscopic effect and allowing the guidance system to maintain orientation.
When an external force is applied, it creates a horizontal torque on the spinning gyroscope, resulting in a change in angular momentum that is also horizontal. The vector sum of the original angular momentum and the change in angular momentum due to the torque is a new angular momentum vector with the same magnitude but a slightly different direction. The gyroscope thus precesses in response to the torque instead of tumbling over, and this precession is predictable and can be accounted for in the guidance system.