Static Equilibrium and magnitude

[emohabatzadeh]

1.we know that generally, every force systems can be replaced by a resultant force(R) and a couple(M) at a point O. the position of point O is optional.
but magnitude and direction of M is dependent to this point while magnitude and direction of R is independent.
In static equilibrium R and M are zero at an optional point O. now this is the question:



2.While M is zero at an optional point O, why should we conclude that M would be zero at every point chosen( infinite in number of points)...pay attention that " magnitude and direction of M is dependent to the point chosen"...

 

[CWatters]

Static implies no translation or rotation. eg No rotation about any point.

 

[BruceW]

Welcome to physics forums, emohabatzadeh! Your name is hard to type! (no offence intended). You should try to answer the question first, before asking for help on this forum (that's the rules). And if you have tried several things, but not gotten very far, then write them down, so we can see where you need help to be able to get to the answer.

 

[emohabatzadeh]

Static implies no translation or rotation. eg No rotation about any point.

"static implies no translation or rotation"...but it seems that for proving "no rotation about any point" you should calculate the resultant couple moment about any point and specify that the resultant couple equals to zero for any point !( because the couple is dependent to the points position) ----I mean we don't know the object is in static equilibrium or not and we want to determine it... why do we consider that if M is zero about a point, it means that it is zero about any point? is there a theorem about this? is it provable? sorry for grammatical errors if I have and hope that you understand what I mean...

 

[emohabatzadeh]

Welcome to physics forums, emohabatzadeh! Your name is hard to type! (no offence intended). You should try to answer the question first, before asking for help on this forum (that's the rules). And if you have tried several things, but not gotten very far, then write them down, so we can see where you need help to be able to get to the answer.

thanks and you can call me with the nickname Estak...!
in fact I have no answer to the question...it's not a numerical problem...it's a fundamental problem...! perhaps the question should be answered by a theorem...

 

[BruceW]

looking back at your first post, I don't really get what the part 1) is trying to say... You said that the part 2) is the actual question. If I was reading just the stuff in part 2), I would guess that M means moment, not couple. What is the exact question? Maybe I will be able to help better if I see that.