Centre of Gravity & Stability

Explained

Centre of gravity, and what makes something hard to knock over

An object's weight is spread through every part of it, which would be awkward to work with. So we treat the whole weight as acting at a single point, called the centre of gravity.

For a uniform, symmetrical object it sits at the geometric centre. For a metre rule that is the 50 cm mark, and for a uniform sphere it is the middle. For an irregular object it can be anywhere, and for a hollow one, such as a ring or a wine glass, it can be at a point where there is no material at all.

Finding it experimentally

Hang the object freely from a point near its edge and let it settle. It comes to rest with its centre of gravity directly below the point of suspension, because in any other position the weight would produce a turning effect.

Hang a plumb line from the same point and draw the vertical line it marks. Repeat from a second point, and again from a third as a check. The centre of gravity is where the lines cross.

The third line is not optional in an exam answer. Two lines always cross somewhere; a third one crossing at the same place is what shows the result is right.

Stability

Tilt an object and its centre of gravity moves. Whether it falls back or topples over depends on one thing: whether the line of action of the weight, straight down from the centre of gravity, falls inside or outside the base.

Inside the base, the weight produces a turning effect that rotates the object back down again, so it is stable. Outside the base, that turning effect continues the rotation and it topples. The moment the line passes over the edge of the base is the moment it is going to fall.

Making something more stable

Two changes help, and both follow from the same rule.

A lower centre of gravity means the object has to be tilted further before the line of action leaves the base. This is why a racing car is low, why a bus carries its engine underneath, and why a tall vase is weighted at the bottom.

A wider base means there is more base for the line to stay inside. This is why a stepladder splays outwards and why you widen your stance on a moving train.

Together they give the standard answer to any stability question: a low centre of gravity and a wide base.

Answering the explain version

Describing the change is not enough on its own. Say what changes, then say what that does to the line of action.

Loading a bus's upper deck raises the centre of gravity, so the vertical line from it passes outside the wheels at a smaller angle of tilt, so the bus topples more easily. Three clauses, and each is normally a mark.