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I was watching this lecture on analysis of stress for mechanics of materials. At time 7:20, the lecturer says that in equilibrium, the sum of forces and "moments" in each direction (x,y,z) must be zero. What exactly is meant by "moments" in this context? Does this mean the "twisting" forces? If so, why are twisting forces counted separately from the other forces in the x,y, and z directions?

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1 Answer

up vote 5 down vote accepted

Some engineering texts use "moment" and "couple" to talk about forces that tend to rotate an assembly (what physicist mean when they say "torque", but the engineers sometimes have a slightly different meaning for that word).

A roughly translation guide is...

  • A "couple" is a pair of opposite forces whose points of action are not co-linear. A couple is sometimes called a "pure torque" because it imparts a tendency to rotate without imparting a tendency to accelerate, and engineers will occasionally shorten this to just "torque", which is why a physicist needs to be careful in talking about these things with engineers.

  • A "moment" is the tendency to rotate imparted by a off-center force (i.e. it is a "torque" in physicist-speak), but because it has not been paired off in a couple you know that you may also have to worry about the linear acceleration that is implied.

In your case the speaker is just saying that the static conditions,

$$ \sum \vec{F} = 0 $$ $$ \sum \vec{\tau} = 0 $$

apply.

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So then, in this case, the moment is the torque, in the physicist's sense? –  Paul Oct 5 '12 at 19:15
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+1 yep, physicists and engineers have differing definitions. But I'd also say a torque twists an object around its main axis, while a moment rotates the main axis. –  Larry Harson Oct 5 '12 at 20:54
    
@LarryHarson Interesting. My familiarity with the engineering uses comes from sitting in on a statics class as a note taker, just once. So it wouldn't surprise me if I missed some subtleties. –  dmckee Oct 5 '12 at 23:04
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A torque is a necklace twisted around itself, and Archemedes used "moment" for the product of a force and its distance from the pivot point, which rotates the main axis. I doubt most authors today are aware of this difference and use the terms interchangeably which confuses people. –  Larry Harson Oct 6 '12 at 21:43
    
@LarryHarson: That makes a lot more sense. –  Paul Oct 7 '12 at 0:07
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