# Interactions

#### Prerequisites

In our everyday life, a change in an object's velocity is usually associated with some other object.  To get a block on the table moving, someone has to hit it with a hammer. To get a box sitting on the floor moving, somebody needs to push it.  To stop a speeding baseball, someone has to catch it, or it has to hit a wall, or roll on the grass, or.... Note that the change doesn't have to be caused by an animate object exerting will or intent!  A ball hitting a wall changes the direction of its velocity because it hits the wall.

[The one example we have where there seem to be changes of velocity that are not associated with any obvious object is when things fall, or roll down a slope, or tip over. We give the cause of those phenomena a name — gravity — but that's really just a meaningless word that summarizes the idea, "given a chance, anything falls."  We'll see that this idea fits in perfectly with the structure that we are building and that the object causing gravity is the earth.  But let's save this discussion for later.]

This suggests that when we see an object's velocity changing, we should look for another object that is causing that change.  The fundamental conceptual idea that we will make a part of the language of Newton's theory of motion is the following:

Every change in velocity an object experiences is caused by the object interacting with some other object.

So we now have three ideas that tell us how to build models of motion:

1. object egotism — Our models will talk about objects.
2. inertia — The critical concept to pay attention to in motion is the change of velocity.
3. interactions   In order to describe an object's motion and change of motion, we need to look for interactions with other objects.

Technical term alert! We'll call what one object does to another in order to change its velocity a force.  This is an unfortunate choice, since it is a word that is common in our everyday speech and it has lots of different meanings. Your mother forced you to eat your mashed potatoes before you could have dessert. Your brother joined the Air Force.  He was a force to be reckoned with. The law came into force on July 1st.  None of these meanings are what we are talking about here.

We will use the term force in its technical sense in physics to mean what one object does to another when they interact and try to change each other's velocities.  I say "try" since there may be other objects interacting with the object we are looking at and multiple forces may wind up cancelling.

Since forces are always an interaction, and since they have both direction and magnitude, we will label them by carefully specifying both the object we are considering (object A) and the object that is causing the force on object A (object B).  Since it has a direction, it should be a vector. We will use the notation

$$\overrightarrow{F}_{B\rightarrow A}$$

(read: F of B acting on A) to describe a force that object B exerts on object A and that could potentially change the motion of object A.

Joe Redish 9/13/11

Article 341