Unit 1 · Lesson 1.4.3
Centre of Gravity
Define centre of gravity, find it for a flat irregular shape using a plumb line, and relate its position to stability.
Centre of Gravity
Centre of Gravity
Definition
- The centre of gravity is the point at which the whole weight of an object appears to act.
Regular shapes
- For a uniform, symmetrical object it lies at the geometric centre, such as the midpoint of a metre rule.
Irregular shapes
- For awkward shapes the centre of gravity is found by experiment, and it may even lie outside the material.
Hanging
- A freely suspended object comes to rest with its centre of gravity vertically below the point of suspension.
Finding It for a Lamina
The plumb line shows the true vertical because gravity pulls it straight down.
1
Make three small holes near the edge of a piece of card in different places.
2
Hang the card from a pin through one hole, and let it swing freely until it stops.
3
Hang a plumb line from the same pin, and mark its vertical line on the card with a pencil.
4
Repeat with the other two holes to draw two more lines.
5
The lines cross at the centre of gravity, which can be checked by balancing the card on a sharpened pencil tip at that point.
Stability
Low centre of gravity
- An object with its centre of gravity low is hard to tip, which is why racing cars are built low.
Wide base
- A wide base means the object has to be tilted further before the weight falls outside the base.
Toppling
- An object topples when the vertical line through its centre of gravity falls outside the base.
Restoring moment
- While the line stays inside the base, the weight gives a moment that turns the object back upright.
| Feature | Stable object | Unstable object |
|---|---|---|
| Centre of gravity | Low | High |
| Base | Wide | Narrow |
| Example | Racing car, bus with load low | Top-heavy lorry, tall narrow stack |
Worked Example
Question: A uniform metre rule of weight 1.2 N is balanced on a pivot at the 20 cm mark. A load W is hung at the 5 cm mark. Calculate W.
- The weight of the rule acts at its centre, the 50 cm mark, which is 0.30 m from the pivot.
- Clockwise moment = 1.2 × 0.30 = 0.36 N m.
- The load is 0.15 m from the pivot, so anticlockwise moment = W × 0.15.
- For balance, W × 0.15 = 0.36, so W = 0.36 ÷ 0.15 = 2.4 N.
Answer: 2.4 N.
Exam Checklist & Tips
1.4.3 – Key Points for the Exam
- Centre of gravity: The point through which the weight of an object appears to act.
- Plumb line: A string with a weight on the end that hangs vertically.
- Lamina: A thin flat sheet of material, such as a piece of card.
- Stable: Able to return to its original position after being slightly tilted.
- Base: The area of support on which an object stands.
Common Mistakes
- Believing the centre of gravity always lies in the middle of the object.
- Drawing the plumb line from a point other than the pin.
- Saying an object topples when its centre of gravity rises; it topples when the weight line leaves the base.
- Hanging the card from holes that are close together, which makes the crossing point less accurate.