Centre of gravity

Definition of Centre of Gravity

The centre of gravity is the point through which the entire weight of an object acts.

Every object is made up of many small parts, each pulled downward by gravity. These individual gravitational forces can be replaced by a single force — the object's total weight — acting at one special point. That point is the centre of gravity.

For a uniform, symmetrical object (such as a ruler or a solid sphere), the centre of gravity lies at its geometric centre. For an irregular object, the centre of gravity may not be at an obvious position, so an experiment is needed to locate it.

MisconceptionStudents sometimes write that the centre of gravity is "the centre of the object." This is only true for uniform, symmetrical shapes. For irregular shapes, the centre of gravity depends on how mass is distributed. Exam cue: Always refer to the point where weight acts, not simply "the centre."

Exam TipThe weight arrow must start from the centre of gravity, not from the edge or the surface of contact.

Finding the Centre of Gravity of an Irregular Lamina

An irregularly shaped plane lamina [a flat sheet of material with no line of symmetry] has its centre of gravity at an unknown position. A simple suspend-and-plumb-line method locates it.

Representation note — plumb line: A plumb line is a length of string with a small heavy weight (bob) tied at the bottom. When suspended freely, it always hangs vertically because the weight pulls it straight down. Any line drawn along it therefore marks a true vertical direction.

The experiment works because, when the lamina hangs freely from any point, it rotates until its centre of gravity is directly below the pivot. The vertical line through the pivot therefore passes through the centre of gravity. Repeating from a different hole gives a second vertical line. The centre of gravity lies where these two lines cross.

Method

1. Use a hole punch to make three small holes near the edge of the lamina, spaced well apart.

2. Push a pin horizontally through one hole into a cork on a clamp stand so the lamina swings freely.

3. Hang a plumb line (string and small mass) from the same pin. Wait until both the lamina and plumb line are stationary.

4. Use a pencil to mark two points along the plumb-line string on the lamina, then draw a straight line connecting them.

5. Remove the lamina, re-hang it from the second hole, and repeat steps 3–4 to draw a second line.

6. The centre of gravity is the point where the two lines intersect. Mark it with a cross.

7. Repeat from the third hole as a check — the third line should pass through the same intersection point.

Key measurement technique: Ensure the lamina swings freely without rubbing against the clamp stand. Wait for all swinging to stop before marking. Use a sharp pencil held close to the string to minimise parallax error when marking points.

Expected result: All three lines intersect at a single point. This confirms the location of the centre of gravity of the lamina.

Exam TipThe lamina must hang freely — the hole must be large enough that the lamina does not stick on the pin.

Examiner InsightCIE papers often ask why three lines are drawn instead of two. The third line acts as a reliability check — if it does not pass through the same point, the experiment contains an error. Exam cue: Always mention the third line as a check in your answer.

Centre of Gravity and Stability

The stability of an object describes how readily it topples when tilted. The position of the centre of gravity is the key factor that determines stability.

When an object stands on a surface, its weight acts downward through the centre of gravity. The object remains stable as long as the vertical line through the centre of gravity falls within the base area [the area enclosed by the points of contact with the surface]. If the object is tilted so that this vertical line moves outside the base area, a resultant turning effect (moment) causes the object to topple over.

Two design features increase stability:

A racing car is a good example: it has a wide wheelbase and a low centre of gravity, so it resists toppling when cornering at high speed. A double-decker bus, by contrast, has a higher centre of gravity, which is why passengers must remain seated on the upper deck to avoid raising the centre of gravity further.

Three states of equilibrium exist:

• Stable equilibrium — when tilted slightly and released, the object returns to its original position because the weight still acts within the base, creating a restoring moment.
• Unstable equilibrium — when tilted slightly, the object topples further because the weight acts outside the base, creating an overturning moment.
• Neutral equilibrium — when displaced, the object stays in its new position because the centre of gravity is neither raised nor lowered (e.g. a ball on a flat surface).

MisconceptionStudents sometimes state that a heavy object is more stable than a light one. Mass alone does not determine stability — the position of the centre of gravity relative to the base determines stability. A tall, narrow heavy object can be less stable than a short, wide light object. Exam cue: Always link stability to the height of the centre of gravity and the width of the base, never just to mass or weight.

Exam TipThe vertical line through the centre of gravity must be drawn truly vertical in every position, not at an angle following the object's tilt.

Exam TipFor neutral equilibrium, show clearly that the height of the centre of gravity does not change when the object is displaced.