The velocity of center of mass of a system of particles is given by the ratio of total system momentum tothe sum of all masses of particles of the system. Similarly the acceleration of center of mass of a systemof particles is given by the ratio of total external force on the system to sum of all masses of particles ofthe systemHere if on the system no external force is acting, the acceleration of center of mass will be zero hencethe velocity of center of mass will be a constant and this states that total system momentum will alsoremain constant.
This phenomenon is known as Law of Conservation of Linear Momentum for a givensystem of particles.
To understand the concept in detail, see the video – https://youtu.be/BUUitwuwq04
Law of Conservation of Linear Momentum is a very important concept used very frequently in solvingproblems related to system of particlesMotion of Center of Mass in absence of external forces : By the Law of Conservation of LinearMomentum we can state that in absence of external forces velocity of center of mass of a systemremain constant (magnitude as well as direction).
If initially in a system, center of mass is at rest then bysome process due to internal forces in the system the center of mass will not be affected and it willremain at rest or if in some case if center of mass is following a trajectory under the influence of somelaws or effects then due to internal processes, the center of mass keep on following the trajectory as itsmotion will not be affected unless there is some change in external force take place.
This is a veryimportant logic used in solving problems related to motion of center of mass as well as problems relatedto linear momentum of a system of particles.
To develop fundamental understanding and applications of Law of Conservation of Linear Momentum,see the example videos below https://youtu.be/Umhaiwyi8o0