Choosing O as origin of the coordinate axis.

1. Then, position of centre of mass from m₁=m₂ dm₁+m₂

           m₁                                                       m₂

                O                        d                       P

2. Position of centre of mass from m₂ = (m₁ d) / m₁ + m₂
3. If position vectors of particles of masses m₁ and m₂ are r₁ and r₂ respectively, then

4. If in a two particle system, particles of masses m₁ and m₂ moving with velocities v₁ and V₂ respectively, then velocity the centre of mass

V_CM=m₁ v₁+m₂ v₂m₁+m₂

5. If accelerations of the particles are a1, and a1respectively, then acceleration of the centre of

Mass

   a_CM= m₁ a₁+m₂ a₂m₁+m₂

6. Centre of mass of an isolated system has a constant velocity.
7. It means isolated system will remain at rest if it is initially rest or will move with a same velocity if it is in motion initially.
8. The position of centre of mass depends upon the shape, size and distribution of the mass of the body.
9. The centre of mass of an object need not to lie with in the object.
10. In symmetrical bodies having homogeneous distribution mass the centre of mass coincides with the geometrical centre the body.
11. The position of centre of mass of an object changes translatory motion but remains unchanged in rotatory motion.