I have confusion understanding moments and couples

[jukos]

TL;DR

I have confusion understanding moments of forces and moments of couples in cartesian co-ordinate system

1) are all Moments of forces and Moments of couples free vectors? Can I move the moment vector computed about point O to a new point "point B" without changing the system? To elaborate on the question, suppose Resultant Moment about point O is computed using several forces and the position vectors to their points of action. My goal is to find Moment of the same forces about Point B. If moments are free vectors, I should be able to move the moment about O to the point B without changing the system. but It seems wrong to me.
2) moment of several forces about point S is known and I need to find moment of the same forces about point P, is this doable using the info about point S? i.e; info of position vector from P to S and secondly moment about S?

 

[mitochan]

Value of angular momentum and torque depends on choice of origin in the coordinate.
$$L=r \times p$$$$N=r \times F$$
Your ambiguity depends on this ?

 

[PhanthomJay]

A couple is 2 equal and opposite forces F separated by a distance d. The magnitude of the couple is F(d). A free vector. Not the same as the moment of a force, as explained above.

 

[mitochan]

free vector.

$$N=r_1 \times F_1 + r_2 \times F_2$$
$$r_2-r_1=d, F_2=-F_1=-F$$
$$N=-d \times F_1=d \times F_2= d/2 \times F_2 + (-d/2) \times F_1$$
Value of N is free from choice of origin in the coordinate. Explicitly mentioning where forces are applied as F(r)
$$N= d/2 \times F_2(r_1+d) + (-d/2) \times F_1(r_1)=N(r_1,d; F)$$
$N(r_1,d; F)$ seems not free from $r_1$ and $d$ that tell where the forces apply. Am I right?

 

[jukos]

A couple is 2 equal and opposite forces F separated by a distance d. The magnitude of the couple is F(d). A free vector. Not the same as the moment of a force, as explained above.

thanks, What confuses me the most is they interchange Moment of Forces and Couples in problems without any distinction. If I'm getting this right, the answer of this should be

2) moment of several forces about point S is known and I need to find moment of the same forces about point P, is this doable using the info about point S? i.e; info of position vector from P to S and secondly moment about S?

Ans: I can't find Moment about S using the info on Moment about P

 

[PhanthomJay]

tex]N= d/2 \times F_2(r_1+d) + (-d/2) \times F_1(r_1)=N(r_1,d; F)[/tex]
$N(r_1,d; F)$ seems not free from $r_1$ and $d$ that tell where the forces apply. Am I right?

What’s this? You have your moments about a point in (force x distance squared) units , which makes no sense. The moment of a couple about any point is the couple itself.

 

[PhanthomJay]

thanks, What confuses me the most is they interchange Moment of Forces and Couples in problems without any distinction. If I'm getting this right, the answer of this should be

Ans: I can't find Moment about S using the info on Moment about P

Unless you know where is point P and where the forces are located, it can’t be solved except if the forces happen to be couples

 

[mitochan]

What’s this? You have your moments about a point in (force x distance squared) units , which makes no sense. The moment of a couple about any point is the couple itself.

Value of dual force does not depend on the choice of origin or where they are.
Where they are, I said $r_1,d$, is important information to know so that we do not search them in the air.