| 1.5.3: CENTRE OF GRAVITY |
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Key Definition The centre of gravity of an object is the single point through which its entire weight appears to act.
For uniform, symmetrical objects, this point coincides with the geometric centre, but for irregular objects the position must be found experimentally.
Suspend-and-Plumb-Line Method
- Hang the lamina freely from a pin at one point so that it can swing and settle, repeating the procedure from at least two different points.
- Suspend a plumb line from the same point and draw a vertical line along it on the lamina each time.
- The intersection of these lines marks the centre of gravity.
- A third suspension acts as a check on accuracy.
The suspend-and-plumb-line method provides a reliable technique for locating the centre of gravity of an irregular lamina.
Stability
The position of the centre of gravity directly determines how stable an object is.
- Stability increases when the centre of gravity is lower.
- Stability increases when the base of the object is wider.
- In both cases, a greater tilt angle is needed before the line of action of the weight falls outside the base area.
Once the vertical line through the centre of gravity moves beyond the base, the weight creates an overturning moment and the object topples.
Equilibrium States
Three equilibrium states describe the response of an object to a small displacement:
- Stable equilibrium: when slightly displaced, the centre of gravity rises and the object returns to its original position.
- Unstable equilibrium: when slightly displaced, the centre of gravity falls and the object moves further away, so it topples.
- Neutral equilibrium: when displaced, the height of the centre of gravity does not change and the object remains in its new position.
These principles explain everyday design choices, from the wide base of a traffic cone to the low body of a racing car.