Now that we have an understanding of how objects move on their own,
how they act under the influence of forces,
the energy inside objects, and how that energy can change
because work is done on those objects,
we're ready for our final topic in the mechanics section of our course
which is momentum.
We're gonna start this with just a discussion of momentum
and what momentum is.
And then we move to
use of momentum in problems, specifically collisions.
So with momentum, we have an object here.
It has some mass.
It has some velocity.
We define the momentum to be its mass times its velocity,
and it's just that simple.
There are few things that are very important about this momentum.
One is that it has units of, as you can see, mass times velocity.
So those units are kilograms meters per second.
The other thing is that it is a vector.
So because momentum is directly related to velocity
rather than velocity squared,
it is a vector unlike energy.
Because energy takes a velocity and squares it,
it gets rid of the vector component of that velocity.
You just get a single number after you've squared your velocity.
With momentum, that's not the case.
We have an actual vector for momentum.
And that vector will be inherited from the velocity of your object.
We can compare momentum to force and see how these two are different.
For force, we also have a vector,
but instead of force p mass times velocity,
the force was the mass times the accelaration of our object.
So there's a clear relationship between momentum and force,
and that is that you can find the force from the momemtum
over some duration of time delta T
by finding the change in the momentum.
In other words, force is measuring
how quickly your momentum is changing.
So if you have some momentum mass times velocity in one direction,
and that momemtum begins to change,
it's because you have a force being applied to you.
So if over other the duration of time delta T,
you know what the change in momentum is of your object,
you can always find the average force that was acting
during the change of momentum
by dividing the change of momentum
by the change in time during the collision.
Finally, the momentum is also a conserved quantity.
So if we are able to right the momentum for a situation
before something happens,
and then right the momentum again after something happens,
we can always equate the initial and final momentum
and find any variables that are being asked for in a problem,
or in some other setting,
just from the equations we get by equating the momentum.
This conservation of momentum is actually rooted in Newton's third law.
So this is a good thing to know in a conceptual sense
for any conceptual questions.
This is because if we consider a system,
we say its momentum is conserved,
and that's because if any two objects in that system
push against each other,
we know the forces on those two objects are equal and opposite.
So if those forces are equal in magnitude, but opposite in direction,
and the force, which is the change of momentum in one direction,
and the change of momentum in the other direction by Newton's third law
means that the total change of momentum
for these objects colliding within our system is zero.
So our system, considering all the objects in it as a whole
cannot have a change in momentum as a total system
because no one part of that system can push the entire system itself.
You cannot lift yourself up by your own boot straps per se.
Finally, we also have a name for this change in momentum,
and that is called the impulse which we represent with the letter J.
So J is the impulse which just represents the change in momentum
and doesn't have anything to do with the time
during which your momentum was changing
So keep the impulse separate from the force.
The force is changing momentum over changing time
while the impulse is simply a name for the change in momentum.