Notes On Motion of Centre of Mass - CBSE Class 11 Physics
Let us consider a system of n particles with its total mass constant with respect to time. Consider particle ‘i’ from the system. In the graph, its position is marked by vector ri and the centre of mass of the given system of particles is denoted as ‘R’.   This means that: The motion of the centre of mass of a system of particles is independent of the internal forces. The centre of mass moves as if the whole mass of the system is concentrated at it and the external force is acting on it. The total momentum of the system of particles is equal to the product of the total mass of the system and the velocity of the centre of mass. We have Fext = dp/dt.  This is Newton’s Second Law of Motion applicable to the system of particles. If the external force acting on the system of particles is zero, then Fext  = 0 and hence p is a constant. This is the Law of Conservation of Momentum applicable to a system of particles: “If the total external force acting on a system of particles is zero, then the linear momentum of the system is constant”.  A rigid body may have both translational and rotational motion. In such cases, it is usually convenient to work with a reference frame that is attached to the centre of mass of the system of particles.

#### Summary

Let us consider a system of n particles with its total mass constant with respect to time. Consider particle ‘i’ from the system. In the graph, its position is marked by vector ri and the centre of mass of the given system of particles is denoted as ‘R’.   This means that: The motion of the centre of mass of a system of particles is independent of the internal forces. The centre of mass moves as if the whole mass of the system is concentrated at it and the external force is acting on it. The total momentum of the system of particles is equal to the product of the total mass of the system and the velocity of the centre of mass. We have Fext = dp/dt.  This is Newton’s Second Law of Motion applicable to the system of particles. If the external force acting on the system of particles is zero, then Fext  = 0 and hence p is a constant. This is the Law of Conservation of Momentum applicable to a system of particles: “If the total external force acting on a system of particles is zero, then the linear momentum of the system is constant”.  A rigid body may have both translational and rotational motion. In such cases, it is usually convenient to work with a reference frame that is attached to the centre of mass of the system of particles.

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