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8.4 Moments at Work

GCSE Physics · AQA · Chapter 8: Forces in Balance

A free GCSE Physics lesson for AQA (8463) from OBA School: the turning effect of a force, M = F d, and levers as force multipliers (physics only). Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Describe the moment of a force as a measure of its turning effect
  • Calculate a moment using M = F d, including rearranging and converting distances to metres
  • Explain why the distance must be measured perpendicular to the line of action of the force
  • Explain how a lever acts as a force multiplier, using the words load, effort and pivot

Key words

  • Moment: The turning effect of a force about a pivot. Measured in newton metres (N m).
  • Pivot: The fixed point about which an object turns (also called the fulcrum).
  • Line of action: The straight line along which a force acts.
  • Perpendicular distance: The shortest distance from the pivot to the line of action, measured at 90° to the line of action.
  • Lever: A rigid bar that turns about a pivot, used to make a job easier.
  • Load and effort: The load is the force the lever has to overcome; the effort is the force applied to the lever.
  • Force multiplier: A device such as a lever that produces a larger force than the effort applied to it.

The turning effect of a force

A force can make an object turn about a pivot: opening a door, turning a tap, undoing a nut. The turning effect of a force is called its moment. You get a bigger turning effect if you:

  • push or pull with a larger force
  • apply the force further from the pivot (for example, use a longer spanner).

Calculating a moment

moment = force × perpendicular distance from the pivot to the line of action of the force

M = F d

M = moment in newton metres (N m) · F = force in newtons (N) · d = perpendicular distance in metres (m)

Rearranged: F = M ÷ d d = M ÷ F

Worked example: the spanner in the figure

M = F d = 60 N × 0.25 m

Answer: M = 15 N m

Worked example: converting centimetres

A child pushes a door with a force of 12 N at a point 75 cm from the hinges. Calculate the moment.
d = 75 cm = 0.75 m (divide by 100).
M = 12 N × 0.75 m = 9.0 N m

Answer: 9.0 N m

Worked example: rearranging

A stiff garden tap needs a moment of 3.6 N m to turn it. A gardener can apply a force of 40 N. What is the shortest handle that will work?
d = M ÷ F = 3.6 ÷ 40 = 0.090 m

Answer: 0.090 m (9.0 cm)

Exam tip: Always change distances to metres before using M = F d. A moment in N m with the distance in cm will be 100 times too big.

Perpendicular distance and direction of turning

If the force does not act at right angles to the lever, you must use the perpendicular distance from the pivot to the line of action of the force – not the distance along the lever. This distance is shorter, so a slanting force has a smaller moment than the same force applied at 90°.

A moment turns an object either clockwise or anticlockwise about the pivot. A force whose line of action passes through the pivot has no moment, because d = 0. That is why pushing a door at its hinges does not open it.

Levers as force multipliers

A lever uses moments to make a job easier. The effort is applied a long way from the pivot and the load is close to the pivot. The moment of the small effort about the pivot can then match the moment of a much larger load, so the lever is a force multiplier.

Key fact: A lever is a force multiplier when the effort is further from the pivot than the load.

Investigating the turning effect of a force

A metre ruler is pivoted at one end on a clamp stand and held horizontal by a newton-meter at the other end. A known weight is hung from the ruler and moved to different distances from the pivot. The newton-meter reading F shows how big a turning effect is needed to hold the ruler level.

The reading increases if the weight is moved further from the pivot or if a heavier weight is used, because the moment of the weight about the pivot gets bigger. Safety: clamp the stand to the bench, keep feet clear of falling weights and wear eye protection.

Common mistakes

  • Leaving the distance in cm. Convert to metres to get N m.
  • Using the distance along the lever when the force is at an angle. Use the perpendicular distance to the line of action.
  • Writing the unit as N/m. A moment is force × distance, so its unit is N m (newton metre).
  • Thinking a lever reduces the load. The load is the same; the lever lets a smaller effort balance it.

Revision questions

Try these, then check your answers below each one.

Question 1. A force of 30 N acts at right angles to a lever, 0.40 m from the pivot. Calculate its moment.

Answer: 12 N m

Working: M = 30 × 0.40 = 12 N m.

Question 2. A force of 50 N is applied at right angles to a door, 25 cm from the hinges. Calculate the moment of the force in N m.

Answer: 12.5 N m

Working: d = 0.25 m. M = 50 × 0.25 = 12.5 N m.

Question 3. A moment of 6.0 N m is needed to turn a valve. The force is applied 0.15 m from the pivot. What force is needed?

Answer: 40 N

Working: F = M ÷ d = 6.0 ÷ 0.15 = 40 N.

Related lessons

Continue in the full course

This lesson is section 8.4 (AGCPH0804) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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