Torque: why where you push matters
We all know a long spanner loosens a bolt better than a short one. What is not obvious is that angling the force has the same effect as shortening the spanner, and for exactly the same reason.
What you are looking at
- The green arrow never changes size. The force is always the same: the only things that move are where and how it is applied.
- The gold bar on the right is the torque, and it is not drawn: it is computed on every frame from the geometry you are watching.
- At the end a dashed gold segment appears between the axis and the line of the force. That is the effective lever arm, and it is what the angle shortens.
01Pushing is not the same as turning
To move something in a straight line, force is enough. To make it turn you need three things: how hard you push, how far from the axis you push, and in which direction you push.
Those three multiply together. If one of them halves, the turning effect halves — no matter which one.
02The part your body already knows
The animation starts with the force at the far end of the spanner and then brings the point of application closer to the axis. Same force, half the distance, half the turning effect.
This surprises nobody who has used a spanner: it is why you grip as far from the bolt as you can, and why lorry wheel wrenches are long.
03The part that is not intuitive
Then the force returns to the far end — the same distance as at the start — and begins to tilt. Torque drops again, even though neither the force nor the distance changed.
What changed is the effective lever arm: the distance from the axis to the line along which the force acts, not to the point where you apply it. When the force points at an angle that distance shortens, and the sine of the angle is exactly that proportion.
With the force perpendicular, the effective arm is the whole spanner. With the force pointing along the spanner, the arm is zero: push as hard as you like and nothing turns.
Where this is used
The handle on your door
It sits on the edge opposite the hinges, and not for looks: that is where the lever arm is largest. Pushing a door ten centimetres from its hinge costs nearly ten times more.
The bolts on a car
They are tightened with a torque wrench, which reads how many N·m you apply. Too little and the wheel works loose; too much and the bolt stretches and snaps. It is not how hard you pull: it is the product.
The gears on a bicycle
Changing chainring changes the radius your foot acts on. It is the same force on the pedals delivering different torque to the wheel — which is why you climb a hill in a small ring.
The boom of a crane
Maximum load drops as the boom extends. A crane load chart is exactly that: the same machine holding less weight the greater the radius.
Explaining it to a child
The idea, in plain wordsA door is easier to open if you push it far from where it is attached to the wall. The further from the edge it turns on, the less force you need.
- Find a door and open it by pushing on the handle. Easy.
- Now have them push with a single finger, but very close to the hinges, where the door meets the wall. It will be much harder, even though they are pushing just as hard.
- Try one last push from the handle, but diagonally, as if pushing the door sideways instead of forwards. It barely moves.
The question to leave them withSo why are door handles always at the edge of the door, and never in the middle?
For the classroom
Ten minutes with the animation, ready to take into a room. Free under CC BY 4.0, like everything else here.
- Without explaining anything, ask them to push the classroom door at the hinge edge. Have them really try it, not imagine it. Then at the free edge.
- Ask: "did you push harder the second time?" Almost everyone will say no, and they are right: the only thing that changed was where.
- Only now play the animation (14 s). Ask them to watch the distance to the axis, not the force arrow.
- Close with the formula on the board. By now it is a summary of what they just felt in their hand, not a new fact.
You have to free a very tight nut and only have a short wrench. What do you do?
Answer: Lengthen the arm: a pipe over the handle, or grip the wrench as far from the bolt as possible. Doubling the distance does what doubling the force does, and it is far easier to arrange.
Why is a door handle always on the edge opposite the hinge?
Answer: Because that is where the distance to the axis is greatest, so one hand is enough. A handle next to the hinge would need an enormous force for the same turn.
Two people push a door with exactly the same force, at the same point, but one pushes perpendicular to the door and the other at an angle. Do they turn it equally?
Answer: No. Only the perpendicular component counts; the part pointing towards the hinge turns nothing, it just squeezes the axis. That is the angle the formula is talking about.
You will hear "you have to push harder". That is not carelessness: it is a documented alternative conception, and it works across almost all of everyday life. Do not correct it with the formula — send them back to the door, where the force was the same and the result was not.
FísicaEterna classroom guide · CC BY 4.0 · fisicaeterna.cl
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The code behind it
It is written in Remotion, which renders video by writing React. The bar and the number are not drawn next to the figure: they come out of the calculation on the same geometry you are watching. If the drawing lies, the number lies with it.
Licence
This animation is under CC BY 4.0: you may copy, redistribute, adapt and use it commercially, as long as you credit the source.
Suggested attributionTorque: why where you push matters — FísicaEterna (fisicaeterna.cl), CC BY 4.0