top of page

8.7 Moments and Equilibrium

GCSE Physics · AQA · Chapter 8: Forces in Balance

A free GCSE Physics lesson for AQA (8463) from OBA School: the principle of moments, balanced beams and seesaws, and finding unknown forces and distances (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

  • Decide whether a force has a clockwise or an anticlockwise moment about a pivot
  • State the principle of moments for an object that is not turning
  • Calculate an unknown force or distance for a balanced object, including more than two forces
  • Use the principle of moments to find the weight of a beam and the effort needed on a wheelbarrow

Key words

  • Clockwise moment: A turning effect in the same direction as the hands of a clock.
  • Anticlockwise moment: A turning effect in the opposite direction to the hands of a clock.
  • Principle of moments: For an object that is not turning, the total clockwise moment about any point equals the total anticlockwise moment about that point.
  • Equilibrium: An object is in equilibrium when the resultant force on it is zero and it has no overall turning effect.
  • Uniform beam: A beam of even thickness and density; its weight acts at its midpoint.

Clockwise and anticlockwise moments

Look at where a force acts compared with the pivot, and imagine which way it would turn the object if it acted alone. On a seesaw, a person sitting on the left gives an anticlockwise moment; a person on the right gives a clockwise moment.

Worked example: checking the seesaw balances

Anticlockwise moment = 300 N × 2.0 m = 600 N m
Clockwise moment = 600 N × 1.0 m = 600 N m

Answer: the moments are equal, so the seesaw does not turn

The principle of moments

Key fact: For an object that is not turning: the sum of the clockwise moments about any point = the sum of the anticlockwise moments about that point.

Worked example: finding an unknown weight

A ruler balances with a 3.0 N weight 0.20 m to the left of the pivot and an unknown weight W 0.15 m to the right.
anticlockwise moment = clockwise moment: 3.0 × 0.20 = W × 0.15
W = 0.60 ÷ 0.15 = 4.0 N

Answer: W = 4.0 N

Exam tip: Be systematic: (1) write down every clockwise moment, (2) write down every anticlockwise moment, (3) set the totals equal and solve. Keep all distances in the same unit (metres).

More than two forces

Add up all the moments on each side. A force whose line of action passes through the pivot (such as the upward push of the pivot itself) has no moment about the pivot, so leave it out of the moment equation.

Worked example: three children on a seesaw

Left of the pivot: 250 N at 1.8 m. Right of the pivot: 300 N at 1.0 m and a third child of weight X at 1.5 m.
Anticlockwise: 250 × 1.8 = 450 N m
Clockwise: 300 × 1.0 + X × 1.5 = 300 + 1.5X
450 = 300 + 1.5X, so 1.5X = 150 and X = 100 N

Answer: X = 100 N

For the seesaw to be in equilibrium, the resultant force must also be zero: the pivot pushes up with a force equal to the total weight (250 + 300 + 100 = 650 N, plus the weight of the plank).

Finding the weight of a beam

A uniform beam’s weight acts at its centre of mass (its midpoint). Balance the beam off-centre using a known weight; the beam’s own weight then provides the moment on the other side.

Worked example: weight of the ruler

Anticlockwise moment of the known weight = 1.2 N × 0.20 m = 0.24 N m
Clockwise moment of the ruler’s weight = W₀ × 0.15 m
W₀ = 0.24 ÷ 0.15 = 1.6 N

Answer: the ruler weighs 1.6 N (mass = 1.6 ÷ 9.8 ≈ 0.16 kg)

Wheelbarrows and trolleys

When you lift the handles of a wheelbarrow, it turns about the wheel axle. The load acts close to the axle; your effort acts far from it. Taking moments about the axle shows why the effort is much smaller than the load.

Worked example: effort to lift the wheelbarrow

Clockwise moment of load = 600 N × 0.40 m = 240 N m
Anticlockwise moment of effort = F × 1.50 m
F = 240 ÷ 1.50 = 160 N

Answer: 160 N – about a quarter of the load

Common mistakes

  • Mixing units: one distance in cm and another in m. Convert all distances to metres first.
  • Adding a clockwise moment to an anticlockwise one. Collect each direction separately, then set the totals equal.
  • Including the pivot’s support force in the moment equation. Its line of action passes through the pivot, so its moment is zero.
  • Measuring the beam’s weight distance from the end of the beam instead of from the pivot to the centre of mass.

Revision questions

Try these, then check your answers below each one.

Question 1. A child of weight 400 N sits 1.5 m from the pivot of a seesaw. How heavy is a child who balances her by sitting 1.2 m from the pivot on the other side?

Answer: 500 N

Working: 400 × 1.5 = W × 1.2, so W = 600 ÷ 1.2 = 500 N.

Question 2. A 6.0 N weight hangs 0.20 m to the left of a pivot. How far to the right of the pivot must a 4.0 N weight hang to balance it?

Answer: 0.3 m

Working: 6.0 × 0.20 = 4.0 × d, so d = 1.2 ÷ 4.0 = 0.30 m.

Question 3. Which statement is the principle of moments? (Choose from: For an object that is not turning, the total clockwise moment about a point equals the total anticlockwise moment about that point, The moment of a force equals the force divided by the distance, For an object that is not turning, the clockwise forces equal the anticlockwise forces, A lever always multiplies the force applied to it.)

Answer: For an object that is not turning, the total clockwise moment about a point equals the total anticlockwise moment about that point

Working: Principle of moments: if an object is not turning, the sum of clockwise moments = the sum of anticlockwise moments about any point.

Related lessons

Continue in the full course

This lesson is section 8.7 (AGCPH0807) 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.

 

 

 

 

 

 

 

bottom of page