Couples & Torque
Couples & Torque
- A single force pushes and turns. There is one arrangement of forces that turns without pushing.
- Two hands on a steering wheel: one pushes up, one pushes down. The wheel turns, but it does not move away.
What a couple is
push downequal push up- A is a pair of forces that are equal in magnitude, opposite in direction, parallel, and not along the same line.
- The two forces cancel as a push (resultant force = 0), so the object does not accelerate away. They do not cancel as a turn. A couple produces rotation without a resultant force.
- The turning effect of a couple is called its .
Definition
2 marksWhat is meant by a couple?
Model answer: A pair of equal, opposite and parallel forces whose lines of action are separated, producing a turning effect but no resultant force.
Definition
1 markWhat is meant by the torque of a couple?
Model answer: One of the forces multiplied by the perpendicular distance between the lines of action of the forces.
Symbols
- = one of the two forces (N)
- = perpendicular distance between the two forces (m)
Worked example
Smallest case: a couple on a tap
Two forces of 8.0 N act as a couple on a tap handle, 0.30 m apart. Find the torque.
- .
Common mistake
Water jets exert two opposite parallel forces of 3.0 N at points 0.15 m apart. Calculate the torque of the couple.
Show worked answer
- .
Answer: 0.45 N m.
Deciding whether two forces form a couple
- The exam shows two forces and asks: do they form a couple? Check all the parts of the definition, one by one.
- Equal in magnitude? Opposite in direction? Parallel? Not along the same line? All four must hold.
- Two forces of different sizes at right angles are not a couple: their resultant force is not zero and they are not parallel.
The torque is the same about any point
Take moments about the centre of the wheel in the figure: each 15 N force acts 0.20 m away, both turning the same way, so the total is N m.
Now take moments about the point where one force acts: that force contributes zero, and the other acts 0.40 m away, giving N m again.
A couple's torque does not depend on the chosen point. That is why a single number, , is enough to describe it.
One force turning about a pivot: moment = F × perpendicular distance from the pivot. Two equal opposite forces: torque = one force × distance between them, about any point.