Edexcel IGCSE Physics · Spec 1.12E
Moments: Using the Equation (Worked Examples)
Worked examples using the moments equation.
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Moments: Using the Equation (Worked Examples)
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Explained
Turning effects, and balancing them
A moment is the turning effect of a force about a pivot. It equals the force multiplied by the perpendicular distance from the pivot to the line of action of the force, and its unit is the newton metre.
The distance is why a long spanner loosens a bolt that a short one will not, and why a door handle is fitted at the far edge rather than next to the hinge. The same force applied further from the pivot produces a larger moment.
Perpendicular distance
Perpendicular means measured at right angles to the force, not along the object. If a force is applied at an angle, the distance you use is shorter than the length of the arm.
At this level the force is usually at right angles already, so the distance is simply the length from the pivot. But the word appears in the definition and is worth including when you state it.
The principle of moments
When an object is balanced, the sum of the clockwise moments about a pivot equals the sum of the anticlockwise moments.
To use it, work out each moment separately as force times distance, put all the clockwise ones on one side and all the anticlockwise ones on the other, and solve.
A child of 400 N sitting 1.5 m from the pivot of a see-saw gives a moment of 600 N m. To balance, a child of 500 N must sit at 600 divided by 500, which is 1.2 m on the other side. Heavier means closer, which is the sense check worth doing on every answer.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards three marks for a single moment calculation: using moment equals force times distance, which may be implied by the substitution, the substitution itself, and the evaluation to two or more significant figures. It ignores units, and accepts either 1.14 newton metres or 114.4 newton centimetres for the same answer.
It then adds that a reverse argument scores one mark at most, meaning that working backwards from the approximate value printed in the question, instead of calculating it yourself, does not earn the full marks.
The examiner report on that paper is blunt about the statement of the principle. Although most candidates quoted it correctly, others confused it with the conservation of momentum or the conservation of energy. Those are three different principles with similar sounding names, and only one is about turning.
The report also singles out unit conversion. It describes one response that failed to convert the distance from centimetres into metres, and praises another for being clear about the conversion before substituting. Since force is in newtons, the distance must be in metres for the answer to be in newton metres.
Making something easier to turn
Questions often ask how to reduce the effort needed. Every answer is an application of the same equation.
Increase the distance from the pivot to where the force is applied, by using a longer handle or lever. Or reduce the moment you are working against, by moving the opposing force closer to the pivot or making it smaller.
An examiner report on a question about a gate records both of those as creditworthy: extending the handle, moving the spring closer to the pivot, and making the spring exert less force.
Where the weight acts
In a balancing problem involving a beam with mass, the weight of the beam acts at its centre of gravity, which for a uniform beam is its midpoint. If the pivot is at the midpoint too, the beam's own weight produces no moment and can be ignored. If the pivot is elsewhere, it must be included as another force.
Missing that term is the usual reason a balancing calculation comes out wrong when every individual moment looks right.
Spec 1.12E
What you need to know
- Use moment equals force times distance
- Apply the principle of moments
- Find an unknown force or distance
Active recall
Quick check
Answer each question before opening the answer.
What is the moment of a 20 N force acting 0.5 m from a pivot?
10 N·m (20 × 0.5).
What are the units of a moment?
Newton metres (N·m).
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