13.4 : معادلة الحركة: مركز الكتلة

The equation of motion for a single particle can be extended to a system of particles. Consider a system with n numbers of particles.

The net force acting on an arbitrarily chosen particle is the sum of the net external and internal forces.

This equation of motion can be applied to any other particle from the system, and adding them all gives the equation of motion for the system of particles.

The internal forces between any two particles exist in collinear pairs that are equal in magnitude but opposite in direction. So, the summation of internal forces becomes zero.

Now, consider the center of mass G, which is expressed in terms of the position vectors of different particles from the system. Differentiating it twice with respect to time gives the equation of motion with respect to the center of mass of the system.

So, the net external forces acting on the system of particles are equivalent to the product of the system's total mass and the acceleration of its center of mass.