Equation 7-34 looks almost exactly like Newton’s second law for a single object of mass \(m\):
\(\sum{\vec{F}_\mathrm{ext}} = m\vec{a}\)
So what Equation 7-34 tells us is that \(\textit{the center of mass of a system of objects moves exactly as if the entire mass \(M_\mathrm{tot}\) of the system were concentrated at the center of mass, and all of the external forces on the system acted on that concentrated mass}\).