How to calculate a moment
A moment is the turning effect of a force. It depends on the size of the force and how far from the pivot it acts:
moment = force × perpendicular distance from the pivot
- M is the moment in newton-metres (N m)
- F is force in newtons (N)
- d is the perpendicular distance from the pivot to the line of action of the force, in metres (m)
A 20 N force on a spanner 40 cm (0.40 m) from the nut gives a moment of 20 × 0.40 = 8.0 N m. Holding the spanner further from the nut gives a bigger moment for the same force, which is why long spanners make nuts easier to undo.
The principle of moments: if an object is balanced, the total clockwise moment about the pivot equals the total anticlockwise moment. On a see-saw, a 300 N child sitting 2.0 m from the pivot (600 N m) balances a 600 N adult sitting 1.0 m from the pivot (600 N m).
The distance must be perpendicular to the force. If you push at an angle, only the perpendicular distance counts.
Common mistakes that cost marks
- Leaving distance in centimetres. 40 cm is 0.40 m, unless the question wants the moment in N cm.
- Using a distance that isn’t perpendicular. Measure from the pivot to the line of the force at right angles.
- Writing the unit as Nm/s or J. Moments are in newton-metres, N m.
- Adding clockwise and anticlockwise moments together. For balance, set them equal to each other.
Practice questions
Try each one on paper first, then reveal the worked answer.
Q1A force of 20 N is applied to a spanner 0.40 m from the nut. Calculate the moment.[2 marks]
- M = F × d
- M = 20 × 0.40
- M = 8.0 N m
Q2A child of weight 300 N sits 2.0 m from the pivot of a see-saw. An adult of weight 600 N sits on the other side. How far from the pivot must the adult sit to balance it?[3 marks]
- Child’s moment = 300 × 2.0 = 600 N m
- Balanced: adult’s moment = 600 N m
- d = M ÷ F = 600 ÷ 600
- d = 1.0 m
Q3A moment of 15 N m is needed to undo a nut. The spanner is 25 cm long. Calculate the force needed at the end of the spanner.[3 marks]
- Rearrange: F = M ÷ d
- Convert: d = 25 ÷ 100 = 0.25 m
- F = 15 ÷ 0.25
- F = 60 N
Endless practice
A new question every time, marked instantly. Work it out on paper, then type your answer.
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Frequently asked questions
What is the equation for a moment?
Moment = force × perpendicular distance from the pivot (M = Fd). The moment is in newton-metres (N m), force in newtons (N) and distance in metres (m).
What is the principle of moments?
If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.
Why is it easier to open a door by pushing far from the hinge?
The moment is force × distance. A bigger distance from the hinge gives the same moment with a smaller force.
Are moments in Combined Science?
In AQA, moments, levers and gears are in GCSE Physics (separate science) only.