Bo: Hey guys
Billy: Hey, Bo
Bobby: Hi, Bo
♫ (lyrics) Flipping Physics ♫
Mr. P.: Ladies and gentlepeople,
the bell has rung, therefore class has begun,
therefore you should be seated in your seat,
ready, and excited to learn
about displacement and distance.
Billy: Yes
Bobby: Yep
Mr. P.: All right, let's start with displacement.
You should already know quite a bit a bunch of stuff
about displacement from your reading last night.
Bo, why don't you tell me something about displacement.
Bo: Displacement, isn't it like the distance
between where you start and end?
Bobby: Yeah, but you also need to add
that it's not just the distance,
but more specifically a straight line distance.
Mr. P.: Exactly, one thing that you should know
about displacement is that it is the straight line distance
between the initial and the final points.
Bobby: Why don't you tell me
something more about displacement.
Bobby: Displacement has direction.
Mr. P.: Yes, this is a very important piece to remember,
displacement absolutely has direction
and whenever you are writing down the displacement,
you need to identify the direction.
Billy, tell me something more about displacement.
Billy: I can't think of anything else.
Mr.P.: How about the the symbol for displacement, Billy?
Billy: The symbol for displacement is triangle x.
Bobby: The name for the triangle is delta.
Bo: It's the greek symbol uppercase delta.
Mr. P.: True, the symbol for displacement is delta x.
Who can tell me what delta stands for here?
Billy: I'm pretty sure that delta
means the change in something.
Mr. P.: Yes Billy, delta does mean change in.
Bo, what does the x mean?
Bo: X means distance.
Mr. P.: Actually, no Bo, x does not mean distance,
people often confuse x with distance,
but x actually stands for position.
X stands for position.
Again, x means position,
and if delta means change in and x means position,
then delta x or displacement actually means
the change in position of an object.
The symbol for displacement is delta x,
and that literally means the
change in a position of an object.
Let's return back to the fact
that displacement is the straight line distance
between the initial and the final points.
Bobby, this brings us to an equation.
What equation does delta mean?
Bobby: I'm not sure.
Billy: Oh I remember,
delta always means final minus initial.
Bobby: Oh yea, so delta x means x final minus x initial.
Bo: Actually, we should probably say,
displacement equals position final
minus position initial, right Mr. P.?
Mr. P.: Yes, let's get in the habit of
actually saying what the letters mean,
rather than just the letters themselves.
I find that we all understand much better,
what's going on when we actually say
what the letter means, and not just saying the letters.
It's a good habit to get into.
Great, we now have the equation for displacement,
or delta x, so the displacement is equal to
position final minus position initial.
Bo, What else do we know about displacement?
Bo: I'm pretty sure it can be negative, right?
Mr. P.: That's true, displacement can
either be positive or negative.
Could you all please give an
example for a dimension for displacement?
Bobby: How about meters?
Billy: Feet?
Bo: Kilometers
Mr. P.: Sure, any linear dimension will work.
Some other examples for possible demensions are
furlongs, rods, angstroms.
The furlong of course, being the distance
that a team of oxen can plow without needing to
take a rest, or the length of one furrow.
A rod being five and a half yards,
and an angstrom one ten billionth of a meter.
The most common dimension for this displacement
would be the base SI dimension for length,
which is, of course, class?
Class: Meters
Mr. P.: Meters, feet, furlongs, rods,
this right here, this number,
is called magnitude of the displacement,
and the magnitude of the displacement is a very important term,
the magnitude simply means the amount of,
the number of the displacement without the direction,
the value without direction.
It is very important that you remember that
displacement has both magnitude and direction.
Class, What 2 things does displacement have?
Class: Magnitude and direction.
Mr. P.: Class, are displacement
and distance the same thing?
Class: No and yes
Mr. P.: Let's try that again, class.
Are displacement and distance the same thing?
Class: No and yes
Mr. P.: Ok, does distance have direction?
Bobby: No
Bo: No
Billy: I don't think so.
Mr. P.: No, distance does not have direction.
Distance does not have direction.
Are displacement and distance the same thing?
Class: No
Billy: Displacement and distance are not the same thing.
Mr. P.: Good, displacement does not equal distance,
they are not the same thing.
