A moment is the turning effect of a force about a pivot. It is force × perpendicular distance from the pivot, measured in newton metres (N m). This skill opens every question on turning effects, balance and levers.
It sits at the start of moments and stability and is used again in every later lesson in the module.
What decides how big a turning effect is?
Two things: how large the force is, and how far from the pivot it acts. A door is easy to push open at the handle and hard to push near the hinge, even though the force is the same.
The pivot is the point the object turns about.
In symbols, moment = F × d. Double the force and the moment doubles. Double the distance and it also doubles.
The distance must be measured from the pivot to the line along which the force acts, at a right angle to that line. In the simplest diagrams the force is at 90° to the object, so the distance is just the length from the pivot to where the force is applied.
How do you calculate it, step by step?
- Mark the pivot on the diagram.
- Write the force in newtons.
- Write the distance from the pivot to the force, in metres.
- Multiply, and write the unit N m.
- Say the direction (clockwise or anticlockwise) if the question asks.
Worked example
A student pushes down on a spanner handle with a force of 18 N, at a point 35 cm from the centre of the nut. The force is at right angles to the spanner. Find the moment about the nut.
Step 1, pivot: the centre of the nut.
Step 2, force: 18 N.
Step 3, distance: 35 cm = 0.35 m (35 ÷ 100).
Step 4, multiply: 18 × 0.35 = 6.3 N m.
Answer: 6.3 N m.
Checking in reverse: 6.3 ÷ 0.35 = 18 N, which matches the force given.
The mistake to watch for
A common slip is to mix units, multiplying the force in N by the distance in cm and then writing N m.
Mistaken working: 18 × 35 = 630 N m
The number is a hundred times too large, because 35 is in centimetres.
The correction is to convert first, or to keep 630 and label it honestly as 630 N cm, which equals 6.3 N m. A quick plausibility check also helps: an 18 N push on a spanner about a third of a metre long cannot produce a turning effect of hundreds of newton metres.
Check yourself
1. A force of 50 N acts at right angles to a crowbar, 0.60 m from the pivot. Find the moment.
Show answer
50 × 0.60 = 30 N m.
2. A door handle is 0.80 m from the hinge. A person pushes it with 15 N at right angles to the door. What is the moment about the hinge?
Show answer
15 × 0.80 = 12 N m.
3. A bolt needs a turning effect of 9.0 N m. A spanner lets you apply the force 45 cm from the bolt centre, at right angles. What force is needed?
Show answer
Distance = 0.45 m. Force = moment ÷ distance = 9.0 ÷ 0.45 = 20 N. Check: 20 × 0.45 = 9.0 N m.
Where this leads next
Next, use moments on both sides of a pivot in clockwise and anticlockwise balance. If rounding in your answers is an issue, the bounds and rounding explainer shows how a rounded measurement carries an interval.
Some students find the formula easy but lose marks on units and distances in longer questions. That pattern is what our teachers look for in online one-to-one Physics tuition.