6. B2 follow the Earth-Moon system around the Sun in precisely the same orbit as if it were a nonrotating body. But the gyro will keep its spin axis aimed at the same point in the "fixed" heavens the whole time - provided no torques are applied to it. Figure 6.Bl depicts this situation. Changing the angular orientation of the spin axis (and therefore of~) of a gyroscope is called precession. Torques can produce precession. A torque vector~ has direction defined by the righthand rotation rule, and magnitude L by the force applied times the length of the moment arm. If a torque is applied to a gyroscope, it affects the angular momentum according to: dH ~ = cE (6. Bl) where tis time. Physically, this means that the gyro attempts to line up its angular momentum with the applied torque. Two cases are of particular interest. If~ is along the z-axis (and thus lined up with~), the direction of H does not change. The magnitude H increases or decreases, depending on the direction of~ (positive-z or negative-z). This case is shown in Figure 6.B2. An applied torque lined up with the spin axis increases the angular momentum until the hull spins at 2 to 3 RPM. The second case is an~ applie~ at right angles to~- Then the magnitude H remains constant, but the direction of~ tends towards L. Figure 6.B3 presents this case. Note that the precession response of the gyro does not move the point of application of the force in the direction of that force (at least not appreciably - more on that later), but instead at right angles to it. The equation governing the precession in this case is: L = Hsl (6. Bl) where~ is the angular velocity of precession. If the torque applied is kept at right angles to~ while~ is sweeping around, then~ will keep on doing so without changing its magnitude.
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