Forces · Quantitative
Moments: the turning effect
Push a door open at the handle and it swings. Push just as hard right beside the hinge and it hardly moves. Same door, same push, different result.
Start here
The same push, ten centimetres from the hinge.
Try it on the next door you go through. Push at the handle with one finger and it opens easily. Then push with the same finger a hand's width from the hinge, and lean.
Why is the same force so much less use near the hinge?
Turning is not decided by the force alone. It is decided by the force and how far from the pivot the force acts — and those two multiply together. The hinge is the pivot. Ten centimetres out you have a tenth of the distance, so a tenth of the turning effect. That product has a name: the moment.
A pivot is the fixed point something turns about — a hinge, a nut, a bolt through a seesaw. The moment of a force is its turning effect about that pivot, and it depends on two things: the size of the force, and its distance from the pivot. Moments are measured in newton metres, N m.
At the bench · spanner and a tight nut
One nut. Two ways to shift it.
Change a control to begin
This nut is done up tight: it needs a moment of 12 N m before it will move at all. Choose a spanner. Choose how hard you pull, at right angles to the handle.
Commit first. You swap a 0.10 m spanner for a 0.20 m one and pull just as hard. What happens to the turning effect?
Distance from the pivot
50 N
Your pull
—
Distance from pivot
—
Moment
—
The nut
—
Writing it down · the shape of this relationship
Moment = force × distance from the pivot
The triangle
Cover the one you want
M = F × d
F = M ÷ d
d = M ÷ F
Two things side by side means multiply. One thing over another means divide.
M · moment · N m
F · force, at right angles to the handle · N
d · distance from the pivot · m
Worked example · one step at a time
A spanner is gripped 0.25 m from the nut and pulled with 40 N. What is the moment?
Step 0 of 5
Convert
40 N stays 40 N · 0.25 m stays 0.25 m
The force is already in newtons and the distance already in metres, so there is nothing to convert.
Formula
moment = force × distance from the pivot
Two quantities multiplied, which is what a triangle means.
Insert
moment = 40 N × 0.25 m
The 0.25 m is measured from the nut, not along your arm.
Fine-tune
40 × 0.25 = 10
Newtons times metres leaves newton metres.
Answer
moment = 10 N m
Ten newton metres, turning the nut about the pivot.
Worked example · one step at a time
A door handle is pushed with 12 N, 80 cm from the hinge. What is the moment?
Step 0 of 5
Convert
80 cm ÷ 100 = 0.80 m
A newton metre needs the distance in metres, and a centimetre is a hundredth of one.
Formula
moment = force × distance from the pivot
The hinge is the pivot.
Insert
moment = 12 N × 0.80 m
The converted distance goes in. The 80 never does.
Fine-tune
12 × 0.80 = 9.6
Newtons times metres leaves newton metres.
Answer
moment = 9.6 N m
Insert 80 instead of 0.80 and the answer comes out a hundred times too big.
Your turn · the same five steps
Your spanner: 50 N at 0.10 m from the pivot.
Write all five lines before you check. The numbers are the ones your own bench is showing.
The five lines, marked
Convert
50 N stays 50 N · 0.10 m stays 0.10 m
The force is already in newtons and the distance already in metres, so there is nothing to convert.
Formula
moment = force × distance from the pivot
A product, so the triangle applies.
Insert
moment = 50 N × 0.10 m
Both values come straight off the bench above.
Fine-tune
50 × 0.10 = 5
Newtons times metres leaves newton metres.
Answer
moment = 5 N m
Less than the 12 N m the nut needs, so it holds.
The five lines give 5 N m, and the handle on the bench is drawn 0.10 m long to match.
A nut is turned with 25 N applied 15 cm from the pivot. What is the moment?
This one needs the Convert line to do some work.
The five lines, marked
Convert
15 cm ÷ 100 = 0.15 m
A newton metre needs the distance in metres, so divide the centimetres by 100.
Formula
moment = force × distance from the pivot
Two quantities multiplied.
