Definition:   r_CM = ∑ m_i r_i/∑ m_i = ∑ m_i r_i/ M → ∫ r dm/ M

We rewrite this definition as:   M r_CM = ∑ m_i r_i

Newton's Law for a composite object

The total momentum is:   p_tot = ∑ m_i v_i = M v_CM

Newton's 2nd law:   d p_tot/dt = M a_CM = F_ext

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