Find Moment and Force in 3-D Plane

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There are two methods to find the moment about an axis in a 3-D plane when a force is applied, involving the "r" vector drawn from the axis to the point of application. Regardless of how the "r" vector is drawn, the moments should remain equal as long as the direction of the vector is consistent. However, reversing the direction of the "r" vector will change the sign of the moment, resulting in an opposite value. A discussion participant noted that there are infinite ways to draw the "r" vector that yield equal moments, and suggested using a specific program in Octave for further exploration. Understanding these concepts is crucial for accurately calculating moments in three-dimensional mechanics.
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I really don't need an answer to a question but I'm trying to show there are two ways to find the moment about an axis in a 3-d plane when a force is being applied.
I know you draw the "r" vector from the axis to the point of where the force is being applied, but sometimes there are two different ways to draw the r vector. My question is that the moments should be equal regardless where the r vector is?
 
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megr_ftw: What do you mean by "two ways"? Did you mean to say "many ways"? If so, and if I am interpreting your question correctly, I think the answer is yes, there are infinite ways to draw the r vector that produce equal moment. And there is a program that might address this issue in post 2195467[/color] (post 6), which you can use in Octave[/color] (free). Or you can convert it to any other language.

However, if you reverse the direction of the r vector, it reverses the sign of the moment, which is not equal but opposite.
 
usually the head of the force joins the tail of the vector r
 

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