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Physics · Forces

Moments, levers and gears

Use \(M = Fd\), the principle of moments for balanced objects, and explain how levers and gears transmit rotational effects.

  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is a pivot?

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    The point about which something turns

  2. 2

    What is the unit of force?

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    Newton

  3. 3

    What is clockwise?

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    The direction the hands of a clock turn

  4. 4

    What is the unit of distance?

    Show answerHide answer

    Metre

  5. 5

    Give an example of a lever.

    Show answerHide answer

    A seesaw, crowbar or spanner

Learning Objectives

  1. 1Describe examples in which forces cause rotation.
  2. 2Recall and apply \(M = Fd\).
  3. 3Use the principle of moments to find an unknown force or distance.
  4. 4Explain how levers and gears transmit the rotational effects of forces.

MOMENTS

moment of a force \(=\) force \(\times\) perpendicular distance from the pivot \(M = Fd\)

The turning effect of a force is called its moment, in newton-metres (Nm). If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment.

Calculating a Moment

A force of 30 N acts 1.5 m from a pivot at right angles. Calculate the moment.

Show the solutionHide the solution
  1. 1 Write the equation \(M = Fd\)
  2. 2 Substitute \(M = 30 \times 1.5\)
  3. 3 Answer \(M = 45\) Nm

Answer45 Nm

A Balanced Seesaw

A 40 N child sits 0.50 m from the pivot of a balanced beam. Another force F acts on the other side 0.80 m from the pivot. Calculate F.

Show the solutionHide the solution
  1. 1 Anticlockwise moment \(40 \times 0.50 = 20\) Nm
  2. 2 Balanced \(F \times 0.80 = 20\)
  3. 3 Rearrange \(F = 20 \div 0.80\)
  4. 4 Answer \(F = 25\) N

Answer25 N

Gears

A gear with 20 teeth drives a gear with 40 teeth. Describe how the second gear turns compared with the first.

Show the solutionHide the solution
  1. 1 Direction It turns in the opposite direction
  2. 2 Speed The larger gear turns more slowly (half the speed)
  3. 3 Turning effect The larger gear has a greater turning effect (moment)

AnswerIt turns the opposite way at half the speed with a larger moment.

Levers and Gears

Transmitting turning effects.

  • Lever

    A rigid bar that turns about a pivot; a longer distance from the pivot means a smaller force is needed.

  • Examples

    A crowbar, spanner, wheelbarrow, scissors.

  • Gears

    Toothed wheels that mesh to transfer rotation.

  • Gear ratio

    A large gear driven by a small gear turns slower but with a greater moment.

Balance the Beam

A beam is balanced. A 60 N weight is 0.40 m to the left of the pivot. Where must a 30 N weight be placed on the right?

1. Find the anticlockwise moment.

2. Equal the clockwise moment.

A good answer shows: Clockwise = anticlockwise: 30 × d = 60 × 0.40 = 24, so d = 0.80 m.

Can I...?

  1. 1Recall M = Fd.
  2. 2Use perpendicular distance.
  3. 3State the principle of moments.
  4. 4Find an unknown force.
  5. 5Find an unknown distance.
  6. 6Explain levers.
  7. 7Explain gears.
  8. 8Use Nm.

Summary & Exam Focus

  • \(M = Fd\).
  • Balanced: total clockwise moment = total anticlockwise moment.
  • Levers: a longer distance from the pivot gives a greater moment.
  • Gears: change direction, speed and turning effect.

Exam focus

A force of 30 N acts 1.5 m from a pivot. Calculate the moment. (2 marks) (2 marks)

Multiply force by distance and give Nm.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Moment
The turning effect of a force, in newton-metres.
Pivot
The point about which an object turns.
Clockwise
In the direction of a clock's hands.
Anticlockwise
Opposite to the hands of a clock.
Lever
A bar that can turn about a pivot.
Gear
A toothed wheel that transmits rotation.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A force of 30 N is applied at a distance of 1.5 m from a pivot. The force acts at right angles. Calculate the moment of the force. Use the equation: moment = force × distance

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    Model answer

    \(30 \times 1.5 = 45\) Nm

    Mark scheme

    • Correct substitution — 1 mark
    • 45 Nm — 1 mark
  2. Question 2 Calculate 3 marks

    The diagram shows a uniform beam balanced on a pivot. A 40 N force acts 0.50 m to the left of the pivot. Calculate the force F.

    A balanced beam with 40 N at 0.50 m on the left and an unknown force F at 0.80 m on the right.
    Show answerHide answer

    Model answer

    Anticlockwise moment \(= 40 \times 0.50 = 20\) Nm. \(F \times 0.80 = 20\), so \(F = 25\) N

    Mark scheme

    • Anticlockwise moment 20 Nm — 1 mark
    • Equates moments — 1 mark
    • 25 N — 1 mark
  3. Question 3 Explain 2 marks

    A spanner is used to undo a nut. Explain why a longer spanner makes it easier.

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    Model answer

    The moment is force × distance, so a longer spanner gives a bigger moment for the same force, or needs a smaller force.

    Mark scheme

    • Moment = force × distance — 1 mark
    • Greater distance means smaller force needed — 1 mark
  4. Question 4 Explain 3 marks

    A gear with 20 teeth is driven by a motor. It meshes with a gear with 40 teeth. Explain how the larger gear turns compared with the smaller gear.

    Show answerHide answer

    Model answer

    The larger gear turns in the opposite direction, at half the speed, and has a larger turning effect (moment).

    Mark scheme

    • Opposite direction — 1 mark
    • Slower (half the speed) — 1 mark
    • Greater moment — 1 mark
  5. Question 5 Calculate 4 marks

    A 60 N weight is 0.40 m to the left of a pivot on a balanced beam. A 30 N weight is on the right. Calculate its distance from the pivot.

    Show answerHide answer

    Model answer

    Anticlockwise \(= 60 \times 0.40 = 24\) Nm; \(30 \times d = 24\); \(d = 0.80\) m

    Mark scheme

    • Anticlockwise moment 24 Nm — 1 mark
    • Balanced moments — 1 mark
    • Correct rearrangement — 1 mark
    • 0.80 m — 1 mark

Quick check

  1. The unit of a moment is...

    1. Anewton
    2. Bjoule per second
    3. Cnewton-metre
    4. Dmetre
    Show answerHide answer

    C: newton-metre

    Force times distance.

  2. A balanced object has...

    1. Azero mass
    2. Bno forces
    3. Ca moment of zero only
    4. Dequal clockwise and anticlockwise moments
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    D: equal clockwise and anticlockwise moments

    The principle of moments.

  3. A 20 N force at 3 m from a pivot has a moment of...

    1. A60 Nm
    2. B23 Nm
    3. C6.7 Nm
    4. D600 Nm
    Show answerHide answer

    A: 60 Nm

    20 × 3.

  4. The distance in M = Fd is...

    1. Athe total length
    2. Bthe perpendicular distance from the pivot
    3. Cthe mass
    4. Dthe height
    Show answerHide answer

    B: the perpendicular distance from the pivot

    It is measured at right angles to the force.

  5. A large gear driven by a small gear turns...

    1. Afaster
    2. Bat the same speed
    3. Cmore slowly
    4. Din the same direction
    Show answerHide answer

    C: more slowly

    Fewer turns but a bigger moment.

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