Centre of Gravity vs Centroid: Difference and Comparison

Every object is said to weigh a certain amount and have mass. Both mass and weight come into play when you try to balance an object. 

While balancing, the object’s centre is where the gravitational force is concentrated. It is at the central point of the object where you can balance it. 

Here, you will come across two terms that are confused. They are the Centre of Gravity and Centroid. Even though they consist of a familiar concept;

Centre of Gravity and Centroid are two terms that differ based on the context in which it is used and the object to which it is used regarding.

Key Takeaways

1. The center of gravity is the point at which the weight of an object is evenly distributed, and the object can be balanced on that point without any tendency to rotate.
2. The centroid is the geometric center of an object, representing the average position of all points within the object’s shape. It coincides with the center of gravity for objects with uniform density.
3. Although the center of gravity and centroid may coincide for certain objects, they are distinct concepts related to weight distribution and geometric center, respectively.

Centre of Gravity vs Centroid

The difference between the terms Centre of Gravity and Centroid is that the former refers to the point where the object’s total weight is focused. In comparison, the latter refers to the geometric centre of an object.

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Comparison Table

Parameter of Comparison	Centre of Gravity	Centroid
Perception	The Centre of gravity is the point where the total weight of the object acts.	Centroid is the geometric centre of the object.
Symbol	The Centre of gravity is referred to with the letter ‘g’.	Centroid is referred to with the use of the letter ‘c’.
Calculation	The Centre of Gravity(CG) can be calculated using the equation W=S x dw.	Centroid can be calculated using the plumb line method or by taking the mean of the median in the case of a triangle.
Object density	The Centre of Gravity applies to objects with any density.	Centroid is the central point of objects with uniform density.
Subject association	Centre of Gravity is a term found in Physics.	Centroid is a term used in Mathematics concerning triangles.

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What is Centre of Gravity?

Centre of Gravity is the term used to refer to the point where the object’s total weight is focused.  The Centre of Gravity is also known as the centre of mass since it is where the object’s mass is concentrated.

It refers to the point where the gravitational force of the entire object acts upon it.  Thus, at this point, the centre’s mass equals the whole body’s mass. 

The Centre of Gravity of any object plays an essential role while trying to balance that object. Here is an example to make it clear:

Consider a can placed on a flat surface. All its weight is focused on the Centre of Gravity.  If tilted slightly, the gravitational pull at the centre creates a new point where the weight is concentrated.

This will lead to the can being pulled into a stable position. 

The Centre of gravity or centre of mass denote the focus point of the total weight of any object with any density, that is, of objects with non-uniform density.

The Centre of gravity is denoted by the symbol or letter ‘g’ or “cg”. Centre of Gravity or cg can be calculated by the equation mentioned above; W = S x dw where, 

1. W – total weight of the object.
2. x – distance from a reference line.
3. Dw – increment of weight.

 

What is Centroid?

Centroid is the term used to refer to the geometric centre of an object.  This term denotes the centre of a body with uniform density. That is, the centre of any object where the density is evenly distributed over its body is called the Centroid. 

When objects have homogeneous density, their Centroid is the same as their Centre of Gravity. When in the context of triangles, a triangle’s centroid is the point of intersection of its three medians.

At that point, all three medians of a triangle meet called the Centroid.

Centroid is denoted by the symbol or letter “c”. To find out the Centroid of an object, you can use the plumb line method proposed by Archimedes. In practical situations, you can find out the Centroid of an object by trying to balance it.

Make a cutout of the object and try to balance it over the tip of a pin. The point where the cutout is balanced perfectly over the tip is the centre of that object.

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Main Differences Between Centre of Gravity and Centroid

1. The main difference between the Centre of Gravity and Centroid is that the former refers to the point where the body’s total weight is concentrated. In contrast, the latter refers to the geometric centre of an object.
2. The Centre of Gravity denotes the total weight of an object with any density. But Centroid is the centre of an object with uniform density.
3. The Centre of gravity is denoted by the symbol “g”, while Centroid is denoted by “c”.
4. Centre of Gravity refers to a physical characteristic of a body, whereas Centroid refers to a geometric characteristic of an object.
5. The centre of gravity is where the gravitational force acts upon the body with any density. Whereas in the case of the centre of an object with homogeneous density, Centroid equals the Centre of Gravity.

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References

1. https://arxiv.org/pdf/1801.06836

Last Updated : 11 June, 2023