The motion of a system is governed by the Momentum Principle. This principle describes how a system changes its motion when it experiences a net force. We observe that when objects move in a straight line at constant speed experience no net force. This observation is critical to our understanding of motion (This observation is often called "Newton's First Law of Motion").

In these notes, you will be introduced to the idea of a system, momentum, net force, and how a system's momentum and the net force it experiences are related. In another set of notes, you find a few useful formula for when the net force acting on a system is a constant vector (fixed magnitude and direction).

You can consider a single object or a collection of objects to be a “system.” Anything that you choose to not be in your system exists in the “surroundings.” In mechanics, you will choose systems by considering what objects you want to predict or explain the motion of. That is, the choice of system is arbitrary to the extent that you only care about predicting or explaining the motion of objects in your system.

Through interactions with the surroundings, systems can change their momentum, energy, angular momentum, and entropy. For the time being, you will work with systems that consist of a single-particle, and you will consider only how single particles change their momentum.

The Momentum Principle is one of three fundamental principles of mechanics. No matter what system you choose the Momentum Principle, which is also known as http://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton.27s_2nd_Law|"Newton's Second Law of Motion", will correctly predict the motion of that system. It is the quantitative form of Newton's First Law; it tells you precisely how the momentum (and thus the velocity) of an system will evolve when it experiences a net force. Mathematically, the Momentum Principle states:

$$\Delta \vec{p} = \vec{F}_{net} \Delta t$$

which you can think of as the change in a system's momentum = the net force acting on the system multiplied by the time interval over which the net force acts. In this formulation of the momentum principle, it must be that the time interval over which the net force acts is sufficiently small that the net force is can be approximated as constant.

If you divide both sides by this time interval ($\Delta t$) and take the limit as the time interval goes to zero, ($\Delta t \rightarrow 0$), you have an exact definition of the net force at an instant,

$$F_{net} = \dfrac{d\vec{p}}{dt}$$