Insert
moment = 25 N × 0.15 m
The converted distance goes in. The 15 never does.
Fine-tune
25 × 0.15 = 3.75
Newtons times metres leaves newton metres.
Answer
moment = 3.75 N m
Insert 15 instead of 0.15 and the answer comes out 375 N m.
The five lines give 3.75 N m. The whole question turned on the first one.
Key fact
The moment of a force is its turning effect about a pivot, and it is the force in newtons multiplied by the distance from the pivot in metres. Double the distance and you double the turning effect for exactly the same pull.
Think again
“A longer spanner means you are pulling harder.”
It does not, and the spring balance proves it: put one on the handle and the reading is the same 50 N whether the handle is short or long. What changes is what those 50 N achieve. A moment is not a force and is not measured in newtons — it is a force multiplied by a distance, measured in newton metres, and a long handle buys you turning effect without buying you strength. This is why the answer to a seized bolt is never simply pull harder: put a length of pipe over the spanner and the same arm shifts it.
“Measure the distance from where you are standing.”
The distance in the formula is measured from the pivot, and nowhere else. Not from the middle of the object, not from your feet, not along your arm. On the bench above, the pivot is the centre of the nut, so a 0.20 m spanner means the pull acts 0.20 m from that centre. Get the pivot wrong and every answer that follows is wrong, which is why identifying it is the first thing to do in any turning problem — hinge, nut, bolt, axle, or in the human body, the joint.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
A spanner is gripped 0.40 m from a bolt and pulled with 30 N at right angles. What is the moment?
Rung 2 · The one that catches people
Two people pull with exactly 50 N on the same stiff bolt. One uses a 0.10 m spanner, the other a 0.40 m spanner. Which statement is right?
Rung 3 · Explain
Door handles are always fitted at the edge furthest from the hinges. Explain why, using the word pivot and the word moment.
Rung 4 · Take it somewhere new
A wheel nut on a car must be tightened to a moment of 110 N m. A driver can pull with about 250 N. Work out the shortest spanner that would do the job, and explain why the manufacturer supplies a long one rather than one of exactly that length.
Key note
A moment is the turning effect of a force about a pivot, and it equals the force in newtons multiplied by its distance from the pivot in metres, giving newton metres. The same force gives a bigger moment further out, which is why handles, levers and spanners are long. A moment is not a force, and the distance is always measured from the pivot.
Going further
Once you can work out a moment, you can work out a balance. On a seesaw there are two moments about the same pivot, one turning it clockwise and one anticlockwise, and it balances when the two are equal — not when the two weights are equal. That is why a child of 300 N sitting 2 m out balances an adult of 600 N sitting 1 m out: both make 600 N m, and the seesaw does not care which is which. The same arithmetic decides whether a crane tips over, how far along a plank a builder can walk, and where the counterweight goes on a tower crane, which is a lump of concrete whose whole job is to make a moment on the other side.
Levers are this idea used deliberately: put the pivot near the load and you can lift something with far less force than its weight, as long as you accept moving your end much further. A crowbar, a wheelbarrow, a bottle opener and a pair of scissors are all the same machine in different clothes. Your own body is full of them too, though it usually trades the other way — many muscles pull very close to the joint, so they need a large force to lift a small load, and buy speed and range of movement with it instead. The biomechanics lesson in the skeleton unit works through the turning effect at a joint, and is the same relationship you have just met here.
Before this lesson
Connects to
At GCSE this becomes
- Moments, the principle of moments for a balanced beam, levers as force multipliers, and gears.
Where to next
Ask Mr Badmus AI
Got a turning problem of your own — a door, a spanner, a seesaw?
The spanner bench is a teaching model. The nut is given a fixed loosening moment of 12 N m so that failure is something you can reach; a real fitting depends on how it was tightened, on corrosion and on whether it has ever been undone. The pull is taken as acting at right angles to the handle, which is the only case handled at this stage, and the handle is drawn to scale while the force arrow uses a separate scale.
Lesson content © MrBadmusAI.