1.5.3 Centre of gravity
- Syllabus
- 0625–2026–2027
- Topic
- 1.5.3
- Level
- —
Learning objectives
1.5.3.1What is meant by centre of gravity• State what is meant by centre of gravity1.5.3.2An experiment to determine the• Describe an experiment to determine the position of the centre of gravity of an irregularly shaped plane lamina1.5.3.3Qualitatively the effect of the• Describe qualitatively the effect of the position of the centre of gravity on the stability of simple objects
Define centre of gravity
The centre of gravity of an object is the point through which its entire weight may be considered to act.
Gravity acts throughout the object, but for forces and moments we represent the combined gravitational effect by one downward force—the object's weight—acting through its centre of gravity.
For a uniform, symmetrical object the centre of gravity is at its geometrical centre. For an irregular shape or uneven mass distribution, it need not be at the geometrical centre and can even lie outside the material of the object.
The centre of gravity is a position, not a separate force. The weight acts through that point vertically downwards.
Find the centre of gravity of an irregular lamina
When a lamina hangs freely from a point, it settles with its centre of gravity vertically below the suspension point.
| Step | Procedure |
|---|---|
| 1 | make a small hole near the edge of the irregular plane lamina and suspend it freely from a pin |
| 2 | hang a plumb line from the same pin and wait until the lamina and line are stationary |
| 3 | draw the vertical line on the lamina along the plumb line |
| 4 | suspend the lamina from a second hole and draw a second vertical line in the same way |
| 5 | mark the intersection of the two lines; this is the centre of gravity |
Each drawn line must pass through the centre of gravity because the centre of gravity lies directly below that suspension point. Two such lines therefore locate the same point by intersection.
Use a third suspension point to check that all three lines meet close to one point. Let the lamina hang without touching the stand, use a fine plumb line, and mark each line without parallax.
Do not choose the geometrical centre by eye: an irregular lamina must be suspended from at least two different points so that vertical lines can be intersected.
Relate centre of gravity to stability
A more stable object can be tilted farther before it topples. Stability increases when the centre of gravity is lower and when the base is wider.
| Change | Effect on stability | Reason |
|---|---|---|
| lower the centre of gravity | increases | a larger tilt is needed before the weight's line of action reaches the edge of the base |
| raise the centre of gravity | decreases | a smaller tilt can move the line of action beyond the base |
| widen the base | increases | the line of action can move farther before reaching an edge |
| narrow the base | decreases | the line of action reaches an edge sooner |
Imagine a vertical line downward through the centre of gravity. While that line falls inside the base, the object's weight produces a restoring effect. At the edge is the tipping point; beyond the edge, the weight produces an overturning moment and the object topples.
Place heavy loads low in a vehicle or ship and keep supports far apart when greater stability is needed. Compare both centre-of-gravity height and base width before deciding which object is most stable.
A heavy object is not automatically more stable. The decisive qualitative test is whether the vertical line of action of its weight stays within its base as it tilts.