Center of Mass

Definition:   rCM = ∑ mi ri/∑ mi = ∑ mi ri/ M → ∫ r dm/ M

We rewrite this definition as:   M rCM = ∑ mi ri

Newton's Law for a composite object

The total momentum is:   ptot = ∑ mi vi = M vCM

Newton's 2nd law:   d ptot/dt = M aCM = Fext

Conclusion:   A composite object is equivalent to a single point of mass M that is located at the center of mass.