Engineering Solving a Moment Vector Direction Problem: An Example from Statics Textbook

AI Thread Summary
The discussion revolves around a moment vector direction problem from a statics textbook, where the user is confused about the correct direction of a couple moment when moving a force to a point not on its line of action. They believe the moment vector should point left (clockwise) based on the right-hand rule and the addition of opposite forces at point "O," while the textbook shows the opposite direction. The user understands the underlying concept of adding equal and opposite forces but struggles with this specific example, questioning the accuracy of the diagram and the relationship between the moment vector directions and the tridimensional representation. They emphasize the importance of the perpendicular relationship between the position vector and force for calculating the moment. Overall, the user is seeking clarity on the discrepancy between their understanding and the textbook's illustration.
mhrob24
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Homework Statement
Moving a force to a point not on the line of action
Relevant Equations
M = FD
This isn’t a HW problem per say, but it’s an example shown in my statics textbook that is used to try an explain that you need to add a couple moment to move a force to a point not on the line of action, and I’m just not seeing how the direction of the couple moment is correct. See the image below:

62875A0F-7B49-4756-9F57-3C4D46B025B1.jpeg

Using the RHR (extending r1 and crossing into F1)and adding an opposite pair of forces at the point you are moving the force to (point “O”), the direction of the moment vector to me looks like it should be pointing to the left (into page, clockwise moment)….but the book is showing the opposite. The only way I see that moment vector direction being correct is if -F is applied What am I not seeing here? I feel like I understand the concept, but this specific example is tripping me up.
 
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This is the preceding example given, and this makes 100% sense to me. You add equal and opposite forces to the point you are moving the force to, and you still end up with an equivalent system: a downward force and a clockwise couple moment. So I know I get it….I just don’t know what I’m not seeing in the other example they give.

0C67DD8D-2F94-45A5-B19B-64EAF1C17B34.jpeg
 
Drawing (a) is poorly constructed and it seems that the directions of the vector moments have little to do with that tridimensional representation.
Those r's and F's must be perpendicular to each other for Mo=rxF.
 

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