## Sunday, January 3, 2016

### Internal Forces effect on Motion of Centre of Mass

Motion of center of mass is effected because of external force applied and internal forces cannot effect the motion of center of mass. Center of mass is a point of a system which represents the motion of the system when some force is applied on it. To prove the influence of the motion we can consider the derivation we have made for the acceleration of the center of mass as shown in the earlier post. By differentiating the acceleration of center of mass, we can get the equation for the for force acting on the system.

It is mathematically proved in the presented video, it is proved that the force on the center of mass of the system is the product of mass of the system and the acceleration of center of mass. The force is actually sum of internal as well as external forces. But we know that internal forces can not influence the motion of center of mass. It is simple like internal collisions inside a gas cylinder can not move it physically from one place to other and we need to apply external force to move it from one place to other.

So in the place of forces, we can simply write the external forces acting on the system. Thus external force is the product of mass of the system and the acceleration of center of mass.

If the external force is equal to zero, then the product of mass of the system and its acceleration of center of mass is equal to zero. Product of two quantities  will be zero when at least on of them is equal to zero. Mass is a fundamental physical quantity and it can not be zero. There is no particle in the nature that has zero mass. Hence the acceleration of center of mass of the system is equal to zero.

So it is clearly exhibited that only external forces can influence the motion of center of mass but not internal forces. It is very clear that internal forces cannot show any influence on the motion of the center of mass.

Let us consider a small example like a bomb thrown from the ground at an angle to the ground from the horizontal. In the middle of the path, let it got exploded into so many pieces. This explosion is happened because of internal forces but not due to any external internal forces. Different particles of the bomb may travel in different directions but the center of mass particle of the bomb continue its parabolic path.

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