Centre of Gravity

What is the Centre of Gravity?

The centre of gravity (CG) of an object is the point at which the entire weight of the object can be considered to be concentrated. It's the point where the object would balance perfectly if supported.

Essentially, it's the average position of the weight distribution within the object. For a uniform object, the CG is at the geometric centre.

Why is the Centre of Gravity Important?

Understanding the centre of gravity is crucial in various areas of physics and engineering. It helps us determine the stability of objects and structures.

For example, a stable object has its CG positioned above its base of support. If the CG falls outside the base of support, the object will topple over.

Factors Affecting the Centre of Gravity

The position of the centre of gravity depends on the shape and distribution of mass within the object.

• Uniform Objects: For a uniform object with a regular shape (like a sphere or a cube), the CG is located at its geometric centre.
• Non-Uniform Objects: For objects with uneven mass distribution, the CG will be shifted towards the side with more mass.

Example: Simple Shapes

Let's consider the centre of gravity for a few simple shapes:

The exact location of the centre of gravity can be determined experimentally by balancing the object on a pivot point.

$$ CG = \frac{\sum m_i x_i}{\sum m_i} $$ where $m_i$ is the mass of each part and $x_i$ is its position.