Well, we’ve done a lot of work

with how fast something moves, let’s see if we can work with

how fast something spins. Let’s see what we can do. Since we’re going to be working

with things spinning, let me draw a circle. Since things that spin

go in circles. And let me just draw the

positive x-axis because it’ll come in handy in a second. That’s the positive x-axis. And let’s say that I have an

object, and the circle is the object’s path. So let’s say this

is the object. And it’s going around

in a circle in a counterclockwise direction. Not squiggly counterclockwise,

it’s just going around this way. Let’s say I wanted to figure

out, or I wanted to quantify how much, or how fast this

thing is spinning. So one thing that you’re

probably familiar with is revolutions per second, or

rotations per second. So let’s write that down, let’s

just say for the sake of argument that this was moving

at, I don’t know, 1 revolution per second. So after 1 second it goes back,

then another second. So that’s how fast

it’s spinning, 1 revolution per second. 1 revolution– I’ll just

put rev– per second. So let’s see if we can quantify

that in angles, and we’ll do it in radians, but you

could always convert it back to degrees, if you want. I don’t know if you

can see that line. Let’s just say that theta is the

angle between the radius from the center to

that object, and the positive x-axis. So if this object is travelling

at 1 revolution per second, how many radians per

second is it traveling? Well, how many radians are

there in a revolution? Well there’s 2 pi radians

in a revolution, right? 1 go-around in a circle

is 2 pi radians. So we could say, so this equals

1 rev per second, times 2 pi radians per rev, right? And then the revolutions

will cancel out. And you have 1 times

2 pi, so you have 2 pi radians per second. So this equals 2 pi radians

per second. So that’s interesting, we now

know exactly after 5 seconds how many radians it has gone. Or after half a second, how

many radians has it gone. But that might be

vaguely useful. Let’s see if we can somehow

convert from this notion of how fast something is spinning

to its actual speed. I was tempted to say velocity,

but its velocity is always changing, because the direction

is always changing. But the magnitude of the

velocity is staying the same, so its speed is staying

the same. But we’ll say v for speed,

because that’s what they tend to do in most formulas

that you’ll see. So let’s think about it this

way, in 1 revolution– so there’s a couple ways you can

think about this, but as we go 1 revolution, how far has

this object traveled? Well, it’s traveled the

circumference of this circle. And in order to know the

circumference, we have to know the radius of the circle. So let’s say that the radius

is r– let’s say it’s in meters, r meters. So how many meters will I travel

in 1 second, then? Well, you could do the

same thing up here. 1 revolution per second, times

2 pi r, where r is the radius– whoops, 2 pi r, you can

ignore that line– meters per revolution, that’s just

the circumference of the thing, of the circle. And that equals– the

revolutions cancel out– 2 pi r meters per second. So it’s interesting, given

the radius and how many revolutions per second, we can

now figure out its velocity. So this right here is how fast

it’s spinning, and this is the object’s actual speed, right? And this term of how fast

something’s spinning, that’s called angular velocity. And of course you know that

the term for how fast something is actually

moving is velocity. And just so you know, the term

for angular velocity is this curvy w, I think that’s

lower case omega, that’s angular velocity. So in this case, angular

velocity is equal to 2 pi radians per second. And what’s the velocity equal

to, or at least the magnitude of the velocity– I know the

direction’s always changing. Well, we know that the velocity

is equal to 2 pi r meters per second. So if we just ignore the units

for a second, where do you see the difference between

the angular velocity and the velocity? The angular velocity in this

case is 2 pi, and the velocity is 2 pi r. So in general, if you just

multiply the angular velocity times r, you get the velocity. So angular velocity times the

