Scalars and Vectors


Mr. Andersen explains the differences between scalar and vectors quantities. He also uses a demonstration to show the importance of vectors and vector addition.


Transcript Provided by YouTube:

00:04
Hi. It’s Mr. Andersen and right now I’m actually playing Angry Birds. Angry
00:13
Birds is a video game where you get to launch angry birds at these pig type characters.
00:19
I like it for two reasons. Number one it’s addictive. But number two it deals with physics.
00:24
And a lot of my favorite games do physics. So let’s go to level two. And so what I’m
00:29
going to talk about today are vectors and scalars. And vectors and scalars are ways
00:33
that we measure quantities in physics. And Angry Birds would be a really boring game
00:39
if I just used scalars. Because if I just used scalars, I would input the speed of the
00:43
bird and then I would just let it go. And it would be boring because I wouldn’t be able
00:47
to vary the direction. And so in Angry Birds I can vary the direction and I can try to
00:51
skip this off of . . . Nice. I can try to skip it off and kill a number of these pigs
01:01
at once. Now I could play this for the whole ten minutes but that would probably be a waste
01:07
of time. And so what I want to do is talk about scalars and vector quantities. Scalar
01:12
and vector quantities, I wanted to start with them at the beginning of physics. Because
01:16
sometimes we get to vectors and people get confused and don’t understand where did they
01:20
come from. And so we have quantities that we measure in science. Especially in physics.
01:26
And we give numbers and units to those. But they come in two different types. And those
01:30
are scalar and vector. To kind of talk about the difference between the two, a scalar quantity
01:36
is going to be a quantity where we just measure the magnitude. And so an example of a scalar
01:41
quantity could be speed. So when you measure the speed of something, and I say how fast
01:48
does your car go? You might say that my car goes 109 miles per hour. Or if you’re a physics
01:57
teacher you might say that my bike goes, I don’t know, like 9.6 meters per second. And
02:05
so this is going to be speed. And the reason it is a scalar quantity is that it simply
02:10
gives me a magnitude. How fast? How far? How big? How quick? All those things are scalar
02:17
quantities. What’s missing from a scalar quantity is direction. And so vector quantities are
02:22
going to tell you, not only the magnitude, but they’re also going to tell you what direction
02:28
that magnitude is in. So let me use a different color maybe. Example of a vector quantity
02:35
would be velocity. And so in science it’s really important that we make this distinction
02:43
between speed and velocity. Speed is just how fast something is going. But velocity
02:49
is also going to contain the direction. In other words I could say that my bike is going
02:54
9.08 meters per second west. Or I could say this pen is being thrown with an initial velocity
03:04
of 2.8 meters per second up or in the positive. And so once we add direction to a quantity,
03:11
now we have a vector. Now you might think to yourself that’s kind of nit picky. Why
03:15
do we care what direction we’re flowing in? And I have a demonstration that will kind
03:19
of show you the importance of that. But a good example would be acceleration. And so
03:25
what is acceleration? Acceleration is simply change in velocity over time. And so acceleration
03:32
is going to be the change in velocity over time. And so I could ask you a question like
03:35
this. Let’s say a car is driving down a road And it’s going 23 meters per second. And it
03:42
stays at 23 meters per second. Is it accelerating? And you would say no. Of course it’s not.
03:48
Let’s say it goes around a corner. And during that movement around the corner it stays at
03:54
23 meters per second. Well what would happen to the scalar quantity of speed around a corner?
03:59
It would still be 23 meters per second. And so if you’re using scalar quantities we’d
04:03
have to say that it’s not accelerating. But since velocity is a vector, if you’re going
04:09
23 meters per second and you’re going around a corner, are you accelerating? Yeah. Because
04:15
you’re not changing the magnitude of your speed but you’re clearly changing the direction.
04:18
And so a change in velocity is going to be acceleration. And so you are accelerating
04:23
when you go around a corner. And so that would be an example of why in physics I’m not trying
04:27
to be nit picky I’m just saying that you have to understand the difference between a scalar
04:31
quantity and then which is just magnitude and a vector which is magnitude and direction.
04:37
There’s a review at the end of this video and so I’ll have you go through a bunch of
04:41
these and we’ll identify a number of them. But for now I wanted to give you a little
04:45
demonstration to show you the importance of a scalar and vector quantities. And so what
04:51
I have here is a 1000 gram weight. Or 1 kilogram weight. And it’s suspend from a scale. And
04:59
I don’t know if you can read that on there. But the scale measures the number of grams.
05:05
And so if this is a 1000 grams and this measures the numbers of grams, and it’s scaled right,
05:12
it should say, and it does, about 1000 grams is the weight of this. Now a question I could
05:21
ask you is this. Let’s say I bring in another scale. And so I’m going to attach another
05:26
scale to it. And so if we had 1 mass that had a mass of 1000 grams, and now I have two
05:33
scales that are bearing the weight of that. And I lift them directly up. What should each
05:38
of the scales read? And if you’re thinking it’s 1000 grams, so each one should read 500
05:44
grams, let me try it, the right answer is yeah. Each of the scales weigh right at about
05:52
500 grams. And so that should make sense to you. In other words 500 plus 500 is 1000.
05:59
So we have the force down of the weight. Force of tension is holding these in position. And
06:05
so we should be good to go. The problem becomes when I start to change the angle. And so what
06:10
I’m going to do, and I’m sure this will go off screen, is I’m going to start to hold
06:14
these at a different angle. And so if I look right here I now find that it’s at 600. And
06:21
so this one is at 600 as well. And so I increase the angle like this, we’ll find that that
06:29
will increase as well. And so when I get it to an angle like this I have 1000 gram weight
06:35
