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 centre of the object is where the gravitational force is concentrated. It is at the central point of the object where you can balance it.

It is here where you will across two terms often confused with each other. They are Centre of Gravity and Centroid. Even though they consist of a common concept; Centre of Gravity and Centroid are two terms that differ based on the context in which it is used and the object it is used in regards to.

**Centre of Gravity vs Centroid**

**The main difference between the terms Centre of Gravity and Centroid is that the former refers to the point where the total weight of the object is focused at. Whereas the latter refers to the geometric centre of an object.**

## Comparison Table Between Centre of Gravity and Centroid

(in Tabular Form)

Parameter of Comparison | Centre of Gravity | Centroid |
---|---|---|

Perception | Centre of gravity is the point where total weight of the object acts. | Centroid is the geometric centre of the object. |

Symbol | Centre of gravity is referred to with the use of the letter ‘g’. | Centroid is referred to with the use of the letter ‘c’. |

Calculation | Centre of Gravity(cg) can be calculated using the equation W=S x dw. | Centroid can be calculated by using the plumb line method or by taking the mean of median, in case of a triangle. |

Object density | Centre of Gravity is applicable to objects with any density. | Centroid is the central point of objects with uniform density. |

Subject association | Centre of Gravity is a term often found in Physics. | Centroid is a term often used in Mathematics, in relation to triangles. |

## What is Centre of Gravity?

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

It refers to the point where the gravitational force of the entire object acts upon. Thus, at this point, the centre’s mass equals the mass of the whole body. The Centre of Gravity of any object plays an important 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 it is 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.

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. 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,

- W – total weight of the object.
- x – distance from a reference line.
- dw – increment of weight.

## What is Centroid?

Centroid is the term used to refer to the geometric centre of an object. This term is used to denote 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, then its Centroid is the same as its Centre of Gravity. When in context of triangles, the centroid of a triangle is the point of intersection of its three medians. That is, the point where all three medians of a triangle meet, is called the Centroid.

Centroid is often denoted by the symbol or letter “c”. In order 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.

**Main Differences Between ****Centre of Gravity and Centroid**

**Centre of Gravity and Centroid**

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

## Conclusion

While Centre of Gravity is the point where the weight of the body is focused, Centroid is the geometric centre of an object. Both these terms involve the concepts of density, weight and balance of any object.

However, both of these terms are related to each other with the respect to the density of the object. If the object does not have uniform density, then its focus point is called Centre of Gravity. Whereas if it is of uniform density, then the Centre of Gravity is equal to its Centroid.

Both Centre of Gravity and Centroid are concepts that are important, to find out the central focus point of objects where the gravitational force acts on the body.

## References

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