Describe couples and calculate their torque
Identify a couple as two equal, opposite, separated forces and calculate its torque from the perpendicular separation.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 4. These original explanations and numerical practice support theory study; they do not demonstrate supervised practical competence. Full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use SI units, resolve perpendicular components, and distinguish force from pressure.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the resultant force of an ideal couple?
What you will learn
- Describe how a couple produces rotation only
- Identify the equal and opposite forces and their separation
- Calculate the torque of a couple
A couple has two forces and no resultant force
A couple consists of two equal-magnitude, parallel forces acting in opposite directions along different lines. Their resultant force is zero, but because the lines are separated they produce a turning effect.
For a pure couple, the pair tends to rotate the object without giving it a resultant translational force. Examples include turning a steering wheel with two hands or twisting a jar lid.
Torque uses the separation between the force lines
The torque of a couple is the magnitude of either force multiplied by the perpendicular separation between the two lines of action. Torque = Fd. Its SI unit is N m.
Use the perpendicular separation between the forces, not the distance from an arbitrary pivot. Do not double the answer by separately adding the two individual moments: their combined effect is already F times the full separation.
Pause and explain
Why can a couple rotate an object despite zero resultant force?
Worked example
Two hands apply equal and opposite 15 N forces to a wheel. Their lines of action are 0.40 m apart. Find the torque of the couple.
Show the worked solution
- The forces are equal, opposite and parallel, so they form a couple.
- Torque = Fd = 15 × 0.40.
- Use the full perpendicular separation between the two force lines once.
Answer 6.0 N m.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A couple is made by two opposite 8.0 N forces whose lines of action are 0.30 m apart. Calculate its torque.
Give me a hint
Use one force magnitude and the full perpendicular separation.
Compare my reasoning
- Torque = Fd.
- Torque = 8.0 × 0.30.
- Give the unit N m.
2.4 N m.
Look for these in your work
- Couple relationship used
- Separation used once
- Correct unit
A mechanic applies a torque of 5.0 N m with two equal opposite forces separated by 0.25 m. Find either force magnitude.
Give me a hint
Rearrange torque = force × separation.
Compare my reasoning
- F = torque/d.
- F = 5.0/0.25.
- Check that N m divided by m gives N.
20 N for each force, acting in opposite directions.
Look for these in your work
- Equation rearranged
- Magnitude calculated
- Paired directions stated
A student pushes a door with two equal opposite forces along lines 0.50 m apart. The torque is 4.0 N m. Find each force and state the couple's resultant force.
Give me a hint
Use the separation of the lines and distinguish torque from net force.
Compare my reasoning
- F = torque/d = 4.0/0.50 = 8.0 N.
- Each force has magnitude 8.0 N.
- Because they are equal and opposite, their resultant force is zero.
Each force is 8.0 N; resultant force is zero while torque is 4.0 N m.
Look for these in your work
- Either force found
- Equal opposite pair retained
- Torque and resultant force distinguished
Common mistakes
- Using the distance from a chosen pivot instead of the separation of force lines
- Adding both force magnitudes before multiplying by the separation
- Calling a single off-centre force a couple
What can you explain now?
What is the resultant force of an ideal couple?
Compare with the explanation
Zero
Its two forces have equal magnitudes and opposite directions.
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Make it stick
How can a force pair have zero resultant force but non-zero torque?
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