Question

What is Centre of Mass of N-Particles System?

Answer

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