# Scalars and Vectors

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

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#### 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.

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This post was previously published on YouTube.

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Photo credit: Screenshot from video.