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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