radius is equal to velocity. Or you can divide both sides of

that by r, and you get the angular velocity is equal

to the velocity divided by the radius. And this is a formula that you

should know by heart, although it’s good to know where

it came from. I guess I did it this way to

maybe give you an intuition, because I always have to

work with numbers. Especially when I’m new to a

concept– so that’s why I said 1 revolution per second,

instead of just putting everything as a variable– but

another way to think about it is, what is the definition

of a radian? By definition, a radian– if

this angle is x radians, it’s an angle, and it also tells us

that the arc that is kind of projected by this angle,

is equal to x radiuses. So if each radius is 2 meters,

it would be x times 2 meters. So if this is x radians,

then this is going to be x times r meters. And that actually comes from the

definition of the radian. And that might be more intuitive

to you, than the original explanation, or

less, so hopefully one of those two works. But as you can see, if this

angle is x, and this distance is x times r, and if omega is

change in that angle, over change in time. Then we know this is true too,

that velocity is just change in this, over change

in time, right. Velocity is change in– the

radius doesn’t change– change in x times r, divided

by change in time. And we know once again

that this is omega. So another way we just showed

again, that omega times the radius is equal to

the velocity. Or the angular velocity

times the radius is equal to the velocity. And this is a useful thing to

learn, we’ll see it in a couple of things, when I do

the proof for centripetal acceleration in calculus, I’m

going to use this fact. And when I– and actually I’m

probably going to record that video now– I’m actually going

to show you the law of conservation of angular

momentum, which is very similar to the law of

conservation of momentum, but it deals with things spinning. And this notion of angular

velocity is going to come in useful. So this is the important

takeaway, that w equals v over r. And hopefully my video has not

confused you, and has shown you that w, the rate at which

the angle is changing, is equal to the velocity of the

object, or the magnitude of the velocity, divided

by the radius of the circle that it’s spinning. I’ll see you in the

next video.

THAAAAAAAAAANK YOU!

radii lol awesome post!

Thank you so much! I completely understood the stuff now.

haha sal radiuses- radii man radii -great video though really gave me an understanding of the concepts

thank you

Why can't you teach my classes???!

You explain in the first 3 minutes what my AP Physics book couldn't in a chapter haha. Thanks Sal! 😀

thanks

nope. still confused

THANKYOU SOOO MUCH. IT HELPED ME SOOO MUCH YOU HAVE NO IDEA…

not "radiusses"

radii (ˈrādēˌī)

plural form of radius .

thanks khan…my fuckin book is useless at teaching this

I learn better from you then my math teacher. Thanks 🙂

this video would only be like 3min long if you didn't repeat everything you said 2-3times…

@duggle07

…… It's long because it is based on the basic principle of virtually every video Khan makes. So that we can get a more solid intuition and so he can go at a pace that is comfortable for everyone. I would rather him repeat everything 100 times even if I have a good understanding of the concept than my teacher explain it once and me being too lost to even formulate a question.

@add1c7i0n I'll second that. My book leaves so many things unexplained, who proofs these things? Hate how I have to pay 100+ dollars for a piss poor book I have absolutely no say in.

The definition of the radian proof really sold it for me. Thanks a lot!

@brothadave loool i haven't hear that since dbz

thank you soooo sooo much, i missed this class in school 🙂

the revolution per second is equal to radian per second how?in the linear velocity and angular velocity relation when we multiply the angular velocity equation by r

Your voice is awesome

i was trying to figure out linear speed…my book says the variable v is for linear speed and the variable lower case omega is for angular speed so now i'm a little confused over what's what because the formula you used for angular velocity matched up with what my books said was the formula for linear speed… i'm actually kinda really confused now.. (and yes i realize speed is different from velocity but i figured they should have similar explanations.. )

really helpful! thanks alot!

Thank you so much for this video!

im 11 and study physics

In other words, stick to the point bro.

Thanks for all sir!

u so smart.. u make me love physics <3

how can you see us in next video?

:)>

awesome easy explanation

god bless you !

If you are confused about diameter, Circumference , radius(I was about 10 min ago :P). I advice you to watch this watch?v=jyLRpr2P0MQ it is also from khanacademy

I would like to speak to you about renting your brain?

