If we take the movement of a rotating gyroscope held horizontally at one end with a rope, then the rotational momentum of the gyroscope's spin exists, as well as the rotational momentum caused by torque applied by gravity over time. This would lead to a linear combination of those rotational momenta, which would require the gyroscope to rotate around the Y (vertical) axis. The question is: If the torque is applied constantly, shouldn't it cause the rotational momentum to get constantly larger, and thus increase the rate of precession, or in simpler terms, shouldn't the gyroscope accelerate while precessing?
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The torque vector (or moment) produced by gravity is equal to the rate of change of the angular momentum vector. In the case of a horizontal gyroscope, both vectors are horizontal and at right angles. The momentum vector changes in direction but not in magnitude.
R.W. Bird
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