Final answer:
A gyroscope maintains its orientation due to angular momentum and exhibits precession when an external torque is applied. This enables its use in navigation and stability control in various vehicles.
Step-by-step explanation:
The two fundamental properties of a gyroscope are its ability to maintain its orientation due to angular momentum and its behavior of precession when an external torque is applied. A gyroscope consists of a spinning disk, and when this disk is spinning, it resists changes to its orientation. This is because of the conservation of angular momentum. The second fundamental property is precession, which occurs when an external torque is applied (such as gravity acting on the gyroscope's center of mass) that is perpendicular to the angular momentum vector. This causes the gyroscope to precess around a vertical axis rather than falling over.
An example often cited is Earth itself, which acts like a gargantuan gyroscope with angular momentum along its axis pointing toward Polaris, the North Star. The behavior of gyroscopes is crucial in applications such as navigation and stability in various vehicles including spacecraft, satellites, and rockets, where maintaining a precise orientation is vital.