## 20110723

### Presentation: Newton's third law

Recall that there are two types of motion (constant and changing), and two types of net forces (zero and non-zero), addressed by two laws: Newton's first law and second law. As we'll see, Newton's third law has nothing to do with motion or net force, but a fundamental property of force itself, regardless of the resulting motion or net force. In a sense, something to do with symmetry.

Let's first address a fundamental property of any force before looking at how to recognize when and how to implement Newton's third law.

All forces are the interactions between two objects. In this case, the dog and owner are using the rope tension force in order to interact with each other. Because two objects are involved, then there will be two different, but valid viewpoints of this interaction--from the dog's point of view, and the owner's point of view.

If there aren't two objects involved, then there is no interaction. If there is nothing on the other side of that cable, then the plane isn't interacting--exerting forces on--anything else. An interaction always involves two objects, each exerting a force on each other.

Did you learn trigonometry using SOH-CAH-TOA? For Newton's third law, we'll use a similar-looking mnemonic from Benjamin Crowell (Fullteron College, CA).

This three-part checklist is used identify if two forces are related via Newton's third law:
• POF: Pair of Opposite Forces?
Are the two forces aren't pointing in opposite directions?
• OST: Of Same Type?
Are the two forces the same type of interaction (weight, normal, tension, static friction, kinetic friction, etc.)?
• ITO: Involving Two Objects?
Are there explicitly two objects interacting with each other?
If these two forces in question satisfy all three parts of the POF-OST-ITO checklist, then Newton's third law applies. However, if even one part of the POF-OST-ITO checklist fails, then Newton's third law does not apply to the two forces in question.

Only after knowing when Newton's third law applies, let's discuss how Newton's third law applies.

On the surface, this "action-reaction" equation seems like a trivial statement, but it embodies each part of the POF-OST-ITO checklist:
• POF: Pair of Opposite Forces?
Due to the negative sign, two forces are in opposite directions.
• OST: Of Same Type?
Both forces must be w = w, N = N, T = T, fs = fs, fk = fk, etc. on either side of the equation.
• ITO: Involving Two Objects?
The two interacting objects exerting a force on each other are in the subscripts on either side of the equation.

Remember, because an interaction involves two objects, there will be two slightly different, but equally valid descriptions of the same force. This is the fundamental statement of symmetry in Newton's third law!

Let's try to distinguish between forces that are equal in magnitude, but opposite in direction due to Newton's first law, versus those forces that are equal in magnitude, but opposite in direction due to Newton's third law. In this example, this stack of books is stationary on a person's head.
According to Newton's first law, the normal force of the person's head on the stack of books is equal in magnitude and opposite in direction to the:
(A) normal force of the stack of books on the person's head.
(B) weight force of Earth on the stack of books.
(C) (Both of the above choices.)
(D) (Neither of the above choices.)
(E) (Unsure/lost/guessing/help!)

According to Newton's third law, the normal force of the person's head on the stack of books is equal in magnitude and opposite in direction to the:
(A) normal force of the stack of books on the person's head.
(B) weight force of Earth on the stack of books.
(C) (Both of the above choices.)
(D) (Neither of the above choices.)
(E) (Unsure/lost/guessing/help!)