Gyroscope- Angular Momentum and Torque

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Discussion Overview

The discussion revolves around the concepts of angular momentum and torque in the context of gyroscopes, particularly focusing on the relationship between these quantities when measured from different reference points and the effects of external forces in various environments. The scope includes theoretical reasoning and conceptual clarification regarding gyroscopic motion and precession.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the measurement of angular momentum from the center of the spinning disk while torque is measured from the pivot point, seeking clarification on the relationship between torque and angular momentum.
  • Another participant asserts that for a gyroscope with no net linear momentum, angular momentum is independent of the choice of reference point for measurement.
  • A participant suggests that torque can be computed from the center of mass of the gyroscope to avoid confusion regarding reference points.
  • One participant inquires whether the change in angular momentum would be the same regardless of where it is measured along the gyroscope's axis.
  • A hypothetical scenario is presented regarding the behavior of a spinning gyroscope in a gravity-free environment when pushed at the pivot, questioning whether a torque couple is necessary for precession.
  • Another participant confirms that angular momentum remains consistent regardless of the measurement point along the axis and discusses the effects of forces in an accelerating frame that mimics gravitational effects.

Areas of Agreement / Disagreement

Participants generally agree that angular momentum can be measured from different points without affecting its value. However, there is uncertainty regarding the necessity of a torque couple for precession in a gravity-free environment, indicating a lack of consensus on that aspect.

Contextual Notes

The discussion does not resolve the implications of measuring torque and angular momentum from different points, nor does it clarify the conditions under which a torque couple is needed for precession in various environments.

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I was reading on gyroscopes, and everything seemed to make sense: the spin angular momentum along the axis of the gyroscope changes due to the torque by gravity, causing precession. However, I can't understand why we are measuring angular momentum (the spin of the gyroscope) from the center of the spinning disk, but the torque from the origin (pivot point). Aren't we supposed to measure torque and angular momentum about the same point to use the relation Torque = dL/dt?

Some clarification would be much appreciated!
 

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For an object with no net linear momentum (e.g. a gyroscope spinning more or less in place), its angular momentum will not depend on what reference point you choose as the origin.

For a torque being applied by a "couple" (a pair of equal but opposite forces that act on parallel lines rather than on the same line, e.g. N and W), it does not matter what reference point you use to compute the net torque.

Or you can avoid the problem and compute the torque produced from the upward force N using a reference point at the center of mass of the gyroscope.
 
Thanks, I see. So it would be safe to say that you get the same change in angular momentum measured anywhere along the axis of the gyroscope?

Also, hypothetically, in a gravity-free environment, if someone were to push a spinning gyroscope at the pivot (acting like the normal force), would it produce the same precession motion? Or is a torque couple needed?
 
Yes, the angular momentum for an object spinning around an axis is the same no matter where on the axis you choose to measure it from.

In a gravity-free environment the gyroscope will be accelerating in the direction of the net force. But you can choose to analyze the system from an accelerating frame in which the center of mass is motionless (like in an elevator that is accelerating upward). In this frame there is a downward inertial force that acts just like gravity. So you can have a force couple if you want one.
 

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