Why is the driven gear's torque's direction clockwise?

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Discussion Overview

The discussion revolves around the direction of torque in a system of two interacting gears, specifically why the torque on gear B is clockwise when gear A is driven with a clockwise torque. The conversation explores concepts related to torque direction, Newton's laws, and the interaction between gears.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that if gear A is turning clockwise, then gear B must turn counterclockwise, leading to a discussion on the direction of the torque applied to each gear.
  • One participant questions whether the torque applied to gear A is against its rotation, suggesting a need for clarification on the nature of the applied torque.
  • Another participant proposes that the torque on gear B is a reaction torque to the torque applied to gear A, referencing Newton's 3rd law.
  • A participant mentions using the Right-Hand Rule to visualize the torque vectors for each gear, indicating a method to understand the torque directions.
  • There is a suggestion that the magnitude of the torque depends on the diameter or number of teeth of each gear, implying a relationship between gear design and torque characteristics.
  • One participant emphasizes that force and resistance are always paired, indicating that a driving torque cannot exist without a corresponding resisting torque.

Areas of Agreement / Disagreement

Participants express differing views on the direction of torque for gear B, with some asserting it is counterclockwise while others argue it is clockwise as a reaction to gear A's torque. The discussion remains unresolved regarding the exact nature of the torque interactions.

Contextual Notes

The discussion includes assumptions about the interaction of forces and torques, as well as the application of Newton's laws, which may not be fully detailed or agreed upon by all participants.

annamal
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TL;DR
Two gears (A and B) are spinning with their centers fixed with the left one being the driver driving the left gear clockwise. Why is the driven gear (gear B to the right) torque clockwise as well?
We have two gears A and B (left and right). Gear A is driven with a clockwise torque. Why is gear B's torque also clockwise? I would say that if gear B is driven to turn counterclockwise, the torque should be in the counterclockwise direction.
Screenshot 2023-09-12 at 7.09.39 PM.png
 
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If the left gear is turning clockwise, the right gear will turn counterclockwise. Is the torque you are applying to A against the rotation or something?
 
berkeman said:
If the left gear is turning clockwise, the right gear will turn counterclockwise. Is the torque you are applying to A against the rotation or something?
No. I am applying a torque just to gear A. And apparently the torque for gear B is in the opposite direction because it is some reaction torque to gear A.
 
I assume what's being described is the force applied by gear B to gear A. If gear A applies a force downwards at the point of contact, gear B must be applying a force back against it upwards per Newton's 3rd law.
 
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annamal said:
No. I am applying a torque just to gear A. And apparently the torque for gear B is in the opposite direction because it is some reaction torque to gear A.
Sure, just use the Right-Hand Rule for torques to help you see what is going on. Draw the force and torque vectors for each gear...
$$\vec \tau = \vec R \times \vec F$$
 
Ah. I figured it out. The torque for the right gear is drawn as the load's torque.
 
annamal said:
Ah. I figured it out. The torque for the right gear is drawn as the load's torque.
Correct.
Consider that the magnitude of each torque depends on the diameter (or number of teeth) of each gear.
Only the tangential contact forces mentioned in post #4 are of equal magnitude and opposite directions.

Force (or torque) and resistance to it are always a pair.
We can't talk about a driving torque, unless we have a resisting torque.
In the same way, we can't exert any weight on the floor of a free-falling elevator.

FREE-BODY-DIAGRAM-OF-TWO-GEAR.png
 

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