Is the Sum of Torques Zero in a System with Equal Forces and Moment Arms?

  • Context: Undergrad 
  • Thread starter Thread starter Kaneki123
  • Start date Start date
  • Tags Tags
    Torque
Click For Summary

Discussion Overview

The discussion revolves around the question of whether the sum of torques is zero in a system where two equal forces act at equal distances from a pivot point, particularly when the forces are applied in a non-linear medium. Participants explore the implications of equal forces and moment arms on torque and motion, considering scenarios of both equal and unequal forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if the sum of torques is zero when equal forces are applied at equal moment arms in a non-linear medium.
  • Another participant notes that without a visual aid, the context is unclear but suggests that equal and opposite forces acting along a common line would not produce torque.
  • A later reply asserts that for equal forces at right angles to equal moment arms, the sum of torques would indeed be zero.
  • Some participants mention that if forces are unequal, there would be a resultant torque, but if they are made equal, the system could achieve uniform circular motion.
  • One participant emphasizes that the forces could act on the same arm with zero angle between them, yet still result in zero torque.
  • Concerns are raised about the need for a reaction force at the pivot to maintain circular motion without linear acceleration.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which the sum of torques is zero, with some agreeing that equal forces lead to zero torque while others highlight the complexity introduced by the medium and the need for additional forces to maintain equilibrium. The discussion remains unresolved regarding the implications of the forces' arrangement and the medium's influence.

Contextual Notes

Participants do not reach a consensus on the impact of the angle between moment arms or the specific configuration of forces, indicating that assumptions about the system's behavior may vary based on these factors.

Kaneki123
Messages
120
Reaction score
3
Okay...I have a question.In the case described in the picture, the medium between the two forces, which would normally cause stationary or uniform circular motion, is not straight..The moment arm of each force is equal, and the forces are also equal...Now my question is, would the sum of torques in this case also be 0, or not?...Like in the sense that, if these forces were unequal (with equal distance from origin), there would be some clockwise or anticlockwise torque, and THEN if one of the forces was made equal to the other, then would the system's motion be uniform circular motion (Sum of torques=0)...
P.S: I intentionally did not write the angle between moment arms, as I thought that would not affect the answer
 
Physics news on Phys.org
Kaneki123 said:
In the case described in the picture
You forgot the picture.
 
Kaneki123 said:
Okay...I have a question.In the case described in the picture, the medium between the two forces, which would normally cause stationary or uniform circular motion, is not straight..The moment arm of each force is equal, and the forces are also equal...Now my question is, would the sum of torques in this case also be 0, or not?...Like in the sense that, if these forces were unequal (with equal distance from origin), there would be some clockwise or anticlockwise torque, and THEN if one of the forces was made equal to the other, then would the system's motion be uniform circular motion (Sum of torques=0)...
P.S: I intentionally did not write the angle between moment arms, as I thought that would not affect the answer
There is no picture. But if you are describing something like the bent arm on a phonograph then the forces at the endpoints are equal, opposite and act along a common line. The bent arm will be under a bending stress in addition to the pure longitudinal stress.

Angular momentum is conserved. Internal torques always sum to zero.
 
Heres the picuture...I apologize for inconvenience
 

Attachments

  • Untitled.png
    Untitled.png
    1.5 KB · Views: 446
Kaneki123 said:
Now my question is, would the sum of torques in this case also be 0, or not?...Like in the sense that, if these forces were unequal (with equal distance from origin), there would be some clockwise or anticlockwise torque, and THEN if one of the forces was made equal to the other, then would the system's motion be uniform circular motion (Sum of torques=0)...
For equal forces at right angles to equal moment arms, one moment arm 90 degrees clockwise from its force and one 90 degrees counter-clockwise, yes. The sum of the torques would be zero.

If you changed one of the forces to get the system spinning and then made the forces equal again, yes. The rotation rate of the system would be constant.
 
  • Like
Likes   Reactions: Kaneki123
Kaneki123 said:
Okay...I have a question.In the case described in the picture, the medium between the two forces, which would normally cause stationary or uniform circular motion, is not straight..The moment arm of each force is equal, and the forces are also equal...Now my question is, would the sum of torques in this case also be 0, or not?...

Yes. The two torques have equal magnitude but opposite direction. Typically you would decide that clockwise (or anti-clockwise) was positive making the other negative. So they sum to zero.
Like in the sense that, if these forces were unequal (with equal distance from origin), there would be some clockwise or anticlockwise torque, and THEN if one of the forces was made equal to the other, then would the system's motion be uniform circular motion (Sum of torques=0)...
P.S: I intentionally did not write the angle between moment arms, as I thought that would not affect the answer

It doesn't. The two forces could even act on the same arm eg zero angle between them.

I note that both of the forces in your diagram have a downward component. If the object is to move in a circular manner around the pivot/origin and not accelerate downwards as well there must also be a reaction force on it at the pivot/origin. As drawn that must have an upward component so the net force is zero. In fact, if it only moves in a circle and doesn't have linear acceleration, at all times the net linear force must be zero. Eg the reaction force at the origin may rotate.
 
  • Like
Likes   Reactions: Kaneki123
I thank you all for your help...Much appreciated...
 

Similar threads

  • · Replies 49 ·
2
Replies
49
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 3 ·
Replies
3
Views
6K
  • · Replies 6 ·
Replies
6
Views
2K