Notes

Centre of Mass of N-Particles System…

Centre of Mass of N-Particles System –
If there are N-particles distributed in space whose masses are m₁, m₂, m₃,…..m_N and position vectors r₁, r₂, r₃,……..r_N respectively, then the coordinates of the centre of mass are given below:
X_CM = m₁x₁ + m₂x₂ + m₃x₃ + …. m_Nx_N/m₁ + m₂ + m₃ + …. +m_N
Y_CM = m₁y₁ + m₂y₂ + m₃y₃ + …. + m_Ny_N/m₁ + m₂ + m₃ + …. + m_N
Z_CM = m₁z₁ + m₂z₂ + m₃z₃ + … + m_Nz_N/m₁ + m₂ + m₃ + … +m_N
We can also write as,
X_CM 1/MΣm_ix_i
Y_CM = 1/MΣm_iy_i
Z_CM = 1/MΣm_iz_i
where, M = m₁ + m₂ + m₃ + … + m_N
The position vector of centre of mass of N-particles system is given by
r_CM = m₁r₁ + m₂r₂ + m₃r₃ + ….. + m_Nr_N/m₁ + m₂ + m₃ + … + m_N