Why do r and F need to be perpendicular for two angles to give the same torque?

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The discussion revolves around the concept of torque in physics, specifically examining the conditions under which two angles can yield the same torque given the magnitudes of the position vector (r) and force (F).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the angles formed by the position vector and the force vector, questioning how torque can remain the same for different angles. Some express difficulty in visualizing the concept, while others reference the definition of torque and the sine function.

Discussion Status

The discussion is active, with participants raising questions about the underlying principles of torque and its dependence on angle. There is an acknowledgment of the mathematical relationship involved, but no consensus has been reached regarding the visualization or implications of the angles.

Contextual Notes

Participants are navigating the definitions and relationships in torque calculations, particularly focusing on the angles involved and their geometric interpretations. There is an indication that the discussion is constrained by the need for clarity on these concepts.

Ronnin
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Unless r and F are perpendicular, there are always two angles between their directions that give the same torque for given magnitudes of r and F. Explain why?

Perhaps I cannot visualize the question, but I cannot see how this can be. As the force moves to the perpendicular position the torque increases. Am I missing something?
 
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Use the definition of torque. If one angle between the p.v and force vector is theta, what about the other?

Edit: I guess this holds only for the magnitude of the torque.
 
Last edited:
[tex]\tau = rF \sin \theta[/tex]

[tex]sin \theta = \sin (\pi - \theta)[/tex]​

:smile:
 
I guess I figured that would put the angle outside of between the two angles.
 

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