Section 1 of 9Centre of gravity
An object is made of many particles, each with weight. The centre of gravity is the single point through which the whole weight of the object appears to act. We can treat the entire weight as acting at this point when calculating moments or when drawing force diagrams.
For a uniform object with a symmetrical shape, such as a ruler, a rectangular plate or a sphere, the centre of gravity is at the geometric centre. For irregular or unevenly loaded objects it is nearer the heavier part. It does not have to be inside the material: the centre of gravity of a ring is in the empty centre.
The centre of gravity can move if the object changes shape.
Section 2 of 9Finding the centre of gravity of a flat shape
This is a common practical.
The card hangs with its centre of gravity directly below the pivot because that gives zero moment; any other position gives a moment that would turn it.
Safety pointsthe pin should be held in a clamp so that the card swings freely, and the plumb line should not be touched as it hangs.
Section 3 of 9Balancing
An object balances on a point if the point is directly below (or directly beneath) its centre of gravity, because then the weight has no moment about the support. A metre rule balances on a finger at its midpoint for a uniform rule. If a mass is hung at one end, the balance point moves towards that end.
Section 4 of 9Stability
An object is stable if, when tilted slightly, it returns to its original position. This happens when the line of action of the weight, drawn vertically down from the centre of gravity, still falls within the base. If it falls outside the base, the weight gives a moment that tips the object over.
The angle through which an object can tilt before toppling is larger for a low centre of gravity and a wide base.
A pencil balanced on its tip is unstable because the centre of gravity is above the support: any tilt moves the weight outside the support point and the moment makes it fall.
Section 5 of 9Examples
Section 6 of 9Link to moments
When using the principle of moments for a uniform rod or beam, take the weight of the rod at the centre of gravity, the midpoint. An irregular object may have the weight acting at a different place, which can be found from the plumb line method or by balancing the object on a thin pivot.
Examiners often ask for a labelled diagram of a plumb-line experiment, so practise sketching the clamp, pin, card, and string. Also be ready to explain why a bus can safely tilt to a certain angle by drawing the line from the centre of gravity and showing where it meets the ground.
Section 7 of 9Worked examples
A uniform 1.0 m rule of weight 0.80 N is pivoted at the 30 cm mark. Find the moment of the rule's weight about the pivot and its direction.
The weight acts at 50 cm, which is 20 cm = 0.20 m from the pivot.
Moment = 0.80 × 0.20 = 0.16 N m clockwise (the weight is on the right of the pivot).
Explain why a bus tilted to 25° may be stable but at 35° topples.
The weight acts vertically down from the centre of gravity. At 25° this line is still inside the wheelbase, so the weight gives a restoring moment. At 35° the line has moved outside the wheels, so the weight gives a moment that rotates the bus over.
A plumb line from a pin passes through the card. Two lines drawn from two different holes cross at a point P. What is P?
P is the centre of gravity of the card, because the weight acts along the vertical through the pivot in each case, and the only point on both lines is where the weight acts.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Centre of gravity | Point where the whole weight of an object appears to act. |
| Plumb line | String with a weight that hangs vertically. |
| Stable | Returns to its original position when tilted slightly. |
| Base | Area of contact with the ground. |
| Topple | Tip over because the weight acts outside the base. |