The centre of gravity of an object is the single point through which the entire weight of the object appears to act. An object is stable — resistant to toppling — when its centre of gravity is low and its base is wide. Whether an object topples depends on where its centre of gravity falls relative to its base.
What is the centre of gravity?
Every particle in an object has weight — a downward gravitational force. Rather than drawing millions of individual weight arrows, physicists treat all of this weight as though it acts at one point: the centre of gravity (CG), sometimes called the centre of mass at GCSE level. (Strictly, centre of mass and centre of gravity are the same point for objects in a uniform gravitational field, such as objects on Earth's surface.)
For regular, uniform objects the centre of gravity is at the geometric centre:
- Uniform ruler — midpoint along the length
- Uniform sphere — the centre
- Uniform rectangle — the intersection of the diagonals
For irregular or non-uniform objects, the centre of gravity must be found experimentally or calculated.
How do you find the centre of gravity of an irregular lamina?
A lamina is a flat, thin object (a 2D shape). The standard practical method uses a plumb line:
Method:
- Make three small holes around the edge of the lamina.
- Hang the lamina from a pin through one hole so it can swing freely. Hold a plumb line (a string with a weight) from the same pin and let it hang vertically.
- Draw the vertical line from the pin across the lamina.
- Repeat for the other two holes — drawing the vertical line each time.
- The three lines will meet at (or very close to) a single point: the centre of gravity.
Why it works: When suspended freely, any object hangs so its centre of gravity is directly below the suspension point. The plumb line shows that vertical direction. The CG must lie somewhere on that line. Two lines intersect at one point — confirming the location. A third line is used to verify.
How does the centre of gravity affect stability?
An object is stable if, when tilted slightly, the restoring force (weight acting through the CG) brings it back to upright rather than causing it to topple.
The rule for toppling: an object will topple if a vertical line drawn through its centre of gravity falls outside the base of support.
- When the object is upright and the vertical through the CG falls within the base → the weight produces a restoring moment → the object returns upright.
- As the object is tilted, the CG's vertical line moves towards the edge of the base.
- At the tipping point, the vertical through the CG passes exactly through the edge of the base → balanced; a tiny extra tilt and it topples.
- Beyond this point → the weight's moment acts to rotate the object further, not restore it → the object topples.
What makes an object more or less stable?
| Factor | More stable | Less stable |
|---|---|---|
| Height of CG | Low centre of gravity | High centre of gravity |
| Width of base | Wide base | Narrow base |
| Distribution of mass | Mass concentrated near base | Mass concentrated near top |
Examples:
- Racing car — very low, wide, heavy chassis; extremely low CG. Highly stable.
- Double-decker bus — tall with passengers on top. Designers load the heaviest components (engine, battery) in the floor to keep the CG low and prevent toppling on bends.
- Cone standing on its point — CG is high, base is tiny → unstable. Standing on its base — CG is low, base is wide → stable.
A simple test: tilt the object gradually. The one that can be tilted to a greater angle before toppling has the lower CG relative to its base.
Worked example: predicting whether an object topples
Question: A rectangular block is 0.20 m wide and 0.60 m tall. Its centre of gravity is at its geometric centre. The block is tilted about one corner. At what angle does it start to topple?
Diagram approach: When tilted, the CG traces an arc. The object topples when the CG is directly above the pivot (the corner).
Half-diagonal: The CG is at the geometric centre, located at half-width = 0.10 m from the side and half-height = 0.30 m from the base.
The angle θ at which toppling begins is the angle the diagonal from the pivot corner to the CG makes with the vertical:
tan θ = (half-width) / (half-height) = 0.10 / 0.30 = 0.333
θ = arctan(0.333) ≈ 18°
So the block topples when tilted more than 18° from vertical. A shorter, wider block would give a larger angle — more stable.
Frequently asked questions
What is the centre of gravity in GCSE physics?
The centre of gravity is the point through which the whole weight of an object appears to act. For uniform, regularly shaped objects it is at the geometric centre. For irregular objects it can be found by the plumb-line method: suspending the object from different points and drawing the vertical through each suspension point — the centre of gravity is where these lines meet. The concept is important for understanding stability, moments, and the conditions under which objects topple.
How does a low centre of gravity make an object more stable?
A low centre of gravity means the object must be tilted further before the vertical line through the CG moves outside the base of support. The wider the base and the lower the CG, the greater the angle of tilt the object can withstand before it topples. This is why sports cars are designed with wide wheelbases and heavy components mounted as low as possible, and why loaded lorries are more prone to toppling when loaded incorrectly with heavy goods stacked high.
What is the difference between centre of gravity and centre of mass?
For objects near Earth's surface, where the gravitational field strength is uniform, the centre of gravity and the centre of mass are the same point. Strictly, centre of mass is the average position of all the mass in an object, while centre of gravity is the point through which gravity acts. If an object is very large (extending across a region where gravity varies, such as a skyscraper or a mountain), the two points differ slightly, but this distinction is not required at GCSE.
How do you find the centre of gravity of an irregular shape experimentally?
Suspend the shape from a pin through one point on its edge, hang a plumb line from the same pin, and draw the vertical line on the shape. Repeat from two other points on the edge. The three lines will intersect at the centre of gravity. A third line is used as a check — if the three lines do not meet at a single point, there has been a drawing or measurement error. The method works because the CG always hangs directly below the suspension point.
For Socratic GCSE physics with Professor Newton — predicting behaviour from first principles before sketching a diagram, then checking with a worked example — visit aitutors.me.