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.