The centre of gravity of an object is the point where all of its weight can be considered to act. For a uniform, regular object, the centre of gravity is at the geometric centre.
Finding the centre of gravity experimentally
For a flat, irregularly shaped object (a lamina):
- Suspend the lamina from a pin at one edge so it hangs freely.
- Hang a plumb line from the same pin and mark the vertical line on the lamina.
- Repeat from a different edge.
- The centre of gravity is where the two lines cross.
A third suspension can verify the result.
Stability
An object is stable when it returns to its original position after being tilted slightly. Stability depends on:
| Factor | More stable | Less stable |
|---|---|---|
| Base area | Wider base | Narrower base |
| Centre of gravity | Lower | Higher |
An object topples when its centre of gravity moves beyond the edge of its base. A wider base and a lower centre of gravity make this less likely.
Three states of equilibrium
- Stable equilibrium: the object returns to its original position when displaced (e.g. a cone on its base).
- Unstable equilibrium: the object moves further from its original position when displaced (e.g. a cone balanced on its tip).
- Neutral equilibrium: the object stays in its new position when displaced (e.g. a ball on a flat surface).
Common errors and how to correct them
Stating the centre of gravity is always at the physical centre of the object. This is only true for uniform, regular shapes. Irregular objects or objects with uneven mass distribution have the centre of gravity shifted toward the heavier region.
Confusing centre of gravity with the pivot point. The centre of gravity is where weight acts; the pivot is the point about which rotation occurs. They are different unless the object is balanced.
How to apply this in an exam
Describe the plumb-line method step by step, including “hang freely,” “draw vertical lines,” and “intersection.” For stability questions, always refer to both the height of the centre of gravity and the width of the base.
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