Scalars and Vectors


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 day.

100 thoughts on “Scalars and Vectors

  1. Thankyou so muchhhh !!!
    I saw a lot of videos on youtube about Scalar and Vector quantities but couldn't completely understand..
    Your video was the best 🙂
    I already subscribed to your channel.

  2. Wow this is way better then what my teacher shows my class. Try learning this stuff/chemistry by a youtuber named crash course.

  3. You did a wonderful job with this video! It gave me great understanding of the difference between a Scalar and a Vector. I got almost all of the Scalers correct in the review. Thank you.  

  4. Mr. Anderson. I'm currently brushing up on some mechanical engineering, even joined the club at my school. Is there any difference between drag and friction?

  5. can someone please explain why is pressure a scalar.
    just like dimension analysis Pr = force / Area where pr is dependent on vector data type – force

  6. Around 8:18 of the video he's talking about how both scales are supporting the kg weight at a angle both with 1kg of force. I thought kilograms were a unit of mass and we use newton's as a unit of force but after watching this it confuses me alot can someone please explain and clarify why this is.

  7. Time in my opinion has direction and can be classified as vector ,
    -10 secs ; 0 sec ("event") ; +10secs

    What do you say Internet ? 🙂

  8. I sat in my introductory Chem/Phys class in college and asked my professor what difference did it make whether I identified something as either scalar or vector…..the light bulb finally turned on.

  9. I love you like a brother man, thank you sooooo much! Keep explaining this specificity and accurately. Thank you, thank you, thank you!

  10. I want all of you to know that //Vectors can be 0 and negative but Scalars can never be zero or negative!!!!

  11. Hey viewers, Mr. Anderson circled pressure to say it is scalar but pressure is just a force/area and force is vector then, how pressure could be scalar?

  12. a train moving with acceleration of 5 m/s^2 have 1 engine of mass 100 kg and 4 coaches of mass 50 kg each find the force exerted by 3rd coach on 4th

  13. Thanks man. …You are so. …much better than those "public" school government bureaucrat teachers. …. I wish we dismantle this Leftist incompetent monstrosity we called Public School Education. ..and give taxpayers money to the Individual citizens/parents…. instead of incompetent government bureaucrats….
    Again man…. THANK YOU. ..

  14. 265K views at this writing and mass/weight (scalar/vector) are consistently confused in the video. Major problem. Mass is a scalar to be measured on a balance in metric units of kg or g. Weight is the vector to be measured on a scale in units of N. The only reason that stupid scale is labeled in g is because mass and weight are proportional since W = mg. This confusion of mass/weight will lead to problems with all of Newton's Laws of Motion and Gravity and Satellites and Energy – basically all of Mechanics.

    These will help with that distinction:
    Mass vs Weight, Balance vs Scale:
    https://www.youtube.com/watch?v=U8z2VwtBHSA&t=1s
    I Was Wrong – Mass vs Weight:
    https://www.youtube.com/watch?v=13GzkUnZiuQ&t=268s

  15. I got all of them except pressure, I guess it's 'complicated' because on the micro level it's definitely vector value.

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