Motion of center of mass can be understood in terms of velocity and acceleration of center of mass. We have derived equations for coordinates of center of mass in the post earlier.Position of center of mass is expression in terms of displacement and differentiating it once with respect to time gives velocity of center of mass.
As the mass of the particle is constant, it is not going to vary with time during differentiating and hence it can be written out side the mathematical differentiation.Thus,we need to differentiate displacement of each particle with time. The rate of change of displacement is velocity. Thus we get velocity of each particle. Hence, we can get the velocity of centre of mass of the system.
In the place of product of mass and velocity,we can substitute the momentum of the each particle. Thus, by adding the momentum of each particle, we can write the momentum of the system. Adding all the particles masses can give the total mass of the system. The product of mass of the system with velocity of center of mass of the system gives the momentum of center of mass.
By differentiating the velocity of center of mass equation with time, we can get the acceleration of center of mass of the system. Rate of change of velocity of each particle with time give acceleration of each particle. Thus we can write the equation for acceleration of center of mass of the system as shown in the video lesson below.
We can write the product of mass and acceleration of the system as the force acting on the system.
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