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3-17 faster you turn the case, the more the gyro will precess, since the amount of precession is proportional to the rate at which you are turning the gyro case. This characteristic of a gyro, when properly used, fits the requirements needed to sense the rate of motion about any axis. Figure 3-15 shows a method of restraining the precession of a gyro to permit the calculation of an angle. Springs have been attached to the crossarm of the output shaft. These springs restrain the free precession of the gyro. The gyro may use other types of restraint, but no matter what type of restraint is used, the gyro is harnessed to produce some useful work. Figure 3-15.—Precession of a spring restrained rate gyro. As the gyro precesses, it exerts a precessional force against the springs that is proportional to the momentum of the spinning wheel and the applied force. For example, suppose you rotate the gyro case (fig. 3-15) at a speed corresponding to a horizontal force of 2 pounds at F. Obviously, the gyro will precess; and as it does, it will cause the crossarm to pull up on spring A with a certain force, say 1 pound. (This amount of force would vary with the length of the crossarm.) If you continue to turn the gyro case at this rate, the precession of the gyro will continually exert a pull on the spring. More precisely, the gyro will precess until the 1 pound pull of the crossarm is exactly counterbalanced by the tension of the spring; it will remain in a fixed position, as shown in figure 3-15. That is, it will remain in the precessed position as long as you continue to rotate the gyro case at the same, constant speed. A pointer attached to the output axis could be used with a calibrated scale to measure precise angular rates. When you stop moving the case, you remove the force at F, and the gyro stops precessing. The spring is still exerting a pull, however, so it pulls the crossarm back to the neutral position and returns the pointer to "zero." Suppose you now rotate the gyro case at a speed twice as fast as before, and in the same direction. This will be equal to a 4-pound force applied at F and a resulting 2-pound pull by the crossarm on spring