# Introduction and Definition

The 1970s saw the popularity of a certain physics toy, a toy in which five steel balls hang in a line from threads (Figure 8-1, called Newton's Cradle). If you swing the left ball to the left and let go, it swings down and hits the other four balls. Then the right ball swings up and rises to almost the height of the initial release.

**Figure 8-1**

Now if you think about it, this is totally amazing. There are five balls undergoing collisions, and each collision involves a rapidly changing force between two balls (Figure 8-2). You might think we would need a supercomputer to deal with the problem. The very simple outcome (one ball swinging to the right) hints that there is some very simple underlying physics as well.

The idea that emerged from experiments like this one was that moving objects contained a certain amount of "motion quality" (or "movage"), which is a constant in any situation. In Figure 8-2 the movage begins in the left ball, transfers through the three balls, and ends up in the right ball.

The idea that emerged from experiments like this one was that moving objects contained a certain amount of "motion quality" (or "movage"), which is a constant in any situation. In Figure 8-2 the movage begins in the left ball, transfers through the three balls, and ends up in the right ball.

**Figure 8-2**

Can we write a formula for this "movage"? Well, it is clear that a moving Mack truck has more movage than a Tonka truck, so mass must be involved. And a sprinter has more of it than a walker, so velocity must be involved. But is it
or

movage =

*mv*movage =

*mv*^{2}or what? It turns out there are two kinds of movage, and we will study them in this chapter and in Chapter 9.

One kind of movage is

One kind of movage is

*momentum*.The momentum of a single object of mass m and velocity v is the vector

The total momentum of several objects taken as a system is the vector sum

â€¦â€¦(1)

The total momentum of several objects taken as a system is the vector sum

â€¦(2)

where are the momenta of the object