I was hoping you could help me with a question since my teacher is horrible (by the way, its gr. 12 university advanced functions) :

the members of a high school basketball team are driving from Calgary to Vancouver, which is a distance of 675 km. Each tire on their van has a radius of 32 cm. if the team members drive at a constant speed and cover the distance in 6h45min, whats the angular velocity, in radians/sec of each tire?

Go to the Khan Academy website. Not many people are going to help you in the comments section of youtube.

nice

is this particular video not on the website? I can't find it in the mechanics section or by searching..

excellent video, thanks for uploading! 1 point of constructive criticism: if you provided example questions and answers at the end, it would be a lot easier to understand as it would mean applying all of this knowledge. thanks again!

lol yeah im pretty sure you meant to say radii!! 🙂

0:36-unamused pacman

Omg thank you dude, you've saved my life, i was completly sure of how the whole thing worked, but you explained it very good… thanks a lot.

Omg the way you showed it is confusing

ur d boss khan

KHAAAAAN!!!

6:08 radii* tard

Super super super super super super super super

Things that spin go in a circle.

Enlightening.

literally i cant even

KHAN makes physics so much easier like damn

Where is this video on your website? It's not in the "Moments, torque and angular momentum" section of physics.

I want to add u on fb

whats ur profile name

thanx for help… u r really good at teaching ……. my class teacher sucks a lot

I want u to solve this for me .. and show me how to do it… lol I m very bad at maths :

*calculate the angular velocity and linear of a tip of minute hand of length 10cm ???

BIG THAAANK YOUUUU

HUGE THANKYOU! You got me a 95% on my quiz 😀

6:14 Radii

KHAN IS GOD

I think the ink is too thick can you please reduce it

Got any more of them pixels?

Thank you so much for explaining v=wr! It brought much more light to me than the book!

I think this was actually kind of confusing. It just boils down to angular velocity being measured in radians/sec and velocity in meters/sec

This guy's handwriting and spacing is so terrible yet he does all of the math/physics videos. Anyone who does math knows how important it is to be organized and neat (to a degree) so others can read your work–except this dude.

can't u just use a blackboard? The video is informative but annoying as well

why the potatoe quality 🙁

potatoYou are the greatest living man on earth right now dude !!! I am love with your teaching .. where did you learn all this stuff ?

Mr. Cox 2016 ✌🏼️

thanks so much for posting the videos, they help a lot!!!!

radii not radiuses

1 Revolution = 2 pi radian

u empowered me cadrd

Anybody heard of " rotational velocity" ? Does rotational velocity means as the same thing as angular velocity?

This curvy w lol

Thanks

What does revolution mean?

waste of time…

shouldnt that be 'orbiting' rather than spinning?

Thank you for the video

thank you a lot

Two gears A and B of radius R1 and R2 touch eachother. A starts rotating with angular velocity w,with whah angular velocity will B rotate

I think it's radii

6:10 The term is "radii", not "radiususes" X-D

can u please upload some Videos on Counter per Revolution

Radii or raduises?

Never disappointed after watching khan academy !

easy to under stand mbipc

Thank you for sharing this post. You always have amazing tutorials! 😀

I'm trying to understand the difference between those terms "How fast it's spinning" and "What is actual speed".

Thank you sir.

Khan has a gift in explaining things and making them sound simpler.

Hey Dude you can really confuse students. Velocity(v) = displacement/time = 2πr/t and Angular velocity(w) = (change in angle)/time =2π/t by inspection v = w.r

Thank you

Thank u

please note that if it's 2 rev per second, we need to multiply angular velocity by two. W =2*pi*n

cool!

hello i want to ask how its possible to obtain the angle of a rotating crankshaft based on the time it needs to do a 360 cycle

and if we know the number of teeths passed and triger time that a tooth passed the crankshaft sensor on a 12-1 wheel(11 teeths with one teeth missing that gives 30 deg per teeth) with accuracy up to 1degg or less

best teacher in the world

Surely it confused me😂😂😂

But what if theres down watd force whilst going up for example going round as we are going up everest for example flat earth. How would going up work out.

Nicely done!