Mechanics: Centre of Gravity

Key Concepts

The centre of gravity of an object is the point through which the weight of the object acts. It can be considered as the point at which all the mass of an object appears to be concentrated.
For a uniform body (a body with equal density throughout), the centre of gravity is at the geometric centre. For example, the centre of gravity of a uniform rod is in the middle of the it.
A body will be in equilibrium when the resultant force and the resultant moment acting on it are both zero. Equilibrium can be either stable, unstable, or neutral.
In stable equilibrium, if a body is slightly displaced, it will tend to return to its original position. This happens when the centre of gravity is below the point of support.
In unstable equilibrium, if a body is slightly displaced, it will move further from its original position. This occurs when the centre of gravity is above the point of support.
In neutral equilibrium, a body stays where it is when slightly displaced. This happens when the centre of gravity is at the same level as the point of support.

To find the centre of gravity of an irregular lamina, suspend it from a point and use a plumb line to draw a vertical line. Then, suspend it from another point and draw another line. The point where the lines intersect is the centre of gravity.
When calculating moments, the force to be considered is the weight of the object, which acts vertically downwards through the centre of gravity. The moment of a force is the force multiplied by the perpendicular distance from the line of action of the force to the pivot.
Equilibrium equates to zero net force and zero net moment. Hence you can set up the sum of forces/moments in one direction equal to the sum in the opposite direction.

Understanding the concept of centre of gravity is crucial in many areas of life, from how a building is designed to stay upright, to why a cat always lands on its feet.
The location of an object’s centre of gravity can be shifted by the addition or removal of mass. This is frequently utilized in sports such as shot put and discus.
Architects and civil engineers need to consider the centre of gravity when designing structures like bridges and skyscrapers. If the centre of gravity is off, the structure could fall.

The position of the centre of gravity affects how an object behaves when it is subjected to forces - whether it will topple over or remain stable.
If a body is freely suspended, it will come to rest with its centre of gravity directly below the point of suspension because this position gives the lowest potential energy and hence the most stable equilibrium.
Knowledge of the centre of gravity is crucial in making objects balance. It’s why tightrope walkers carry long poles and why double-decker buses are wide.
The concept of stable, unstable, and neutral equilibrium provides the basis for understanding the balance and stability of objects in many fields, from basic mechanics to civil engineering and design.