Moments and Centre of Gravity
A moment is the turning effect of a force. The arithmetic is a single multiplication — the marks are lost in measuring the distance from the wrong point and in mixing up units.
1. What a moment is
Moment = Force × perpendicular distance from the pivot M = F × d
Units: newton metres (N m) — force in newtons, distance in metres.
It is force MULTIPLIED by distance, not divided. Confusing “force by distance” with “force divided by distance” was a recorded error, and it inverts the whole calculation.
The distance must be measured from the PIVOT, and perpendicular to the line of the force. Identifying distances from the wrong point was one of the most frequent errors in this topic.
Convert to metres and newtons first. Distances given in cm must become m (÷100), and a mass in kg must become a weight in newtons (× g). Using kilometres, or using mass where weight was needed, were both recorded.
Everyday examples: a longer spanner turns a nut more easily; a door handle is placed far from the hinges to maximise the turning effect for a given push.
A door handle is far from the hinge to give a LARGER MOMENT — a bigger distance means more turning effect for the same force. One student suggested it was “to balance the force”; the reason is the distance term in M = F × d.
2. The principle of moments
For an object in equilibrium: total clockwise moments = total anticlockwise moments
Method for any balance problem:
- Identify the pivot
- Work out each distance from the pivot
- Classify each force as turning the beam clockwise or anticlockwise
- Set clockwise total = anticlockwise total
- Solve
Worked example. A uniform metre rule is pivoted at its centre (50 cm). A 4 N weight hangs at the 20 cm mark. Where must a 2 N weight hang to balance it?
- 4 N is 30 cm = 0.3 m from the pivot, turning it anticlockwise
- Anticlockwise moment = 4 × 0.3 = 1.2 N m
- Clockwise moment must also be 1.2 N m: 2 × d = 1.2 → d = 0.6 m = 60 cm from the pivot
- So the 2 N weight hangs at the 50 + 60 = 110 cm mark — impossible on a metre rule, which tells you the weight must be larger or placed differently
Distances are measured from the PIVOT, not from the end of the ruler. A weight at the 20 cm mark on a rule pivoted at 50 cm is 30 cm from the pivot. Calculating “the distance from the zero end” instead was recorded twice, and it is the single biggest cause of wrong answers here.
Multiply each force by its OWN distance, then add. Adding the forces first and multiplying once was a recorded error — moments must be worked out individually.
3. Equilibrium
An object is in equilibrium when: 1. The resultant FORCE is zero (it doesn’t accelerate) 2. The resultant MOMENT is zero (it doesn’t rotate)
Both conditions are needed, and questions often test them together: a beam on two supports needs the upward forces to equal the total weight and the moments to balance.
Beam on two supports — the standard hard question:
To find one support force, take moments about the other support. That makes the unknown force’s moment zero (its distance from that pivot is zero), leaving one unknown.
Then use total up = total down to find the second force.
Choosing the pivot cleverly removes an unknown. You may take moments about any point — pick the one that eliminates the force you don’t want.
The weight of a uniform beam acts at its CENTRE, so include it as a single downward force at the midpoint.
4. Centre of gravity
The centre of gravity is the point where the entire weight of an object appears to act.
For a uniform, symmetrical object, it is at the centre.
Finding it experimentally — the plumb line method
- Hang the irregular lamina from a pin so it swings freely
- Hang a plumb line from the same pin
- Draw the vertical line along the plumb line
- Repeat from a different point
- The centre of gravity is where the lines cross
Two lines minimum, and three is better — the third acts as a check. The object must swing freely, so it hangs with its centre of gravity directly below the pivot.
5. Stability and toppling
An object topples when its centre of gravity lies outside its base.
Equivalently: it topples when the line of action of its weight falls outside the base area.
To make an object more stable:
Lower the centre of gravity, and widen the base.
That is why a racing car is low and wide, and why a Bunsen burner has a heavy base.
Types of equilibrium:
- Stable — nudged, it returns; the centre of gravity rises when tilted
- Unstable — nudged, it topples; the centre of gravity falls
- Neutral — it stays where it is put (a ball on a flat table)
6. Mistakes that cost marks
Dividing force by distance instead of multiplying.
Measuring distance from the end of the ruler instead of the pivot.
Adding forces before multiplying rather than taking each moment separately.
Using cm instead of m, or mass instead of weight.
Mixing up clockwise and anticlockwise.
Using the wrong value of g.
Forgetting the weight of the beam itself in a uniform-beam question.
Giving only one condition for equilibrium.
Wrong units — a moment is N m, not N or m.
Rounding to the wrong number of significant figures.
Frequently asked questions
What is a moment? The turning effect of a force: M = F × d.
What are the units of a moment? Newton metres (N m).
Where is the distance measured from? The pivot, perpendicular to the force.
What is the principle of moments? For a balanced object, total clockwise moments = total anticlockwise moments.
What are the two conditions for equilibrium? Resultant force = 0 and resultant moment = 0.
What is the centre of gravity? The point where the object’s entire weight appears to act.
How do you find the centre of gravity of an irregular shape? Hang it freely from two or three points with a plumb line and find where the vertical lines cross.
When does an object topple? When its centre of gravity falls outside its base.
How do you make an object more stable? Lower the centre of gravity and widen the base.
Why is a door handle far from the hinges? A greater distance gives a larger moment for the same force.
Quick revision checklist
- I know moment = force × perpendicular distance from the pivot
- I know the unit is N m
- I measure distances from the pivot
- I convert cm to m and mass to weight
- I calculate each moment separately
- I can apply the principle of moments
- I know both conditions for equilibrium
- I can choose a pivot to eliminate an unknown force
- I include the weight of a uniform beam at its centre
- I can define centre of gravity
- I can describe the plumb line experiment
- I know when an object topples
- I can explain how to increase stability
- I can distinguish stable, unstable and neutral equilibrium
These notes cover moments and centre of gravity in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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