How Do Equal and Opposite Torques Work with Different Moment Arms?

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Discussion Overview

The discussion revolves around the concept of equal and opposite torques in the context of angular momentum, particularly focusing on the implications of different moment arms when two objects exert forces on each other. Participants explore the relationship between torque, force, and moment arm length, questioning how these elements interact under various conditions.

Discussion Character

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

Main Points Raised

  • One participant asserts that angular momentum is conserved, leading to equal and opposite torques between two objects, but questions how this holds if their moment arms differ.
  • Another participant clarifies that angular momentum can be defined around any specified point, and that for contact forces, the moment arms are equal since they originate from the same point.
  • A further contribution emphasizes that equal torques must be computed around the same point, suggesting that different moment arms could complicate the equality of torques.
  • A later reply expresses gratitude for the clarifications provided, indicating a desire to learn more formally about the topic.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between moment arms and torques, with some suggesting that moment arms must be equal while others indicate that this is not necessarily the case. The discussion remains unresolved regarding the implications of differing moment arms in the context of equal and opposite torques.

Contextual Notes

Participants highlight the importance of specifying the point around which angular momentum is defined, as well as the complexities introduced by forces acting at a distance. There are unresolved aspects regarding the conditions under which torques can be considered equal and opposite.

BrainSalad
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Angular momentum is conserved, which means that the change in angular momentum of object A must be exactly canceled by the change in angular momentum of the object exerting a torque on object A. So, the objects, A and B, exert equal and opposite torques on each other. But, the contact forces between the objects must also be equal (Newton's 3rd). Torque= F x r, so what if the moment arm (r) of object A is larger than object B? If torques are equal and forces are equal, moment arms must also be equal, but this is certainly not always the case. What's going on?
 
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"angular momentum" encompasses more than just the rotation of rigid objects around their centers of mass. A moving, non-rotating object also has angular momentum around any specified point. Before you can even have a well-defined angular momentum, you have to specify that point.

Say you have specified that point and you have two objects that are interacting with a contact force -- they bump into each other. By Newton's third law, the forces are equal and opposite [as you have understood]. By the definition of angular momentum, the moment arms are equal -- it is a contact force so both forces act at the same point and both moment arms originate at the same point. It follows that the two torques are equal and opposite.

If you have a force-at-a-distance, things are a little messier, but it works out that the cross product of force times moment arm is still equal and opposite.
 
BrainSalad said:
If torques are equal and forces are equal, moment arms must also be equal, but this is certainly not always the case.
The equal but opposite torques must be both computed around the same point.
 
Thanks to both of you, that clears things up. Can't wait to learn this stuff formally.
 

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