## Question:

I am in AP Physics as a junior in highschool, and i seem to be
having an extremely hard time with some of the concepts they are
teaching us. one in particular is linear momentum. I've only
been taught it in the application of one object hitting another,
but what about a problem such as a rocket and the force of the
propelling gases on it? please help!!!!
## Answer:

To help you think about the rocket situation you mentioned in
your email we need to talk a bit about cause and effect. The
conservation of linear momentum is one of those things very near
to the heart of what makes the universe work. For our purposes it
is a cause, not an effect. That means we do not say linear
momentum is conserved because... Rather we say this or that
happens because linear momentum is conserved. If we take the
conservation of linear momentum to be a "law of nature"
then we can conclude all sorts of interesting things from that.
Suppose for example that we have a rocket loaded with fuel,
initially at rest in our frame of reference. When we start the
engines, some of the fuel is ejected at high speed from the
exhaust of the rocket. The exhausted fuel now has some linear
momentum in our reference frame. The total linear momentum before
the firing of the engines was zero. Since it is conserved, the
total must remain zero. This means that the momentum of the fuel
in the backward direction must be exactly balanced by the
momentum of the rocket in the forward direction. Therefore the
rocket moves forward.

Linear momentum is the product of mass times velocity. If we
know the mass and speed of the exhausting fuel at any instant,
knowing that the product of those numbers must equal the mass of
the rocket plus its remaining fuel, times the rocket's speed
you could calculate the speed of the rocket without knowing
anything about the forces involved, just from the conservation of
linear momentum. Of course we could calculate the force
experienced by the rocket once we know how its speed changes over
time by applying Newton's second law that force equals mass
times acceleration.

These ideas are easy to express in words as I have done here,
but the mathematics in the case of real rockets gets very messy.
You can probably find some examples in your text book, set up to
be easily solved.

This information is brought to you by M. Casco Associates, a
company dedicated to helping humankind reach the stars through
understanding how the universe works. My name is James D. Jones.
If I can be of more help, please let me know.

JDJ