 # 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.

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

This post was previously published on YouTube.

Photo credit: Screenshot from video.