Is the torque of a couple equal to the resultant torque?

AI Thread Summary
The torque of a couple is indeed equal to the resultant torque of the system when only couples are acting. In a system with both forces and couples, the resultant torque is the sum of all torques, including those from individual forces and couples. An example illustrates that a force and a couple can create a total moment that is independent of the couple's location. The moment of a couple does not depend on the point about which it is calculated, as it remains constant regardless of the pivot point chosen. Understanding these principles is crucial for solving problems involving torque and couples in physics.
Andy21
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Homework Statement


If the only forces acting in a system are a couple, will the torque of the couple be the resultant torque of the sytem?


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The Attempt at a Solution

 
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I don't believe this is a homework question, and that you are are just asking a general physics question. But to be sure, please indicate your thoughts on this. I believe you are asking if only one couple acts on a system, say a 10 N upward force and an equal and opposite 10 N downward force located 2 meters away from the upward force, then is the couple of 20 N-m the resultant torque on the system and that there is no resultant force per se?
 
This question is part of my homework. I am asking if the resultant torque in a system is equal to the sum of all of the torques or moments of the forces such as those from couples or from individual forces in the system.
 
Andy21 said:
This question is part of my homework. I am asking if the resultant torque in a system is equal to the sum of all of the torques or moments of the forces such as those from couples or from individual forces in the system.
OK, thank you.

Your question is bit unclear, so I hope my response is also not unclear.

Consider a horizontal massless rod (the system) of length 10 m that is subject to a force of 5N acting down at 3 m from the left of the rod, and a couple of 25 N-m acting clockwise at 7 meters from the left end of the rod. This force-couple system produces a moment about the left end of (5)(3) + 25 = 40 N-m. This moment is independent of the location of the 25 N-m couple. This 40 N-m moment is equivalent to the moment of the 5 N force acting 8 m from the left end. This 5 N force acting 8 m from the left end is the resultant of the force-couple system. Note that you don't have to sum moments about the left end to get the resultant force. You should prove this to yourself by summing moments about any point in the system, to achieve the same result. You might want to post a specific example problem you have in mind, and show your work, for further comment.
 
Hey... The moment of a torque is very interesting. However, i am confused as to Couples. Does the moment of a couple depend on the point about which it is rotated? How do I determine this?
 

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