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# What is Centre of Gravity?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The ancient Greek mathematician, scientist, and engineer Archimedes of Syracuse thoroughly studied the idea of a **centre of gravity** or weight. He arrived at the mathematical properties of what we now refer to as the centre of mass by working with simplified gravity assumptions that amount to a uniform field.

The region where the resultant torque brought on by gravity forces disappears is known as a body’s centre of gravity. When a gravitational field is homogeneous, the mass centre and the centre of gravity will be identical. However, for satellites orbiting a planet, in the absence of any additional torques, the minor gradient in the gravitational field between closer to (stronger) and further from (weaker) the planet can provide a torque that will tend to align the satellite such that its long axis is vertical. Making the distinction between the mass centre and the centre of gravity is crucial in such a situation.

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## What is Centre of Gravity?

The weight of a body, which is the result of gravitational forces acting on it, acts through a location known as the body’s centre of gravity. The distribution of weight within the body consequently determines the centre of gravity. In dynamics, the centre of mass of a body, a characteristic of how the body’s mass is distributed inside it and the location through which the resulting inertia force acts, is an important term.

However, we find that the centres of mass and gravity coincide in most situations since weight and mass only differ by a constant factor (assuming that the gravitational field is uniform). Differences only appear in situations when the gravitational field is not uniform. Thus, it should not be surprising that engineers use the phrases centre of mass and centre of gravity interchangeably.

### Define Centre of Gravity

“The point through which a body’s entire weight acts is known as the centre of gravity. A body can only have one centre of gravity in any given position.” It is symbolized or indicated by the letters C.G. or G. In other words; we can say that “the location where a body’s total weight is concentrated, so that if supported at this location, the body would maintain equilibrium in any configuration.”

## Centre of Gravity Formula

The most common example of a distributed force is the weight of a body. The weight of a differential volume element dV for a body occupying the region is given by DW = dV, where is the weight density (weight per unit volume). As a result, the body’s total weight W is the product of an infinite number of parallel forces dW:

The centre of weight, or the centre of gravity of the body, is the point G through which the weight W acts. The resultant moment of the dispersed weight can be used to get the coordinates of G by equating it to the moment of W about the coordinate axes.

## What is the Centroid?

The centroid of an area is the location where the entire area of a plane figure—such as a circle, rectangle, triangle, square, quadrilateral, etc.—is thought to be concentrated. C.G. or G can also be used to denote the centroid. The centroid and the centre of gravity are located at the same point. The centre of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle’s three medians intersect. It can be described as the location where the three medians come together. The median is a line that connects the middle of a side to the triangular opposite vertex.

## Difference Between the Centre of Gravity and the Centre of Mass

Despite common belief, the centre of mass and centre of gravity are not identical.

The centre of mass, independent of the gravitational field, is a location where the mass distribution is equal in all directions. The centre of gravity, which is affected by the gravitational field, is a location on an item where the weight is distributed equally in all directions. In a uniform gravitational field, an object’s centre of mass and centre of gravity is located at the same location.

## How to Find the Centre of Gravity

The three techniques listed below can be used to determine an object’s centre of gravity:

- By geometrical consideration
- By the method of moments
- By the method of integration

**Geometrical Consideration**

The centre of gravity of square- or rectangle-shaped objects is determined by the junction point of the lines joining their diagonals. The triangle-shaped item’s centres of gravity are determined by where the lines connecting their midpoints and opposite vertices intersect. Circular objects have their centres of gravity at their midpoints.

**Method of Moments**

The principle of moments is employed in this method to determine the location of the object’s centres of gravity. The moment of a resultant force is equal to the sum of the moments created by the component forces, according to the method of moments. Any complex-shaped object’s centre of gravity can be located using this method.

**Method of Integration**

The method of integration is identical to the method of moments. This approach starts by breaking the provided object into smaller components and locating its centre of gravity. The object’s centre of gravity is then determined by integrating the result.

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