Centre of gravity

An object’s weight acts on every part of it. For many purposes, the whole weight can be treated as a single downward force acting through one point: the centre of gravity.

When an object is freely suspended, it can turn about its point of suspension. If its centre of gravity is not vertically below that point, the weight produces a turning effect. The object turns until it comes to rest with its centre of gravity vertically below the point of suspension.

Locating the centre of gravity of an irregular lamina

A lamina is a thin, flat sheet. The centre of gravity of an irregular lamina can be found by suspending it from two different points. A plumb line is a string with a weight at its lower end; when it is at rest, it hangs vertically.

Suspend the lamina freely from a point near its edge. Hang a plumb line from the same point.

When both the lamina and the plumb line are at rest, draw a line on the lamina along the plumb line.

Suspend the lamina from a different point near its edge and repeat the process, drawing a second line.

For each suspension, the centre of gravity lies vertically below the suspension point, so it lies somewhere on the line drawn along the plumb line. It must therefore be at the intersection of the two lines.

Centre of gravity and stability

An object is stable if it tends to return to its original position after being tilted, rather than toppling over. Its stability depends on where its weight acts relative to its base of support.

The centre of gravity is the point through which the object's weight acts. Weight always acts vertically downwards, even when the object is tilted. As the object tilts, the vertical line through its centre of gravity moves relative to its base.

When an object topples

As an object tips, it turns about an edge of its base:

If the vertical line of action of its weight remains inside the base, the weight produces a turning effect towards the original position.
If the line passes beyond the tipping edge, the weight produces a turning effect that makes the object topple.

The critical position occurs when the line of action passes through the tipping edge. At that point, the weight has no turning effect about that edge.

Effect of centre of gravity height

For objects with the same base, a lower centre of gravity generally makes an object more stable. The object can be tilted further before the vertical line of action of its weight passes beyond the tipping edge.

A higher centre of gravity makes the line pass beyond the edge at a smaller tilt, so the object topples more easily.