Moments questions are some of the most predictable marks in the O-Level Combined Science Physics paper. Almost every year there is a balanced beam, a seesaw, a spanner or a crane, and almost every year students lose marks not because the physics is hard, but because they measure the wrong distance or forget to state equilibrium. Here is the exact method our tutors used when we sat these papers, plus the phrasing markers want to see.
What the syllabus actually asks for
For Combined Science Physics you need to be able to:
- Define the moment of a force as force multiplied by the perpendicular distance from the pivot.
- Apply the principle of moments to a body in equilibrium.
- Explain everyday situations such as levers, spanners, wheelbarrows and toppling.
Two definitions must be word-perfect in your head:
Moment of a force = force × perpendicular distance from the pivot. Unit: newton metre (N m).
Principle of moments: when a body is in equilibrium, the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments about that pivot.
Notice the word "perpendicular". That single word is where a lot of marks disappear.
The five-step method
Use the same five steps every single time, even for a question that looks easy. Consistency is what stops careless errors under time pressure.
- Draw and label every force. Arrows for each weight, each pull, and the weight of the beam itself if the question says the beam is uniform or gives its mass. Remember weight = mass × gravitational field strength, so 200 g becomes 0.2 kg becomes about 2 N.
- Mark the pivot clearly. It is usually a knife edge, a fulcrum, a hinge or the point of support.
- Write down perpendicular distances in metres. Distances on a metre rule are given in centimetres, so convert. Always measure from the pivot, not from the end of the rule.
- Set up the equation. Sum of anticlockwise moments = sum of clockwise moments. Write it out in symbols and numbers before you touch the calculator.
- Solve, then state the unit and check plausibility. A 30 cm answer on a 100 cm rule is sensible. A 130 cm answer means you made a sign or distance error.
Worked example 1: Where to hang the mass
A uniform metre rule is pivoted at the 50 cm mark. A 0.50 N weight hangs at the 20 cm mark. Where must a 1.0 N weight be hung so that the rule balances?
Because the rule is uniform and pivoted at its centre of gravity, its own weight acts through the pivot and produces zero moment. Say that in your working, because it shows understanding.
Anticlockwise moment = 0.50 × (0.50 − 0.20) = 0.50 × 0.30 = 0.15 N m
Clockwise moment = 1.0 × d
For equilibrium: 1.0 × d = 0.15, so d = 0.15 m from the pivot.
The weight is hung at the 65 cm mark.
Worked example 2: Finding the weight of the rule
A uniform metre rule is pivoted at the 30 cm mark. A 0.60 N weight hung at the 10 cm mark keeps it horizontal. Find the weight of the rule.
Here the rule's weight acts at the 50 cm mark, which is 0.20 m from the pivot on the clockwise side.
Anticlockwise: 0.60 × 0.20 = 0.12 N m
Clockwise: W × 0.20
So W × 0.20 = 0.12, giving W = 0.60 N.
The key insight is that a uniform beam behaves as if all its weight is concentrated at its centre of gravity. Examiners love testing this.
Mistakes that cost marks
- Measuring from the end of the rule instead of the pivot. Always subtract the pivot position.
- Leaving distances in centimetres. Your moment then comes out 100 times too large.
- Forgetting the weight of the beam when the question says "uniform beam of mass 2 kg".
- Using the slanted distance when a force is at an angle. Moments questions in Combined Science usually keep forces vertical, but if a rope is at an angle, the horizontal distance from the pivot is what counts.
- Writing Nm without checking. N m or N·m are safest. Never write "N/m".
- Skipping the equilibrium statement. In explanation questions, write "the beam is in equilibrium, so the total clockwise moment about the pivot equals the total anticlockwise moment". That sentence alone is often worth a mark.
Explanation questions: the phrasing that scores
If asked why a longer spanner makes it easier to loosen a nut: "A longer spanner gives a larger perpendicular distance from the pivot, so for the same force the moment is larger, and the nut turns more easily."
If asked why a bus with passengers on the lower deck is more stable: "The centre of gravity is lower, so the bus can tilt through a larger angle before its centre of gravity falls outside its base, making it less likely to topple."
Notice the structure: cause, then physics quantity, then consequence. Practise writing in that order and your marks become much more reliable.
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