What is the Centre of Mass?

The centre of mass of a body or system of particles is a point at which the whole of the mass of the body or all the masses of a system of particles appears to be concentrated. In physics, this point is also known as the balance point, and is the centre of the distribution of mass in space, where the weighted relative position of the distributed mass has a sum of zero. In simpler terms, the centre of mass is the average position of all the parts of the system, or the mean location of a distribution of mass in space. It is the point where force is usually applied that results in linear acceleration without any angular acceleration.

When studying the dynamics of the motion of a system of particles as a whole, we should not be concerned with the dynamics of individual particles, but rather focus on the dynamics of a single point that corresponds to the system.

The concept of centre of mass (COM) is useful for analyzing the motion of a system of objects, especially when two or more objects collide or an object explodes into fragments. The motion of this point, which is equal to the motion of a single particle whose mass is equal to the sum of all individual particles of the system and the resultant of all the forces exerted on all the particles of the system by surrounding bodies (or) action of a field of force is exerted directly to that particle, is called the centre of mass of the system of particles.

Centre of Gravity

The Centre of Gravity (COG) can be taken as the point through which the force of gravity acts on an object or system. It is the point around which the resultant torque due to gravity forces disappears. In cases where the gravitational field is assumed to be uniform, the Centre of Gravity and Centre of Mass will be the same. Sometimes these two terms – the Centre of Gravity and Centre of Mass are used interchangeably as they are often said to be at the same position or location.

System of Particles

The system of particles refers to a collection of particles, which may or may not interact with one another or be connected to each other. These particles can be actual particles or rigid bodies in translational motion. When particles interact, they apply forces on one another.

The force of interaction $\overrightarrow{{{F}_{\hat{i},\hat{j}}}}$ and $\overrightarrow{{{F}_{\hat{j},\hat{i}}}}$ between a pair of $i^{th}$ and $i^{th}$ particle are called the internal force of the system.