We now have the answer to the question “When is momentum conserved?” Equation 7-13 says that the total momentum does not change over the time interval \(\Delta{t}\) if the net external force on the system is zero. Then the left-hand side of Equation 7-13 is zero, and so there is zero difference between the final total momentum \(\vec{P}_f = \vec{p}_{Af} + \vec{p}_{Bf}\) and the initial total momentum \(\vec{P}_i = \vec{p}_{Ai} + \vec{p}_{Bi}\).