The centre of gravity of an object is the single point where the entire weight of the object appears to act.
Plumb-line method for irregular shapes
- Make a small hole near the edge of the flat shape.
- Suspend the shape from a pin through the hole so it hangs freely.
- Hang a plumb line (string with a weight) from the same pin.
- When both are stationary, draw a line along the string on the shape.
- Repeat from a different hole.
- The centre of gravity is where the two lines cross.
The shape hangs with its centre of gravity directly below the suspension point. Two lines from different suspension points are enough to locate it.
Why this works
When suspended, the object rotates until its centre of gravity is directly below the pivot. At that point, the weight produces zero moment about the pivot (perpendicular distance = 0).
Centre of gravity for regular shapes
| Shape | Centre of gravity |
|---|---|
| Rectangle / square | Intersection of diagonals |
| Circle | Centre |
| Triangle | Intersection of medians (1/3 from each base) |
| Uniform sphere | Centre |
Centre of gravity and stability
An object is stable when its centre of gravity is low and its base is wide. It topples when the line of action of its weight falls outside its base.
Common errors and how to correct them
- Drawing only one line (you need at least two intersecting lines).
- Not waiting for the shape and plumb line to stop swinging before drawing.
How to apply this in an exam
Describe the method step by step. Explain why the centre of gravity lies on the plumb line (zero moment about the suspension point).
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