The moment of a couple
To find the moment of a couple, one of the forces and the distance between the lines is all you need.
The moment of a couple
The moment of a couple is equal to the product of the magnitude of one of its forces and the perpendicular distance between the lines along which the two forces act.
moment of a couple = force × distance between the lines
The unit of the moment of a couple is N m as well.
M = F × d
F = the magnitude of one force · d = the perpendicular distance between the lines of action
Why not multiply by both forces?
The formula carries one F, not 2F. Working out the two moments separately and adding them shows why.
Check it for yourself
Let the distance between the lines be d, and let the body turn about the point halfway between them. Each force then acts d/2 from that point.
moment of the first force = F × d/2
moment of the second force = F × d/2
Both act the same way round, so the total = F × d/2 + F × d/2 = F × d
So multiplying one force by the full distance between the lines is exactly the same as working out both moments separately and adding them.
It does not matter where the axis is
An ordinary moment depends on which axis you choose to take it about. The moment of a couple does not — wherever you pick the point, the answer is still F × d. That is why you never have to find an axis before calculating one.