Centre of GravityCambridge IGCSE Physics: Revision notes

The centre of gravity of an object is the single point through which the whole weight of the object appears to act. Every part of an object is pulled down by gravity, but for calculations we treat all of that pulling force as if it acts at one point.

• For a regular, uniform shape (a ruler, a rectangular block, a sphere), the centre of gravity is at the geometric centre.
• For an irregular shape, the centre of gravity can be off-centre and must be found experimentally.
• The position of the centre of gravity affects how an object balances and how stable it is.

A plane lamina is a flat sheet of material. To find the centre of gravity of an irregularly shaped lamina experimentally:

1. Make a small hole near the edge of the lamina and hang it freely from a pin so it can swing.
2. Hang a plumb line (a thread with a small weight on the end) from the same pin.
3. Once the lamina and plumb line have stopped swinging, mark the line of the thread on the lamina.
4. Repeat steps 1–3 with the hole in a different position near a different edge.
5. The centre of gravity is the point where the two (or more) marked lines cross.

This works because when the lamina hangs freely, its centre of gravity always settles directly below the pivot — the plumb line marks that vertical line each time.

An object is in equilibrium when there is no resultant force and no resultant moment acting on it — it is neither accelerating nor starting to turn.

For an object balanced on a pivot with forces on both sides:

• The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about a pivot equals the sum of the anticlockwise moments.
• This applies even when there is more than one force on each side of the pivot — you simply add up all the clockwise moments and all the anticlockwise moments separately before comparing them.

A simple experiment uses a metre rule balanced on a pivot (a knife edge) at its centre of gravity, with weights hung from strings at measured distances on each side.

1. Balance the metre rule on the pivot alone first, so its own weight produces no net moment.
2. Hang known weights at measured distances from the pivot on both sides.
3. Adjust the distances until the rule is exactly horizontal and stationary.
4. Calculate the sum of the clockwise moments and the sum of the anticlockwise moments.
5. Within experimental error, the two sums are equal, showing there is no resultant moment when the rule is in equilibrium.

An object's stability depends on where its centre of gravity is relative to its base:

An object tips over when it is tilted far enough that the line of action of its weight (a vertical line straight down from the centre of gravity) falls outside its base — at that point, the weight creates a moment that continues the tipping motion instead of restoring the object to its original position.