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Centre of Mass of N-Particles System #8211; If there are N-particles distributed in space whose masses are m<sub>1</sub>, m<sub>2</sub>, m<sub>3</sub>,…..m<sub>N</sub> and position vectors r<sub>1</sub>, r<sub>2</sub>, r<sub>3</sub>,#8230;r<sub>N</sub> respectively, then the coordinates of the centre of mass are given below: X<sub>CM</sub> = m<sub>1</sub>x<sub>1</sub> + m<sub>2</sub>x<sub>2</sub> + m<sub>3</sub>x<sub>3</sub> + #8230; m<sub>N</sub>x<sub>N</sub>/m<sub>1</sub> + m<sub>2</sub> + m<sub>3</sub> + #8230;. +m<sub>N</sub> Y<sub>CM</sub> = m<sub>1</sub>y<sub>1</sub> + m<sub>2</sub>y<sub>2</sub> + m<sub>3</sub>y<sub>3</sub> + #8230;. + m<sub>N</sub>y<sub>N</sub>/m<sub>1</sub> + m<sub>2</sub> + m<sub>3</sub> + #8230;. + m<sub>N</sub> Z<sub>CM</sub> = m<sub>1</sub>z<sub>1</sub> + m<sub>2</sub>z<sub>2</sub> + m<sub>3</sub>z<sub>3</sub> + #8230; + m<sub>N</sub>z<sub>N</sub>/m<sub>1</sub> + m<sub>2</sub> + m<sub>3</sub> + #8230; +m<sub>N</sub> We can also write as, X<sub>CM</sub> 1/MΣm<sub>i</sub>x<sub>i</sub> Y<sub>CM</sub> = 1/MΣm<sub>i</sub>y<sub>i</sub> Z<sub>CM</sub> = 1/MΣm<sub>i</sub>z<sub>i</sub> where, M = m<sub>1</sub> + m<sub>2</sub> + m<sub>3</sub> + #8230; + m<sub>N</sub> The position vector of centre of mass of N-particles system is given by r<sub>CM</sub> = m<sub>1</sub>r<sub>1</sub> + m<sub>2</sub>r<sub>2</sub> + m<sub>3</sub>r<sub>3</sub> + #8230;.. + m<sub>N</sub>r<sub>N</sub>/m<sub>1</sub> + m<sub>2</sub> + m<sub>3</sub> + #8230; + m<sub>N</sub>
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