Introduction to vectors and scalars Distance, displacement, speed and velocity. Difference between vectors and scalars
Introduction to vectors and scalars
- What I want to do in this video is talk about the difference
- between vectors and scalars.
- And they might sound like very complicated ideas
- but we'll see over the course of the videos
- that they're actually very simple ideas.
- So first I'll give you a little bit of a definition
- and then I'll give you a bunch of examples
- and I think the examples will make things super clear.
- Hopefully they'll make things super clear.
- A vector is something that has a magnitude -
- or you can kind of view that as a size -
- and it has a direction.
- So, and it has a direction. And it has a direction.
- A scalar only has a magnitude or size.
- And if that if that doesn't make sense to you,
- it will hopefully make sense to you in a second when I show you an example.
- For example: let's say that I have a ...
- Let's say, that's the ground right there -
- Let me do the ground in a more appropriate ground-like color.
- So, this is green right over here...
- And let's say that I pick and I have a brick here
- I have a brick on the ground.
- And I pick up that brick,
- and I move it over to this place right over here.
- So I move the brick right over there
- and then I take a ruler out and I say,
- "Wow, I have moved the brick five meters."
- So my question to you: is my measurement of five meters,
- is it a vector or a scalar?
- Well if I just tell you five meters,
- you just know the size of the movement.
- You just know the magnitude of the movement.
- So if someone were to just say "five meters",
- this is a scalar quantity.
- When we're referring to moving something
- or how much something has, I guess, changed its position
- and I don't give you the direction, we're talking about distance.
- and I'm assuming you've heard the word distance:
- how far of a distance has something traveled?
- So this is distance.
- So we can say that this block or this brick,
- because of my picking it up and moving it,
- has moved a distance of five meters.
- But if I didn't show you this picture here
- and someone just told you that it moved a distance of five meters,
- you wouldn't know if it moved to the right five meters,
- you wouldn't know if it moved to the left five meters,
- or if it moved up or down or in or out -
- You don't know what direction it moved five meters.
- You just know it moved five meters.
- If you want to specify that,
- we could say this brick right over here
- that it moved five meters to the left.
- Now we have specified a magnitude - right over there,
- so that is a magnitude -
- and we have specified a direction: "to the left".
- So you now explicitly know that it went five meters to the-
- oh, sorry, it should be five meters to the right. Let me change that.
- So five meters to the right is what it got moved to.
- It started here, it went five meters to the right.
- So once again:
- the magnitude is five meters,
- and the direction is to the right.
- So what I've just described to you right here is a vector quantity.
- So all of this business over here - this is a vector.
- And when you talk about the movement, the change in position,
- and you give its direction - the vector version of distance,
- I guess you could call it - is displacement.
- So, this right here is displacement.
- So the correct thing to say:
- you would say that this brick has been displaced 5 meters to the right,
- or it has been moved a distance of 5 meters.
- Distance is a scalar quantity.
- I didn't tell you what direction we moved it in.
- Displacement is a vector quantity.
- We told you that it is to the right.
- Now let's explore this.
- If we talk about the actual speed or velocity of something,
- so let's say that this 5 meters was traveled,
- and let's say that the change in time.
- (let me, just... because you're probably not familiar with what that means)
- Let's say that the change in time right here - change in time
- when I moved this block five meters.
- Let's say that the change in time was 2 seconds.
- So maybe right when the block started moving,
- maybe on my stopwatch it said zero,
- and then on my stopwatch when it stopped moving, it said -
- or when it got to this position, I should say -
- When it left from this position my stopwatch said zero.
- When it got to this position my stopwatch said 2 seconds.
- So the change in time or the duration we're dealing with is 2 seconds.
- For all we know, time only goes in the positive direction.
- So you can pick that as a vector or a scalar quantity I guess
- because there's only one direction for time as far as we know
- or at least in what we're going to deal with for the simple physics.
- So what's a measure of how fast this thing moved?
- How fast did this thing move?
- So we could say it moved five meters in two seconds.
- Let me write this down.
- So it moved 5 meters per 2 seconds.
- Or, we could write this as 5/2 of a meter per second
- or five divided by two is 2.5 meters per second.
- This right here is just the 5 divided by 2.
- (let me make that clear)
- That right there is just the 5 divided by the 2.
- So my question to you: this 2.5 meters per second,
- tells you how far it travelled in a certain amount of time -
- is this a vector or a scalar quantity?
- It is telling you how fast it went,
- but is it giving you just a size of how fast it went?
- Or is it also giving you direction?
- Well I don't see any direction here.
- So this is a scalar quantity.
- And the scalar quantity for how fast something is going is speed.
- So we could say that the speed of the brick is 2.5 meters per second.
- Now if we do the same calculation, if we say it went 5 meters -
- I'll just write "m" for meters -
- 5 meters to the right in 2 seconds.
- Then, what do we get?
- We get 2.5 meters per second -
- I'll just abbreviate them -
- as meters per second to the right.
- So is this a vector or a scalar quantity?
- I'm telling you the magnitude of the speed that's right here.
- This is the magnitude: 2.5 meters per second -
- and I'm also telling you the direction: to the right.
- So this is a vector quantity.
- And when you specify both the speed and the direction -
- so the 2.5 meters is a scalar and the direction -
- you are talking about velocity.
- So, easy way to think about it:
- If you're thinking about change in position
- and you specify the direction of the change in position,
- you're talking about displacement.
- If you're not talking about the direction,
- you want the scalar version, you're talking about distance.
- If you're talking about how fast something is going
- and you give the direction that it's going in,
- you're talking about velocity.
- If you don't give the direction, you are talking about speed.
- Hopefully that helps you a little bit -
- and in the next video we're going to start working with these a little bit
- and start solving some basic questions
- about how fast something is going or how far it might travel
- or how long it might take it to get someplace.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
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This is great, I finally understand quadratic functions!
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At 2:33, Sal said "single bonds" but meant "covalent bonds."
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