A point at which the entire mass of the body or system of bodies is supposed to be concentrated is known as the centre of mass.
Centre Of Mass For A System Of Two Particles
Let the distances of the two particles be x₁ and x₂ respectively from origin O. Let m₁ and m₂ be their masses. The centre of mass of the system is that point C which is at a distance Xcm from O.
Where M = m₁+m₂ = Total mass of system
If the two particles have the same mass m₁ = m₂ = m, Then
Thus for two particles of equal mass, the centre of mass lies exactly midway between them.
Centre Of Mass For A System Of n Particles
Let a system of n particles having masses m₁, m₂, m₃,…….mₙ occupying along x-coordinate and their distances from origin be x₁, x₂, x₃,…….xₙ respectively.
If the particles are distributed in three dimensional space, then the centre of mass has three coordinates, which are