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

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SUMMARY

The discussion clarifies the relationship between the torque directions of two interacting gears, A and B. When gear A is driven with a clockwise torque, gear B experiences a counterclockwise torque due to Newton's Third Law, which states that for every action, there is an equal and opposite reaction. The Right-Hand Rule is recommended for visualizing torque vectors, and the magnitude of torque is influenced by the gear's diameter or number of teeth. Understanding these principles is essential for analyzing gear interactions in mechanical systems.

PREREQUISITES
  • Understanding of Newton's Third Law of Motion
  • Familiarity with torque and its vector representation
  • Knowledge of the Right-Hand Rule for torque direction
  • Basic concepts of gear mechanics, including gear ratios and contact forces
NEXT STEPS
  • Research the application of the Right-Hand Rule in mechanical systems
  • Explore the principles of gear ratios and their impact on torque
  • Study the effects of gear diameter and tooth count on torque magnitude
  • Investigate the relationship between driving and resisting torques in mechanical systems
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in the design or analysis of gear systems will benefit from this discussion.

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.
 
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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