# Why I hate “equal and opposite”

How many times in physics do students say “these forces are equal and opposite?” And often, they follow that up with, “so the object can’t move.” Of course, these statements are twisting together Newton’s first and third laws in ways that are tricky and difficult for novice students to see. In their first exposure to physics, students see two different cases of “equal and opposite” forces:

case 1. In Newton’s 3rd law situations: When A pushes on B, B pushes on A. These forces are equal and opposite. But you can’t add these forces, because they act on different objects.

case 2. In situations where an object has a constant velocity, and only two forces are acting on it. Imagine a book at rest on a table. Here, there are two forces (gravitational force of earth, normal force of table), and the total force is zero. The only way for these two forces to add to zero is for the forces to be “equal and opposite.”

Novice students really have no way of distinguishing situations like case 1 from situations involving case 2. This is why I prefer not to use the words “equal and opposite” at all. I think students too quickly see a situation where something is equal, say “equal and opposite,” and rush through the thoughtful analysis that is critical to understanding. Instead, with N3, I say something like

These forces are:

- same size
- opposite direction
- same type

This, and I test to see if kids understand this difference extensively, so that kids can get feedback on how well they understand this subtle but important idea.

I tend to stress the interaction between two objects before I talk about the effects of forces on individual objects. When I use the word forces in terms of N3, I say that forces come in pairs and draw the analogy to a pair of shoes: equal, opposite, and they fit on different feet.

Definitely. We do this, and draw interaction diagrams (system schemas), and make sure that you don’t describe a force without fully describing the object that exerts the force and experiences the force (no “force of gravity). Still, I find that kids can’t really explain why two forces must be equal and opposite, and they often try to add N3 pairs. pushing them out of this super comfortable “equal and opposite” language, which I think they say without reflecting, tends to help a bit.