Define centre of gravity and locate a weight line
Represent the total gravitational force at one point without assuming it is always the geometric centre.
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Describe weight as a gravitational force.
- Identify a force's line of action.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which direction does an object's weight act near Earth in the usual local model?
What you will learn
- State what is meant by centre of gravity.
- Explain geometric-centre and empty-space examples with their assumptions.
One point represents the distributed weight
An object's centre of gravity is the point through which its resultant weight may be considered to act. Near Earth's surface in an approximately uniform gravitational field, a downward vertical line through that point represents the total weight's line of action. This is a useful model of gravitational turning effects, rather than a claim that all the object's material has gathered at one particle.
For a uniform rectangle or disc in that common-field model, symmetry places the centre of gravity at its geometric centre. A non-uniform object may have its centre of gravity closer to the more heavily weighted region. Do not use the outline's visual centre without information about the mass distribution or a suitable determination.
The point need not lie in the material
A uniform ring has its centre of gravity at the centre of its empty hole. The point can lie outside the material even though the gravitational forces act on the ring's actual parts. Its resultant weight line is still the vertical line through that centre for the ordinary common-field model.
Turning the same rigid object changes the point's position in the room with the object; it does not make the centre of gravity arbitrarily jump to whichever part is lowest. Adding or moving substantial mass can change its location relative to the object. Keep the object's weight line distinct from the support force when checking its balance.
Sources for this lesson
Pause and explain
Must centre of gravity always lie in the object's material?
Worked example
Where is the centre of gravity of a uniform ring near Earth, and does the point have to contain material?
Show the worked solution
- Use the ring's symmetrical uniform mass distribution.
- The centre of gravity is at the ring's geometric centre.
- That point lies in the hole; the resultant-weight model does not require material at the point.
Answer At the ring centre, in the empty hole.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
State the centre of gravity of a uniform ring near Earth and draw the weight line.
Give me a hint
Use the stated uniform symmetry and a local vertical gravitational direction.
Compare my reasoning
- Symmetry places the centre of gravity at the ring centre.
- That centre is in the hole rather than in the material.
- Draw a downward vertical weight line through it.
Ring centre in the hole; downward vertical weight line through it.
Look for these in your work
- Use the stated uniformity.
- Separate the model point from material presence.
Compare a uniform rectangle with a similarly shaped rectangle carrying a heavy added mass near one end. Must both centres of gravity be at the outline centre?
Give me a hint
Consider how the mass distribution differs despite the similar outlines.
Compare my reasoning
- The uniform rectangle has its centre at the geometric centre in the common-field model.
- The added end mass changes the mass distribution.
- The combined centre moves towards that added mass and need not be at the outline centre.
No; only the stated uniform rectangle is justified at its geometric centre, while the added mass shifts the combined centre towards that end.
Look for these in your work
- State the symmetry assumption.
- Use mass distribution rather than shape alone.
A student says a rigid ring's centre of gravity moves to its lowest edge whenever it is rotated. Explain the error in the uniform common-field model.
Give me a hint
Track the model point with the same rigid distribution rather than replacing it by the lowest visible material.
Compare my reasoning
- The uniform ring keeps its symmetrical mass distribution.
- Its centre of gravity remains at its geometric centre relative to the ring.
- Rotation changes orientation in the room but does not relocate the point to the lowest edge.
It remains at the ring centre relative to the object, not its lowest edge.
Look for these in your work
- Keep the rigid-object assumptions.
- Distinguish orientation from changed mass distribution.
Common mistakes
- Use the point of resultant weight rather than an arbitrary outline centre.
- Uniformity and symmetry justify simple geometric-centre examples.
- Centre of gravity may lie in empty space.
What can you explain now?
What line represents resultant weight in the ordinary near-Earth model?
Compare with the explanation
The downward vertical line through the centre of gravity.
The point locates the force line used in a turning-effect calculation.
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Make it stick
Define centre of gravity and explain why it can be away from the outline centre or outside the material.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.