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Today we will discuss what we call "uniform circular motion." What is uniform circular motion? An object goes around in a circle, has radius r and the object is here.

This is the velocity.

It's a vector, perpendicular.

And later in time when the object is here the velocity has changed, but the speed has not changed.

We introduce T, what we call the period —

of course it's in seconds —

which is the time to go around once.

We introduce the frequency, f, which we call the frequency which is the number of rotations per second.

And so the units are either seconds minus one

or, as most physicists will call it, "hertz" and so frequency is one divided by T.

We also introduce angular velocity, omega which we call angular velocity.

Angular velocity means not how many meters per second

but how many radians per second.

So since there are two pi radians in one circumference —

in one full circle —

and it takes T seconds to go around once it is immediately obvious that omega equals two pi divided by T.

This is something that I would like you to remember.

Omega equals two pi divided by T —

two pi radians in capital T seconds.

The speed, v, is, of course, the circumference two pi r divided by the time to go around once but since two pi divided by T is omega you can also write for this "omega r." And this is also something that I want you to remember.

These two things you really want to remember.

The speed is not changing, but the velocity vector is changing.

Therefore there must be an acceleration.

That is non-negotiable.

You can derive what that acceleration must be in terms of magnitude and in terms of direction.

It's about a five, six minutes derivation.

You'll find it in your book.

I have decided to give you the results so that you read up on the book so that we can more talk about the physics rather than on the derivation.

This acceleration that is necessary to make the change in the velocity vector is always pointing towards the center of the circle.

We call it "centripetal acceleration." Centripetal, pointing towards the center.

And here, also pointing towards the center.

It's a vector.

And the magnitude of the centripetal acceleration equals v squared divided by r, which is this v and therefore it's also omega squared r.

And so now we have three equations and those are the only three you really would like to remember.

We can have a simple example.

Let's have a vacuum cleaner, which has a rotor inside which scoops the air out or in, whichever way you look at it.

And let's assume that the vacuum cleaner these scoops have a radius r of about ten centimeters and that it goes around 600 revolutions per minute, 600 rpm.

600 rpm would translate into a frequency, f, of 10 Hz so it would translate into a period going around in one-tenth of a second.

So omega, angular velocity, which is two pi divided by T is then approximately 63 radians per second and the speed, v, equals omega r is then roughly 6.3 meters per second.

The centripetal acceleration —

and that's really my goal —

the centripetal acceleration would be omega squared r or if you prefer, you can take v squared over r.

You will get the same answer, of course, and you will find that that is about 400 meters per second squared.

And that is huge.

That is 40 times the acceleration due to gravity.

It's a phenomenal acceleration, the simple vacuum cleaner.

This is the velocity.

It's a vector, perpendicular.

And later in time when the object is here the velocity has changed, but the speed has not changed.

We introduce T, what we call the period —

of course it's in seconds —

which is the time to go around once.

We introduce the frequency, f, which we call the frequency which is the number of rotations per second.

And so the units are either seconds minus one

or, as most physicists will call it, "hertz" and so frequency is one divided by T.

We also introduce angular velocity, omega which we call angular velocity.

Angular velocity means not how many meters per second

but how many radians per second.

So since there are two pi radians in one circumference —

in one full circle —

and it takes T seconds to go around once it is immediately obvious that omega equals two pi divided by T.

This is something that I would like you to remember.

Omega equals two pi divided by T —

two pi radians in capital T seconds.

The speed, v, is, of course, the circumference two pi r divided by the time to go around once but since two pi divided by T is omega you can also write for this "omega r." And this is also something that I want you to remember.

These two things you really want to remember.

The speed is not changing, but the velocity vector is changing.

Therefore there must be an acceleration.

That is non-negotiable.

You can derive what that acceleration must be in terms of magnitude and in terms of direction.

It's about a five, six minutes derivation.

You'll find it in your book.

I have decided to give you the results so that you read up on the book so that we can more talk about the physics rather than on the derivation.

This acceleration that is necessary to make the change in the velocity vector is always pointing towards the center of the circle.

We call it "centripetal acceleration." Centripetal, pointing towards the center.

And here, also pointing towards the center.

It's a vector.

And the magnitude of the centripetal acceleration equals v squared divided by r, which is this v and therefore it's also omega squared r.

And so now we have three equations and those are the only three you really would like to remember.

We can have a simple example.

Let's have a vacuum cleaner, which has a rotor inside which scoops the air out or in, whichever way you look at it.

And let's assume that the vacuum cleaner these scoops have a radius r of about ten centimeters and that it goes around 600 revolutions per minute, 600 rpm.

600 rpm would translate into a frequency, f, of 10 Hz so it would translate into a period going around in one-tenth of a second.

So omega, angular velocity, which is two pi divided by T is then approximately 63 radians per second and the speed, v, equals omega r is then roughly 6.3 meters per second.

The centripetal acceleration —

and that's really my goal —

the centripetal acceleration would be omega squared r or if you prefer, you can take v squared over r.

You will get the same answer, of course, and you will find that that is about 400 meters per second squared.

And that is huge.

That is 40 times the acceleration due to gravity.

It's a phenomenal acceleration, the simple vacuum cleaner.

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