7.10. What to Remember from Lesson

7.10.1. 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

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

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.