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CENTRE
OF MASS
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DEFINITION
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The
centre of mass of a body or a system of particles is defined as
"A single point at which the whole mass of the body or system is imagined to be concentrated and all the applied forces acts at that point." |
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EXPLANATION
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translational motion each point on a body undergoes the same displacement
as any other point as time passes, so that motion of one
particle represents the motion of the whole body. But when a body rotates
or vibrates, there is one point on the body, called "centre
of mass", that moves in the same way that a single
particle would move under the influence of the same external forces. Centre of mass of a body is that point that moves when forces are applied on the body. The motion of a body can be described as the motion of its centre of mass. The centre of mass , has translational motion under the influence of forces. If a single force acts on a body and the line of action of the force passes through the centre of mass, the body will have linear acceleration but possess no angular acceleration. |
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CENTRE
OF MASS
& CENTRE OF GRAVITY |
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| The centre of mass often confused with the centre of gravity. The two terms are so similar in many respects that one can use the two interchangeably. The centre of gravity of an extended object coincides with its centre of mass if the object is in a completely uniform gravitational field. If the body is not located in a uniform gravitational field,its centre of mass and centre of gravity will be at two different locations. | |||
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CENTRE
OF MASS OF
DIFFERENT OBJECTS |
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| Centre
of mass of a body depends on its geometrical shape. If a body is symmetrical
and of uniform composition, the centre of mass will be
located at its geometrical centre. For example:  Centre
of mass of a square is at the point of intersection of its diagonals.Centre
of mass of a sphere is at its centre. Centre
of mass of a rigid bar is at the middle point. |
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DETERMINATION
OF
CENTRE OF MASS OF |
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Consider
a system of "n" particles of masses  whose
position vectors are  respectively.The centre of mass of the system is defined as the point having the position vector "r" and is equal to: |
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If
 are
the coordinates of the centre of mass of a system of "n" particles
then, |
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Thus
are the coordinates of the centre of mass.
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