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4.1MechanicsCore

Moments

A moment measures the turning effect of a force about a point. It depends on the size of the force and its perpendicular distance from the pivot — the basis of all rigid-body statics.

24 min Moments
Edexcel A Level Maths: 4.1 Moments (Forces)Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Define the moment of a force
  • Use moment = force × perpendicular distance
  • Identify clockwise and anticlockwise moments
  • Work in newton-metres (N m)
1

Moment of a force

The moment of a force about a point is moment=F×d\text{moment} = F \times d, where dd is the perpendicular\textbf{perpendicular} distance from the point to the line of action of the force. The unit is the newton-metre (N m).

moment=F×d\text{moment} = F \times d
Force × perpendicular distance.
Example 1Find the moment of a 10 N force acting 0.5 m from a pivot (perpendicular).
1moment=10×0.5\text{moment} = 10 \times 0.5.
2=5= 5 N m.
Answer
55 N m

Tip — Always use the PERPENDICULAR distance from the pivot to the force’s line of action.

2

Direction

Moments are either clockwise\textbf{clockwise} or anticlockwise\textbf{anticlockwise} about the pivot. State the sense, as it matters when combining moments.

Formula recap

moment=F×d\text{moment} = F \times d
Perpendicular distance.
units: N m\text{units: N m}
Newton-metres.

Common mistakes to avoid

Using the slant distance instead of the perpendicular distance.
Use the perpendicular distance to the line of action.
Ignoring the sense (clockwise/anticlockwise).
State the direction of each moment.

Key takeaways

  • Moment = F × perpendicular distance.
  • Unit is the newton-metre (N m).
  • Moments are clockwise or anticlockwise.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

  1. The moment of a force is:

    • F×dF \times d (perpendicular)
    • F+dF + d
    • F/dF / d
    • F×d2F \times d^2
    Show answer and explanation

    Answer: F×dF \times d (perpendicular)

    Turning effect.

  2. The unit of a moment is:

    • N m
    • N
    • m
    • N/m
    Show answer and explanation

    Answer: N m

    Newton-metre.

  3. A 10 N force 0.5 m from a pivot has moment:

    • 55 N m
    • 10.510.5 N m
    • 2020 N m
    • 22 N m
    Show answer and explanation

    Answer: 55 N m

    10 × 0.5.

  4. The distance used is the:

    • perpendicular distance
    • slant distance
    • total length
    • height
    Show answer and explanation

    Answer: perpendicular distance

    To the line of action.

  5. Moments act in which senses?

    • clockwise or anticlockwise
    • up or down
    • left or right
    • in or out
    Show answer and explanation

    Answer: clockwise or anticlockwise

    Turning directions.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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