Locate the centre of gravity of an irregular lamina by suspension
Trace plumb lines from separate suspension points and find their common intersection.
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- State the definition of centre of gravity.
- Explain why resting equilibrium needs zero resultant moment.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a freely settled plumb line indicate?
What you will learn
- Describe a supervised suspension and plumb-line procedure.
- Explain why several traced lines locate centre of gravity.
Use the resting suspended shape
For a thin rigid irregular plane lamina, use teacher-approved suspension holes and stable apparatus. Suspend it freely from one point so that it can settle without touching the support or surroundings. Hang a plumb line from the same suspension point and trace its vertical direction on the lamina once both are still. Keep hands and any sharp pins or suspended weights controlled under supervision.
The lamina's weight acts through its centre of gravity. When it hangs at rest, that weight line passes vertically through the suspension point, giving no turning moment about it. The first traced plumb line therefore contains the centre of gravity, but it identifies a line rather than one unique point.
Intersect independent traces on the same lamina
Repeat from a second suitable suspension point that gives a distinct non-parallel trace on the lamina. Where the two traces cross is the determined centre of gravity. A third separate suspension provides a check: its traced line should pass near the same point within drawing and settling uncertainty. Mark every line on the same object or a consistent fixed outline, even though the shape hangs in different room orientations.
The drawing overlays traces after different suspensions; its differently directed lines are not several simultaneous vertical lines in the room. Avoid a sticking pivot, a plumb line that brushes the lamina, or marking before motion settles. Thick pencil lines and friction can prevent exact intersection, so report the supported region rather than invented precision. This written procedure is not evidence that a student has performed the practical.
Sources for this lesson
Pause and explain
Does one suspension trace uniquely determine centre of gravity?
Worked example
One settled suspension gives a traced vertical line on an irregular lamina. What further evidence locates and checks its centre of gravity?
Show the worked solution
- Repeat suspension from a different point to obtain a distinct trace.
- Mark the intersection of the two traces as the determined centre of gravity.
- Use a third suspension to check that its trace passes near the intersection within uncertainty.
Answer Intersect two distinct traced plumb lines; check with a third separate suspension.
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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.
Explain how two separate suspensions determine an irregular plane lamina's centre of gravity.
Give me a hint
For each settled suspension, identify the weight-line trace on the lamina.
Compare my reasoning
- Suspend freely from point A and trace the settled plumb line.
- Repeat from point B to obtain a distinct line on the same lamina.
- Their intersection locates the determined centre of gravity.
Intersection of two distinct settled plumb-line traces.
Look for these in your work
- Describe two separate suspension points.
- Explain why each trace contains the centre of gravity.
Two distinct traces meet near one point, but the third misses it by the thickness of the pencil marks. Explain the conclusion and one improvement.
Give me a hint
Compare the mismatch with drawing uncertainty before rejecting every observation.
Compare my reasoning
- A small miss comparable to the mark thickness does not establish a different exact centre.
- The crossing region is the supported position within this drawing uncertainty.
- Use finer marks, wait for settling and check for pivot or plumb-line contact.
A crossing region is supported within marking uncertainty; improve marks and free settling or contact checks.
Look for these in your work
- Acknowledge the supplied uncertainty.
- Give a concrete improvement to the procedure.
A student draws several vertical lines on a fixed sheet without resuspending the lamina, then labels their intersection as its centre of gravity. Explain what the actual method requires.
Give me a hint
The object must change its hanging orientation while traces are recorded on one consistent outline.
Compare my reasoning
- Each valid trace comes from a separate freely settled suspension of the lamina.
- The traces are transferred to the same object outline, so their orientations on it differ.
- Unrelated lines on a fixed sheet do not supply the required weight-line observations.
Use separately settled suspensions and trace them on the same lamina; arbitrary sheet lines do not determine its centre of gravity.
Look for these in your work
- Identify the missing physical observations.
- Explain the common-outline requirement.
Common mistakes
- One trace locates a line, not a unique point.
- Trace each settled suspension onto one consistent lamina outline.
- Prevent contact, sticking and motion while reading.
What can you explain now?
Why should the centre of gravity lie vertically below the suspension point at rest?
Compare with the explanation
Otherwise its weight would create a turning moment about that point.
Settled free suspension needs the weight line to pass through the pivot.
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Make it stick
Describe three suspensions and explain why the overlaid traces need not look parallel on the lamina.
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.