defination of motion of centre of mass
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The center-of-mass (COM) is the single point on a structure which characterizes the motion of the object if the object shrinks to a point mass. ... If a net force is applied to the COM the resulting motion will be translation (the object will not rotate).
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Centre of mass of a body or system of a particle is defined as, a point at which whole of the mass of the body or all the masses of a system of particle appeared to be concentrated.
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