A gyroscope is a spinning wheel mounted in such a way that its axis can tilt in any direction. Because of the property known as rotational inertia, a spinning wheel will tend to resist any change in the direction of the axis of rotation. It is this property that makes it easy to ride a bicycle in a straight line without tipping over, even though it is virtually impossible to balance a bicycle in the upright position when it is not moving. Similarly, to change the direction in which the bicycle is heading, and thus the direction in which the axles of the wheels are pointing, it is not enough to rotate the handlebar—the rider must also shift his or her weight to provide a significant torque on the wheels.
The relationship between torque and angular momentum requires some fairly complex mathematics to be described in full detail. Some basic insight, however, may be provided by a simple children’s toy—the spinning top. A top that is not spinning will simply fall over when placed upright and released. If it is spinning, however, it will move, as it begins to tip over, so that its axis describes circles in space. The torque—produced by gravity pulling on its center of mass, which is a distance from the point of contact with the floor—now results in this circular motion, or precession instead of a simple falling over.
In a toy gyroscope, the wheel spins on an axis which turns with very low friction within a metal frame which is itself free to rotate about its base point. The low friction allows the wheel to spin at a higher rate than the toy top so the effect lasts longer and is more dramatic. If the frame, also known as a gimbal ring, is mounted inside a second frame and then a third, all with low friction bearings in mutually perpendicular directions, the gyroscope axis will be free to assume any direction in space. In addition, since both ends of the axis can move, the center of mass remains stationary, and since gravitational torques are balanced about this point, the axis direction can remain fixed in space no matter how the outer frame is moved.
In a good quality gyroscope, the axis of rotation will continue to point in the same direction in space, and, since Earth is rotating, it will appear to rotate or precess about a fixed line once a day. The effect is analogous to that exhibited by the famous Foucault pendulum, in which a large mass on the end of a long cord swings as a slow pendulum, and the plane of swing rotates by 360 degrees every 24 hours. To turn the gyroscope into a gyrocompass that always points towards geographic north a spring force or other source of torque is provided to counterbalance the precession due to Earth’s motion.
Applications of gyroscopes
The most obvious application of gyroscopes is to use their property of being able to remember directions, so they are used in automatic pilots and compasses in aircraft for navigational guidance. They are also essential for the guidance and control of space vehicles.
In the design of wind generators of electricity, the collector fan blades are often made to follow the wind. If the wind speed is excessive, the gyroscopic torque may break the blades off the mounting shaft. Gyrodynamics had to be carefully studied in the design of flywheel-driven buses, tried in Europe in the 1950s. These flywheels were about 18 in. (46 cm) in diameter and reached speeds approaching 20,000 rpm. The smaller 2 to 3 in. (5–8 cm) brass wheels used in early autopilots for aircraft were spun at 85,000 rpm although modern autopilot gyros are much slower. The highest rotational speed achieved is 90 million rpm with a gyroscope designed by the American physicist Jesse W. Beams.
In 1933, the designers of the Italian ocean liner Conte di Savoia, recognizing the huge twisting force that could be applied by large spinning wheels, fitted three giant gyroscope rotors on a vertical shaft in the bowels of the ship to act as stabilizers. Each wheel had a diameter of 13 ft. (4 m) and weighed 108 tons (97 tonnes).
Gyroscopes are also mounted on theodolites used in underground mine exploration. It is necessary to use gyrocoscopes because ordinary magnetic compasses are affected by changes in magnetism caused by metal deposits.
