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Motion of the Center of Mass

# Motion of the Center of Mass - Motion of the Center of Mass...

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Motion of the Center of Mass The definition of the center of mass of a system of particles can be rewritten as where M is the total mass of the system. Differentiating this equation with respect to time shows where v cm is the velocity of the center of mass and v i is the velocity of mass m i . The acceleration of the center of mass can be obtained by once again differentiating this expression with respect to time where a cm is the acceleration of the center of mass and a i is the acceleration of mass m i . Using Newton's second law we can identify m i a i with the force acting on mass m i . This shows that This equation shows that the motion of the center of mass is only determined by the external forces . Forces exerted by one part of the system on other parts of the system are called internal forces. According to Newton's third law, the sum of all internal forces cancel out (for each interaction there are two forces acting on two parts: they are equal in magnitude but pointing in an opposite direction and cancel if we take the vector sum of all internal forces). See Figure 9.5.

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Motion of the Center of Mass - Motion of the Center of Mass...

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