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The principle of moments states that for an object in equilibrium, total clockwise moments equal total anticlockwise moments about a pivot. Free notes.
Moments and Equilibrium is part of Moments, levers and gears (physics only) in GCSE AQA Higher Physics.
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The principle of moments states that for an object in equilibrium, total clockwise moments equal total anticlockwise moments about a pivot. Free notes.
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Use this lesson to stay inside Moments, levers and gears (physics only) while connecting the detail back to the wider Forces topic.
Read the core explanations from Moments and Equilibrium before testing yourself from memory.
Why can you open a heavy door easily by pushing near the handle, but struggle when pushing near the hinges? The answer lies in moments - the turning effect of forces.
Moments explain everything from playground seesaws to massive construction cranes. Understanding them helps you predict when objects will tip over, balance perfectly, or start rotating.
A moment depends on two things: the size of the force and how far that force acts from the pivot. This is why a long spanner is easier to use than a short one. The same force produces a larger turning effect when it is applied further from the pivot.
When you calculate moments in GCSE questions, focus on the perpendicular distance to the line of action of the force. Examiners often include extra measurements to see if you can identify the correct distance. A total beam length is not always the same as the distance that matters in the calculation.
Equilibrium problems are really balance problems. If clockwise moments are larger, the object turns clockwise. If anticlockwise moments are larger, it turns the other way. A balanced beam, seesaw or sign has equal clockwise and anticlockwise moments about the pivot, so there is no overall turning effect.
The key word is perpendicular. You measure the shortest distance from the pivot to the line along which the force acts. If the force isn't at right angles to the lever, you need the perpendicular component.
Worked example: Calculating a Moment from a Perpendicular Force
A spanner is 0.25 m long. A 60 N force is applied at right angles to the end. Calculate the moment about the pivot.
Answer: 15 Nm
When an object is balanced (in equilibrium), something special happens. The total clockwise moments exactly equal the total anticlockwise moments about any pivot point.
This is the principle of moments: For equilibrium, clockwise moments = anticlockwise moments. This applies to everything from balanced scales to construction cranes.
Worked example: Solving Equilibrium Problems
A 3m beam balances on a pivot 1m from the left end. A 20N weight hangs from the left end. What weight is needed at the right end? [4 marks]
Answer: 10 N weight needed at the right end
Moments aren't just exam questions - they're everywhere in real life. Playground seesaws use the principle of moments. A lighter child can balance a heavier one by sitting further from the pivot.
Construction cranes rely on moments too. The counterweight on the back creates an anticlockwise moment that balances the clockwise moment from the load being lifted. Without this balance, the crane would topple over.
Moment questions follow predictable patterns. Examiners love testing whether you can identify the pivot, measure perpendicular distances correctly, and apply the principle of moments to find unknown forces.
Common exam trap: Questions often give distances in centimetres but expect answers in Nm. Always convert cm to m by dividing by 100, or your moment will be 100 times too large if you substitute centimetres directly into the formula.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
The principle of moments states that for an object in equilibrium, the total clockwise moments equal the total anticlockwise moments about any pivot point. If one set of moments is larger, the object turns that way.
A moment uses the perpendicular distance, the shortest distance from the pivot to the line along which the force acts. Questions often include extra measurements, and a total beam length is not always the distance that matters in the calculation.
A seesaw balances when the clockwise and anticlockwise moments about the pivot are equal. A lighter child can balance a heavier one by sitting further from the pivot, because a moment depends on both force and distance.
A crane's counterweight creates an anticlockwise moment that balances the clockwise moment from the load being lifted. Without this balance, the crane would topple over.
Find each distance from the pivot, calculate the known moment, then set clockwise moments equal to anticlockwise moments. A 3m beam pivoted 1m from the left with 20N at the left end needs F × 2 = 20 × 1, so F = 10 N at the right end.
A 60 N force applied at right angles to the end of a 0.25 m spanner gives a moment of 15 Nm. Moment = force × distance = 60 × 0.25 = 15 Nm.
If clockwise moments are larger than anticlockwise moments, the object turns clockwise; if anticlockwise moments are larger, it turns the other way. A balanced beam, seesaw or sign has equal clockwise and anticlockwise moments, so there is no overall turning effect.
Equilibrium is the state when an object is balanced and not rotating, where the total clockwise moments equal the total anticlockwise moments about the pivot.
A long spanner is easier to use because the same force produces a larger turning effect when applied further from the pivot. A moment depends on both the size of the force and its distance from the pivot.
Distances in centimetres must be converted to metres by dividing by 100, because moments are in Nm. Substituting centimetres directly makes the moment 100 times too large.
An unknown force is found by calculating the known moment on one side of the pivot, making the other side's moment equal to it, then dividing by the distance. On a beam with 20 Nm clockwise, a force 2 m away needs F × 2 = 20, so F = 10 N.