All language subtitles for W1_U1_P1-en

JASON HAFNER: We begin with kinematics.

I like to give simple, straightforward definitions of concepts,

so kinematics I'll define as describing motion with equations and graphs.

Two of your favorite things-- equations and graphs.

Kinematics does not explain why a motion occurs,

it simply describes the motion mathematically.

OK?

So let's start with an example.

Let's just do a simple example.

A motionless ball.

There you go.

We're going to do it as a demo with this.

This is a 76.2 millimeter diameter steel sphere.

And we're going to use it a lot in the first week of the course-- a lot

of the demonstrations-- so I've given it a name.

Its name is Hal.

OK?

Hal is going to sit on this track right here,

and it's going to remain motionless.

Ta-da!

There you go.

The demos get better, I promise.

But this is our current demo, a motionless ball.

Now when you approach anything in physics,

you should draw a diagram for yourself.

OK?

If you have scratch paper, envelope, whatever you've got,

you should draw it.

So let's draw this one.

There is the track.

These marks kind of mean it's a solid surface.

And here is the ball sitting on the track.

OK.

So there we have the demo.

We have our drawing.

Now, if we're going to describe this mathematically,

we need to give it an axis.

It needs to be described its position on an axis.

So here I'll draw an axis in my drawing like this.

This is the plus x direction on this one dimensional axis and this is 0.

So now we could keep up with where the ball is.

And we'll do that in the demo as well.

So let's see.

Here is a two meter stick, and I'll put it here.

And you can see that the ball is sitting there.

And now you can read where the ball is.

OK, now we're all set up to do kinematics.

Here we go.

Equations and graphs.

Let's do graphs, first.

We're going to make a graph of this motion.

So what we're going to do is say, let's figure out

where this ball is at all times.

So in kinematics, you usually put time on the horizontal axis.

That's like the independent variable.

As we vary time, what are we trying to figure out?

We're trying to figure out position.

So this is called a position-time graph.

Right?

It's a plot of what is a position at every point in time.

So to get started we need to know, where is the ball?

So, Hal, what is your location on the x-axis?

Hal?

Respond, Hal.

Where are you, Hal?

Do you read me, Hal?

What's your position on the x-axis?

Oh, I have to read it.

I forgot.

Ah, 81.

So at time 0, it's at 81 centimeters.

This is the origin.

Mathematically you think of the origin as where the axes cross,

and in physics, for now, we will also make it the origin.

So this is 0 in time and 0 in position.

And then we've moved up to 81 centimeters

for the position of the ball.

So now, if we wait to some later time, say when I read it was 81.

Now, 10 seconds later, what is it?

Well, it's still 81.

So we could put another point there.

And we could wait a little bit longer.

And we could say, oh, maybe I should check, because it moved.

If it's motionless it better not have moved.

Ah, still 81.

So as long as we check it, it's going to be 81 at every time.

And if we were to fill in a lot of those points, it would look like this.

Just a line.

So there is your first position-time graph.

It's for something that's not moving and it's simply a flat line.

OK?

So that's the graph.

Now let's do the equation.

Let's see, for the equation we're going to write the position x.

And really here this is a function.

We really mean x is a function of time.

But when you write x or y or z to the left of the equal sign by itself,

you usually are implying that it's a function.

You may have seen before-- you'd write it

like this-- x is a function of time with parentheses.

So you can do that, it's just sometimes it gets mixed up.

It looks like you're multiplying.

So usually we leave that off, and it's just implied.

This x is a function of time.

So let's see.

A function of time.

And in this case, what is it?

It's 81 centimeters.

But in this case it's constant.

Nothing is changing in time.

So actually-- actually constant this time, in this case.

So as we get into more complicated kinematics,

this side would have had some numbers and symbols

and would have had t for time in it because it would change with time.

In this case, since it's constant, it's just x equal 81 centimeters.

So that is your first example of describing motion, a fairly simple

motion, with equations and graphs.