Centre of mass: Every physical system has related with it a certain point whose motion characterizes the motion of the entire system. When the system goes under some external forces than this point goes as if the whole mass of the system is concentrated at this point and also the external force is operated at his point of translational motion. This point is known the centre of mass of the system.
Centre of mass of object of n point masses or n particles is that point about which moment of mass of the system is zero, it seems that if about a particular origin the moment of mass of system of n point masses is zero, then that particular origin is the centre of mass of the object.
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The concept of centre of mass is a pure mathematical relation. If there are n particles having mass m1, m2 ....m n and are placed in space (x1, y1, z1), (x2, y2, z2) ..........(x n, y n, z n) then centre of mass of system is described as (X, Y, Z) where
 is the net mass of X the system.
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Find the point with coordinates (X, Y, Z). This point is known the centre of mass of the given collection of the particles. If the position vector of the i th object is ri, the centre of mass is described to have the position vector
Where
= i x cm + j y cm + k (z cm)
This is equation for centre of mass of n point masses.
Centre of mass of continuous bodies:
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If we suppose the object to have continuous distribution of matter, the addition in the formula of centre of mass should be removed by integration. If z, x, y are the coordinates of this small mass dm, we write the coordinates of the centre of mass as
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The integration is to be done under proper limits so that as the integration variable goes through the limits, the components cover the entire body.
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