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| Generalisation to N - Particles |
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| Consider a system of N particles of masses m1, m2, m3,------------ mN. |
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Let a, b, c, ……………. represent the particle numbers ranging from 1 to  . |
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Let the particle a be acted upon by some
external force  and by an
internal force  from every other particle in the system. |
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| According to Newton's second law, |
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| According to Newton's third law, |
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| For any ath particle |
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| Substituting a = 1, 2,……….. N. We have N equations. Adding them all, |
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| The position vector of the centre of mass of the whole system is given by, |
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| Where M = m1+m2+-------mN |
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is the weighted average of the position vectors of the particles of the system. It moves according to the equation of motion. |
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