## Friday, January 1, 2016

### Center of Mass Representation of Translatory Motion an Introduction

Centre of mass is a point of a body which represents the actual motion of the body. In mechanics we are always interested in studying the motion of the body. To move a body from one position to another position, we shall apply sufficient external force. The body will be able to move only when the applied forces sufficient to overcome the inertia of the body. Once if the body starts moving, we would like to study the motion of the body like what is the path of the body.

If all particles of the body are having a similar kind of displacement and the path, that kind of the motion is called as translatory motion. In translatory motion any point of the body represents the actual motion of the body. But practically all the particles of the body every time won’t represent the actual motion of the body. In that case, to understand the translatory motion we shall consider a point which actually represents the motion of the body. The point of the body which represents the actual motion of a body is called Centre of mass. If we want to replace the body and put a point we shall put the point and the location of the Centre of mass.

It may happen sometimes that at the point of Centre of Mars, there won’t be mass at all. For example in the case of the motion of the ring on a floor, we can study the motion of the ring taking the Centre of mass at the centre of the ring and actually at the centre of the ring there is no content and there is no mass. Centre of mass doesn’t mean there shall be mass and it is just a point which represents the actual motion of the body, Having a mass at the Centre of mass is not mandatory.

Taking any point of the body to study the motion of the body every time will not give you the correct way of understanding the motion of the body.

If we consider a point of the surface of a tire of a vehicle who is moving to study the motion of the tire, we get the motion of that point is a complicated one as shown in the video. But actually the tire is moving in a more organized way and to study the motion of the tire we shall consider a point called Centre of mass. For any regular and organized bodies, Centre of mass is at the geometrical centre of the system. Different particles of body may be representing different kinds of motion, but the actual motion of the body is represented by the Centre of mass.

Motion of a single body are a system of the particles which are together treated like a system, can be studied basing on the concept of Centre of mass.

Let us consider the sun and the earth system. We know that the earth is revolving around the Sun in a specified orbit. We also know that it is because of the gravitational force between the sun and the earth, the Earth is revolving around the Sun in a specified orbit. We also know that during the process earth is also having a spin motion. Now we would like to study the motion of the earth around the Sun. Taking any point on the surface of the earth and if we identify the path taken by it around the Sun, it will be as shown in the given video. It can be noticed that the party is quite complicated and we don’t express the path of the earth in that way. It is simply because the point that we have taken the earth is not the Centre of mass of the earth. If we consider the point of Centre of mass of the earth and study the motion of the earth around the Sun, we can see a clear elliptical path.

Therefore Centre of mass is a point of your body or a system which represents the actual motion of the body. There may be mass are there may not be mass at the Centre of mass point and if it is representing the motion of the body are system, it shall be treated like a Centre of mass.

For all uniform and geometrically organized shape bodies Centre of mass coincides with the geometrical Centre and the Centre of gravity of the body. Centre of gravity is a point of your body or system which represents the place where the acceleration due to gravity is acting on the body.

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