Choosing a system is one of the most important choices you make (either explicitly or implicitly) when solving a physics a problem. What you define as “inside” and “outside” will influence the physical quantities that you are solving for, how you set up your equations, and how you model the situation. While you are free to define your system as you wish, there are often certain choices of system(s) that will make your calculations easier or more efficiently use the information you are given. In this course, we will ask you to be explicit about your choice of system and how that influenced your solution.

The system is the object or the collection of objects that you would like to describe. A system has various physical quantities associated with it: mass, energy, momentum, angular momentum, and entropy. These quantities can change for a system by interacting with the surroundings. Typically in Mechanics, you pick the object that is in motion as your system because you are primarily interested in describing that motion or how that motion is changing.

When we refer to a quantity as “internal,” we are referring to something that is inside the system we chose.

The surroundings contain everything that you are not interested in describing. Objects that are in the surroundings can certainly influence or interact with the system, but generally, you are not interested in describing the impact of the system on the surroundings. For example, if you drop a ball, you are typically very interested in describing how the ball's motion changes: it speeds up, gets closer to floor, it experiences a gravitational force from the Earth, etc. However, you do not talk about how the Earth's motion changes because you dropped the ball (largely because these changes are so small that they are negligible). In this case, we would choose the ball as the system and the Earth as the surroundings.

When we refer to a quantity as “external,” we are referring to something that is outside the system we chose.

Choosing your system has particularly largely implications for the 3 Fundamental Principles of Mechanics:

• If you choose your system so that there are no external forces on the system, then momentum is conserved for that system. (This is particularly relevant for collisions.)
• If you choose your system so that there is no external work or heat transferred, then energy is conserved for that system.
• If you choose your system so that there is no external torque on the system, then angular momentum is conserved for that system.