1.5.3 Centre of Gravity Revision Notes

1. Overview

The centre of gravity is a fundamental concept in mechanics that simplifies how we look at forces. By identifying the single point where an object's weight acts, we can predict how objects balance, rotate, and stay stable in everyday situations.

Key Definitions

• Centre of Gravity (CG): The point through which the entire weight of an object acts.
• Lamina: A flat, two-dimensional shape (such as a piece of cardboard or a metal plate).
• Plumb Line: A string with a weight attached to the end used to find a perfectly vertical line.
• Stability: A measure of an object's ability to maintain its balance and resist toppling over.

Core Content

Determining the Centre of Gravity

For regular, uniform objects (like a square or a circle), the centre of gravity is at the geometric centre. However, for an irregularly shaped plane lamina, you must use the following experiment:

Experiment: Finding the CG of an Irregular Lamina

1. Make three small holes near the edges of the lamina.
2. Suspend the lamina from a pin through one of the holes so that it can swing freely.
3. Hang a plumb line from the same pin in front of the lamina.
4. Once the lamina and plumb line stop moving, draw a line on the lamina following the path of the plumb line string.
5. Repeat this process using the other two holes.
6. The point where all three lines intersect is the centre of gravity.

Stability of Simple Objects

Stability describes how easy it is to knock an object over. Whether an object topples depends on the position of its centre of gravity relative to its base.

• Two factors for high stability:
  1. A wide base: The larger the area the object sits on, the harder it is to tip.
  2. A low centre of gravity: The closer the CG is to the ground, the more stable the object.
• When does an object topple?
  • An object is stable as long as the vertical line acting downwards from its centre of gravity falls inside its base.
  • If the object is tilted so far that the line of action of its weight falls outside the edge of the base, the weight creates a moment (turning effect) that causes the object to topple over.

Extended Content (Extended Only)

There is no additional supplement-specific content for this sub-topic in the current IGCSE Physics syllabus.

Key Equations

While this topic is primarily conceptual, it is closely linked to the Weight equation: $$W = m \times g$$

• W: Weight (Newtons, N) - this is the force that acts through the Centre of Gravity.
• m: Mass (Kilograms, kg)
• g: Acceleration due to gravity (approximately $9.8\text{ m/s}^2$ on Earth)

Common Mistakes to Avoid

• ❌ Wrong: Assuming the centre of gravity is always in the exact middle of an object.
• ✓ Right: The CG is only in the geometric centre if the object is uniform (even density throughout).
• ❌ Wrong: Saying an object is more stable just because it has a wide base.
• ✓ Right: You must consider both the base area and the height of the centre of gravity. A wide object with a very high CG can still be unstable.
• ❌ Wrong: Thinking any force applied to an object causes it to rotate.
• ✓ Right: A force only causes rotation if its line of action does not pass through the pivot (it needs a "lever arm").

Exam Tips

1. Experiment Description: When describing the experiment for an irregular lamina, always mention using three holes. This is for accuracy—two lines will intersect at a point, but the third line confirms that the point is correct.
2. Explain the "Why": In questions about toppling, use the phrase: "The line of action of the weight falls outside the base, creating a turning effect (moment)." This specific phrasing often earns the highest marks.