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