and it’s being supported by 2 scales now that are reading 1000. And it’s going to vary as
06:42
I come back to here. And if you do any weight lifting you understand kind of how that works.
06:47
And so the question becomes how do we do math? The problem with this then is that the numbers
06:56
don’t add up. And so if I’ve got a 500 gram weight, excuse me, a 1000 gram weight being
07:02
supported by 2 scales, it made sense that it was weighing 500 each. But now we all of
07:07
a sudden have a 1000 gram weight being supported by two scales that are each reading 1000.
07:11
And so this doesn’t make sense. Or the math doesn’t make sense. And the reason why is
07:15
that you’re trying to solve the problem from a scalar perspective. And you’ll never be
07:21
able to get the right answer. Because it’s going to change. And it’s going to change
07:23
depending on the angle that we lift them at. So to understand this in a vector method,
07:30
and we’ll get way into detail, so I just want to kind of touch on it for just a second,
07:34
what we had was a weight. So we’ll say there’s a weight like this. And we’ll say that’s a
07:40
1000 gram weight. And then we have two scales. And each of those scales are pulling at 500
07:47
grams. And so if you add the vectors up. So this is one vector and this is another vector.
07:53
So each of these is 500 grams, so I make the 500 in length, then we balance out. In other
07:59
words we have the balancing of this weight with these two weights that are on top of
08:03
it. Now if we go to the vector problem, in the vector problem, again we had a 1000 gram
08:09
weight. So 1000 grams in the middle. And then we had a force in this direction of 1000 and
08:16
a force in that direction of 1000. So we have a force down of 1000. But we had a force of
08:24
1000 in this direction. And a force of 1000 in that direction. And so if you start to
08:29
look at it like a vector quantity, imagine this. That we’ve got a weight right here but
08:34
you have to have two people pulling on it. And so it’s like this tug of war where it’s
08:38
not just in one direction, but it’s actually in two. And so you can start to see how these
08:42
forces are going to balance out. But only if we look at it from the vector perspective.
08:47
Let me show you what that would actually look like. So if we put these tails up, this would
08:53
be that force down of 1000 grams. This would be the force of the weight. But we also had
09:00
a force in this direction. So I’m doing the same rule where I’m lining up my vector from
09:05
the tail to the tip. And the tail to the tip. And so that diagram that I had on the last
09:11
slide, I’m actually moving this one force and you can see that they all sum up to zero.
09:16
And so the reason I like to start talking about vectors and scalars at this problem
09:21
is that you could never solve the problem if you’re going to go at it from a scalar
09:24
perspective. And we’re going to do some really cool problems. Let’s say I’m sliding a box
09:28
across the floor. But how often do you slide a box across the floor and actually pull it
09:34
straight across like that? If you’re like me you’re pulling a sled or something, you’re
09:38
normally pulling it at angle. And once we start pulling it at an angle it becomes a
09:42
totally different force. And we can’t solve problems in a scalar way. We have to go and
09:47
solve if from a vector prospective. And so that’s the importance of vectors. Now it’s
09:51
a huge thing. So there are lots of things that we can measure in physics. And so what
09:55
I’m going to try to do, and hopefully I can get this right, is go through and circle all
09:59
the scalar quantities and then go back and circle all the vector quantities. And so if
10:04
you’re watching this video a good thing to do would be to pause it right now. And then
10:07
you go through it and circle the ones that you think are scalar and vector. And then
10:11
we’ll see if we match up at the end. Scalar quantities remember are simply going to be
10:16
magnitude. And so the question I always ask myself when I’m doing this is, okay. Does
10:20
it have a direction? And so length is simply the length of a side of something. And so
10:26
I would put that in the scalar perspective. This is kind of philosophical. Does time have
10:30
a direction? I would say no. Acceleration we already talked about that. That’s changing
10:37
in velocity. What about density? The density of something, that definitely is a scalar
10:43
quantity. If I say the density of that is 12.8 grams per cubic centimeter north, it
10:48
doesn’t make sense at all. Where are some other scalar quantities? Temperature would
10:52
be a scalar quantity. It’s just how fast the molecules are moving. But it’s not in one
10:58
certain direction. Pressure would be another one that’s scalar. It’s not directional. It’s
11:03
not in one direction. The pressure is, remember air pressure is the one that I always think
11:08
of as being in all directions. So we wouldn’t say that. Let’s see mass. The mass of something
11:14
is going to be a scalar quantity as well. And so it doesn’t change. Now weight, and
11:19
we’ll talk about that more later in the year, would actually be a vector quantity. Let’s
11:25
see if I’m missing any. No I think this would be good. So let’s change color for a second.
11:29
So displacement is how far you move from a location. And that’s in a direction. So we
11:35
call that a vector quantity. Acceleration I mentioned before. Force is going to be a
11:40
vector. And we’ll do these force diagrams which are really fun later in the year. Drag
11:45
is something slowing you down. So if you’re a car it’s what is slowing you down in the
11:49
opposite direction of your movement. And so the direction is important. Momentum is a
11:54
product of velocity and the mass of an object. And lift we get from like an airplane wing.
12:00
That would be a vector quantity because it’s in a direction. And so these are all vector
12:05
quantities. The ones that I circled in red. But there are way more that we’re going to
12:09
find out there. And scalar quantities remember, it’s simply just magnitude. Or how big it
12:14
is. And so as we go through physics, be thinking to yourself, is this a scalar quantity or
12:20
vector? And if it’s vector my problem is a little bit harder, but like Angry Birds, it’s
12:26
more fun when you go the vector route. And so I hope that’s helpful and have a great
12:32
day.


This post was previously published on YouTube.

Photo credit: Screenshot from video.