Difference Between Centre of Gravity and Centroid

The words centre and gravity are derived from the Latin or Greek words which mean “centrum” and “gravitation”. The centre of gravity (CG) of any object is referred to as the point where gravity acts on the body. While the centroid refers to the geometrical centre of a uniform density object. Let’s discuss the topic in detail along with a few important questions.

What is Centre of Gravity? 

The centre of gravity or centre of mass is the point, where the whole mass of the body is concentrated. It means that the point where the gravitational force, the weight of the body, acts generally in any orientation of the body. As we know that the centre of gravity is directly proportional to the stability of the body. For example, if the center of gravity of a car is low then its stability is higher. The centre of gravity of any object can be calculated by summing the weight of the body and dividing it by its origin.

What is Centroid? 

The centroid is the point of the geometric centre of any object, where the density is wholly distributed over the body. For example, make a cutout on an object and try to balance the object over the tip of the pin. 

Hence, the point where the cutout is balanced perfectly is the centre of the object. The centroid of a body can be calculated by using the plumb line method proposed by Archimedes. 

Difference between Centre of Gravity and Centroid

The Centre of Gravity is located at the point of an elementary body where the whole weight of the body is concentrated and Centroid is the geometrical centre of an object where the cutout of the shape of an object is perfectly balanced. Both of these terms have been involved in the concepts of weight, density, and balance of an object. Since both of them are related to each other in terms of the density of the object. If the given object does not have a uniform density, then the focus point is known as the Centre of Gravity. However, if the density of the object throughout the body is the same i.e. the body is homogeneous, then the centre of gravity is equivalent or equal to the centroid. The concepts of Centroid, as well as Center of Gravity, are important in finding out the central focus point of the body where the gravitational force acts. 

The position that is considered as the centre of gravity for the particle in the Cartesian coordinate system can be found out by the vector or the radius vector rS = Σmiri / Σmi. Where the mi is the mass of the particles and ri is the radius vector of the particles. The position that indicates the centre of the mass of the rigid body in the Cartesian coordinate system is to be found out by the radius vector that is rS = (∫rρdV) / M, where letter r is the unit vector, symbol ρ is the body’s density, symbol V volume, and M is the mass of the body.

Below we have discussed the center of gravity and centroid on various parameters.
 

The principle of Archimedes was the first to describe the process by which the centroid can be found out. He introduced the cutting process of cardboard according to the objects’ shape and piercing several holes in it. Then it has to be nailed on the wall on one of the holes and be hanged freely. Then we need to hang plumb on the same nail and draw with a pencil the direction which is determined by the end of the plumb. This direction is the centre of gravity which is of the object. Hang the body on the other holes as well and repeat the procedure.

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Things to Remember

• The centre of gravity or centre of mass is the point, where the whole mass of the body is concentrated. 
• The Centre of gravity can be calculated by the equation W=S x dw.
• The centroid is the point of the geometric centre of any object, where the density is wholly distributed over the body.
• The centroid is calculated using the plumb line method or by taking the mean of the median.
• Both of these terms have been involved in the concepts of weight, density, and balance of an object.