## What to Remember from Lesson

### Momentum Conservation

The big idea of this lesson is one that will be with us for the whole of QS&BB: in any process the momentum of the constituents at the beginning of the process must equal the momentum of the constituents after the process. In one dimension, restricting ourselves to a process involving two objects, $A$ and $B$, this means that nature always arranges that

$$p_{0}(A) +  p_{0}(B)  = p(A) + p(B).$$


Much of this lesson tried to illustrate this in a variety of different collisions. 

If the collision happens in two dimensions, then momentum is conserved along any directions one wants to choose. We typically use $x$ and $y$ directions, so nature would arrange for two conditions to be satisfied

$$\begin{align*}
p_{0,x}(A) +  p_{0,x}(B)  &= p_{x}(A) + p_{x}(B)
p_{0,y}(A) +  p_{0,y}(B)  &= p_{y}(A) + p_{y}(B) \\
\end{align*}$$

We’ll not solve any two dimensional momentum equations in QS&BB, but we will sometimes ask what might happen in some collision and because you’re now comfortable with the idea of momentum conservation, you’ll be able to answer. Without a calculation.