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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?

GameOver
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  • You are asking about how an applied torque is affecting the spinning gyroscope. That question already has an answer. Note that the applied torque can either come from an external weight or from the weight of the gyro wheel itself; there's no real difference there See: Precession of a gyroscope – Cleonis May 12 '20 at 16:43
  • I understand that it is spinning, but I do not understand why it is not accelerating in that direction while spinning. – GameOver May 12 '20 at 16:50

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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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  • did you mean "but not in magnitude"? – GameOver May 13 '20 at 04:01
  • yes I understand that, but shouldn't the angular momentum vector caused by gravitational torque increase in magnitude over time? – GameOver May 13 '20 at 04:02
  • You are correct. It should be "but not in magnitude". I have made the correction. The torque from gravity causes a constant horizontal rate of change for the angular momentum of the gyroscope, so the vertical angular momentum vector associated with the motion of the center of mass around the point of support does not change. Friction with the air or at the point of support does cause a vertical torque which causes the angular momentum vector for the gyroscope to slowly swing downward. – R.W. Bird May 13 '20 at 13:29