The Couple
Two forces, zero push, pure turn
What this lesson covers
Why it matters
You can't open a tap with one finger pushing sideways — you'd just bend it. You use two fingers, twisting opposite ways. Two forces that cancel… and yet everything turns.
The idea in plain words
The steering-wheel equation. Tap the terms.
moment of couple = F × couple arm
Each hand applies 5 N on opposite sides of a 40 cm steering wheel. Moment of the couple?
τ = 2 N·m of pure turning
- the setup: couple — two EQUAL forces, OPPOSITE in direction, with different lines of action
- newton: F — magnitude of EACH force (not their sum — their sum is zero!)
- metre: couple arm — perpendicular distance BETWEEN the two lines of action
- couple arm = wheel diameter = 0.4 m
- τ = F × arm = 5 × 0.4
Predict first
Two equal forces act on a wheel's rim in OPPOSITE directions on opposite sides. The wheel…
Net force zero → no sliding. But BOTH moments turn the same way, so they add: a couple. Pure rotation.
- spins in place — the forces cancel but their moments add — correct
- stays still — equal and opposite forces cancel everything
- slides sideways
What you do
Set the two forces to make a 6 N·m couple. Then flip them to the SAME direction and see the difference between a couple and a shove.
Check yourself
Which of these is turned by a couple?
Key, tap, steering wheel, corkscrew — thumb and finger push opposite ways across the width: classic couples.
The resultant FORCE of a couple is…
That's the beauty: nothing to push the body anywhere, everything to turn it.
To double a couple's turning effect without stronger hands, you…
τ = F × arm. Bus steering wheels are huge precisely so drivers' small forces make big moments.
- A key in a lock — correct
- A nail hit by a hammer
- A box pushed across the floor
- zero — yet its moment is not — correct
- 2F
- zero force and zero moment
- double the distance between the two forces (bigger wheel) — correct
- apply both forces on the same side
- push twice as long in time