Let's summarize with some important facts
that we've discussed about energy.
What we said is first, we have a kinetic energy
which is equal to 1/2 the mass
times the velocity of an object squared.
We introduce two different types of potential energy
in this lecture.
We have the gravitational potential energy
from an objects being in the air which it can unleash
by letting go of the object and turning it into kinetic energy.
That gravitational potential energy
was m times g times the height the object was
from the zero of your coordinate system.
We introduce the spring potential energy,
1/2 k times the displacement of your spring from equilibrium square.
And then we said that the total energy
which is conserved is equal to the kinetic plus the potential energy.
Now at this point,
here we've introduced all of these variables with their different unit.
So it's a good idea to look at this,
to think about them and make sure
that you don't get confuse between each one.
We have our energy which is potential or kinetic or total.
And each one of these energies has units of joules
because all energy always has unit of joules.
Now, we've now added this to sort of our,
our set of variables that we have, including masses,
velocities, heights and the spring constant
which came to our potential energy equation for the spring.
One final note and this is something that many students get confused by
and it's a common question.
If I say that the potential energy of an object is mass
times gravity times the height of that object from the ground.
Could I just dig a hole below the object
and then the new ground level would be a new zero below the object,
sort of increasing the potential energy of the object,
is that something we could do
just by changing our ground level and digging a hole?
The answer is no because the potential energy
has nothing to do with the coordinate system that you've defined,
so really what you're doing if you're digging a hole
is not changing what the coordinate system is.
If you move your zero point from a one height to another
all you've done is change your coordinate system.
So that's not really adding potential energy.
The number that you have for potential energy
will change if you change the zero point of your coordinate system.
But potential energy does not care about its absolute value,
the only time potential energy comes into a problem
as the ones we've seen is with changes in height,
changes in potential energy.
So for example, suppose I define two different coordinate systems.
On the left in the green,
I have a coordinate system where I call the ground position equals 100
and you're always free to do this.
And then if I had a height of one,
my new height would be 101.
In a different coordinate system,
if I call the ground zero,
a height of one would bring me to x equals 1.
In each of these cases,
I have completely different coordinate systems
and very different expressions for the potential energy
of an object that was lifted to a particular height
but the difference between my two locations,
my ground in a particular height does not change.
And therefore the potential energy,
the way that the potential energy changes
and contributes to the kinetic energy, that won't change.
And again, so the potential energy
it only cares about changes in potential energy
because only if you change the potential energy
converts some to kinetic energy for example,
we get something physical.
And so keep this in mind, potential energy is relative,
it's not absolute to a particular coordinate system
and so feel free to always define any coordinate system you like
because the fact that we've introduce
potential energy expression of mgh
does not mean that you have to pick the ground level to be zero
for whatever problem you're doing.
So you can pick your coordinate system as long as you stick to it
throughout the entirety of a problem.
So it's a long overview,
what we have now is the Equations of motion,
Newton's laws and Torque which is how we talked about force
and we've just covered what energy is,
both kinetic and a few types of potential
as well as the total energy which is conserved
when we haven't talked about energy lose to friction or anything like that.
We are going to discuss that now with Work,
where Work is sort of the way that the energy changes
when forces are acting on our object
and so we'll discuss Work next followed by Momentum
and that will finish our mechanic section
at the beginning of this course.
Thanks for listening.