Fill in the blanksQuestion 1 · Recall
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By the end you can explain what the centre of gravity is, find it for uniform objects and by experiment for a flat card, and use it to work out moments due to weight.
Balance a uniform ruler on one finger. It only balances in one place: the 50 cm mark.
Every tiny bit of the ruler has its own weight pulling down. Yet the ruler behaves as if all of its weight acted at one point, right above your finger.
Centre of gravity
The centre of gravity of an object is the point at which the whole weight of the object may be considered to act.
Gravity pulls on every particle. Add up all those little weights and you get one total force, , acting downwards.
The centre of gravity is the point where that single force has the same turning effect about any pivot as all the little weights together. So in a diagram you draw one arrow, , from the centre of gravity.
For a uniform object (mass spread evenly) with a symmetrical shape, it's at the geometric centre:
| Uniform object | Centre of gravity |
|---|---|
| rod, ruler, plank | at its midpoint |
| rectangular sheet | where the diagonals cross |
| disc or solid sphere | at its centre |
| ring or hollow tube | at the centre, in thin air |
A non-uniform object, like a hammer or a cricket bat, has its centre of gravity nearer the heavy end.
Worked example: Easy one first: an off-centre pivot
A uniform metre rule of weight is pivoted at its 30 cm mark, with the 0 cm end on the left. What is the moment of its weight about the pivot?