We'll go through some examples in just a moment
that illustrate that fact, but before we do so,
let's talk about and illustrate some directions.
We generally have 3 different
ways of describing direction.
One of them is the cartesian coordinate plane
with positive y and negative y,
and positive x and negative x.
We can also talk about relative directions,
with up, down, left, and right.
Please notice that my default,
up is positive, down is negative,
right is positive, and left is negative.
Notice how this follows the cartesian coordinate system.
Again, up is positive, down is negative,
right is positive, left is negative.
These are the defaults for these,
we can, of course, change them,
but by default, that is true.
Sometimes we're also going to use cardinal directions,
for example, north, south, east, and west.
It's very important that we know these.
We're actually going to take a moment to review them.
We are gonna take a moment
to review the cardinal directions,
because I wanna make sure everybody is
on the same page and knows their cardinal directions.
Please understand that you are all actually
facing north at the moment, which will help you out.
Everyone please point east.
Good, please point west.
Now point north.
Unfortunately this is a common mistake
that students make, which is the
main reason we're actually going through this.
The fact that up and north are not the same thing.
Please remember up, north, not the same thing.
One more time, please point north.
Now point up, north, south, great,
we got our cardinal directions down.
Next, let's go through some examples.
Let's say that I start right here,
and I end right here.
Bo, what was my displacement?
Bo: 2 meters
Bobby: You forgot about the direction.
Bo: Oh yeah, 2 meters east.
Mr. P.: Yes, 2 meters east,
that direction is so important.
We could also describe it as 2 meters
with positive x direction, 2 meters to the right,
or, of course, 2 meters east, as you said.
Bobby, what was my distance traveled?
Bobby: 2 meters
Mr. P.: Yes, my distance traveled was 2 meters
and my displacement was 2 meters east.
That means, in this particular case,
that the magnitude displacement and the
distance traveled, were the same.
Bobby: Yeah, because you walked in a straight line.
Mr. P.: Let's do another example.
Let's say that I start here,
and I end here.
Billy, what is my displacement this time?
Billy: Let's see, I need the straight line distance
from your initial point to your final point,
but those 2 points
are in the exact same location,
so your displacement is 0 meters.
Bobby: We don't need dimensions on 0.
Bo: We would if it were temperature.
Bobby: This isn't temperature.
Bo: True. I was just saying.
Mr. P.: Yes, because I started
and ended at the same point,
the straight line distance between my initial
and final points, is equal to 0,
and 0 does not have any dimensions.
What then, would be the direction
on my displacement, Bo?
Bo: You can't have direction on 0.
Mr. P.: Correct, so my displacement was 0,
and we do not have a direction.
We do not have dimensions on that.
Let's do one more example.
Let's say that I start here.
Bo: This guy is strange.
Bobby: Yeah
(laughs) Billy, what was my displacement?
Billy: The displacement is actually exactly the same as the first example.
Your initial and final points we're the same as the first example,
it doesn't matter what you did between those 2 points, the displacement
will be the same as the first example.
2 meters east, 2 meters in the positive x direction,
or 2 meters to our right.
Mr. P.: Exactly right, none of the middle stuff matters,
only initial and final points.
Bo: Can the distance ever be less than the displacement?
Mr. P.: That's a great question, Bo, however I do need to add one word to your question,
and that word is magnitude.
Will the distance traveled ever be less than the magnitude of the displacement?
Bobby, what do you think?
Bobby: Well, the shortest distance between 2 points is a straight line,
and that by definition is the displacement.
Mr. P.: The magnitude of the displacement.
Bobby: The magnitude of the displacement.
The distance traveled can never be smaller than the magnitude of the displacement.
Billy: In fact, that means that the distance traveled will always be greater than
or equal to the magnitude of the displacement, right?
Mr. P.: Absolutely, because the shortest distance between any 2 points
is a straight line, and displacement is defined as the straight line
distance between the initial and final points.
The distance traveled will always be greater than
or equal to the magnitude of the displacement.
That is my introduction to displacement, and the differences between displacement and distance.
I hope that you enjoyed learning with me today.
I enjoyed learning with you.
I think I might go take a nap.
Lecture notes are available at flippingphysics.com.
Please enjoy lecture notes responsibly.