# Linear Momentum: Conservation of Momentum

### Introduction and Summary Conservation of Momentum

Up to this point we have studied the mechanics of single particles. We have generated kinematic equations for projectile motion, developed Newton's Laws for the motion of a single particle, and established the work and energy of a single particle. To gain a further understanding of classical mechanics, we must now turn to the mechanics of a system of mutually interacting particles. We can study both the overall motion of a given system, and the interactions that occur in the system. In this way we can further extend our principles of mechanics.

We begin by establishing the concept of a center of mass of a system of particles. This quantity will be essential to making calculations regarding the overall motion of a given system. Next we will introduce the concepts of impulse and momentum, and relate the two in the powerful and useful Impulse-Momentum Theorem. Finally, we will study the momentum of a system of particles, and bring in our knowledge of center of mass to establish our second conservation law: the conservation of linear momentum. This law is the goal of this section, and will govern calculations in essentially any physics course.

In a sense the endeavor of this topic mirrors that in Work, Energy, and Power. There, we developed the idea of work, and derived from it the conservation of energy. Here, we develop the idea of impulse and derive from it the conservation of momentum. It is no coincidence that the topics are similar: the result of each one is a universal law of conservation.

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