Final answer:
The total linear momentum of a crowd in Times Square on New Year's Eve can be approximated as zero due to the random and varied movements of the people in the crowd, balancing each other out.
Step-by-step explanation:
When considering the total linear momentum of a system like the crowd in Times Square on New Year's Eve, we must consider that the system is made up of individuals moving in various directions with different velocities. According to the physical definition of momentum, which is the product of mass and velocity (P = mv), every person has their own momentum. If we assume an idealized situation where movement is random and there is as much motion in one direction as in any other, the total momentum of the system can approximatively be zero at any given instant due to the cancellation of people's momentums in opposite directions. Moreover, because people are not likely to all be moving in the same direction with the same speed at the same time, the net velocity (and thus momentum) of the system may be negligible if averaged over time.
According to Newton's second law in terms of momentum, in the absence of an external force, there would be no change in the total momentum of the system. Therefore, assuming Times Square is a closed system with no significant external forces acting on it, and given the randomness of movement, it can be approximated that the total linear momentum of the crowd is approximately zero.1