How is Angular Momentum Transferred From One Bumper Car to Another?

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En provenance du cours de University of Virginia

How Things Work: An Introduction to Physics

800 notes

University of Virginia

How Things Work: An Introduction to Physics

800 notes

An introduction to physics in the context of everyday objects.

À partir de la leçon

Bumper Cars

Professor Bloomfield examines the physics concepts of momentum, impulse, angular momentum, angular impulse, and the relationship between potential energy and force using bumper cars.

Does a Spinning Bumper Car Carry a Torque?17:28

How is Angular Momentum Transferred From One Bumper Car to Another?15:47

How Does a Bumper Car Move on an Uneven Floor?15:11

Rencontrer les enseignants

Louis A. Bloomfield
Professor of Physics

How is angular momentum transferred from one bumper car to another?

The answer to that question, is that the first bumper car does an angular impulse

on the second bumper car. Just as you can transfer energy by doing

work and linear momentum by doing a impulse, you can transfer angular

momentum by doing a angular impulse. So, what exactly is an angular impulse?

An angular impulse is a torque exhorted for time, for example, I can do an

angular impulse on this bumper car by twisting it, that's the torque, as time

passes, here we go. Okay, I did an angular impulse on that

bumper car and I transfer a momentum to it.

So, that product, my torque times the time over which it acted i the angular

impulse, and therefore, the amount of angular momentum that I transfer to the

bumper car. And angular impulse transfers a vector

quantity, angular momentum, so that angular impulse itself is a vector

quantity. It points in the direction of the torque

that's responsible for it. So, for example, if I twist the bumper

car, downward, I transfer downward angular momentum to the, to the bumper

car. So I did downward angular impulse.

On the other hand, if I twist it upward, that's upward torque produced an upward

angular impulse that produce that resulted in an upward transfer of angular

momentum to the bumper car. And also like impulses, I have some

flexibility in the angular impulse I'm doing.

For example, can do the same angular impulse with different combinations of

Torque and time or, or rather duration. For example, here is an angular impulse

that involves a medium torque exerted for a medium amount of time.

Here it goes,[NOISE]. Okay.

I transferred a certain amount of angular momentum, in this case downward, into the

bumper car. And I did it with a medium torque exerted

for a medium time. I could also use a much larger torque,

exerted for a very short time. And that was the same angular impulse,

but with a bigger torque for a shorter time.

And finally, I can do the same angular impulse with a smaller torque exerted for

a longer time. [NOISE] It's a little hard, 'kay?

But you get the idea. And, in bumper cars, many of the twisting

jolts that you experience you feel during the, during the motion around the arena,

occurred during these collisions that transfer a lot of angular momentum in a

very short period of time. And so they are high torque, short

duration, and your impulses that really,[LAUGH] spin you around, hard.

Also, like anger, like ordinary impulses, like the impulses that transfer momentum,

anger impulses come in equal but opposite pairs.

When I twist this bumper car downward, that's a downward twist.

I did, I, downward transfer of angular momentum by way of a downward angular

impulse. It does an angular impulse back on me in

the opposite direction. So, I transferred downward angular

momentum to it. It, on the other hand, twisted me

backwards, because it has to. That's, that's Newton's third law of

rotational motion, motion. It twisted me upward and did an angular

impulse upward on me and gave me upward angular momentum, which is the same as a

deficit. A negative amount of downward angular

momentum, it took away the downward angular momentum that I gave to it and

that makes the transfer complete. I gave the bumper car downward angular

momentum. At the same time, it took away downward

angular momentum from me. So that what I lost, it gained.

Angular momentum is conserved. And this has to happen.

Whatever I give it, I have to give up. All right.

Well, so far, I'm just doing all of this with my hands and a bumper car.

But in the bumper car, most of the angular impulses, and certainly the ones

that are most exciting involve collisions.

And the angular impulses in those contexts, in the collision context, are

kind of subtle and they often involve frictional forces.

So let me show you how an angular impulse occurs in bumper cars.

as I say, they often involve friction, and so, having these rubber bumpers,

which have a lot of friction, they, they really grip each other pretty well, is

important. Now, angular momentum, like all the

rotational quantities is defined around, about a center of rotation, so we have to

pick it and stick with it. The center of rotation I'm going to pick

is the center of mass of this car. This is the, this is our center of

attention, too. We're going to pay attention to this car.

This guy is just an interlope where it's going to come through and spin the first

car. At the start of the story, the angular

momentum will be present already. It will be in the form of this cars

moving around, it will effect orbiting. It's going around the center of rotation,

for our story. It won't actually be travelling in a

circle. It'll be travelling in a straight line

as, as objects do when they're free of external forces.

But the fact that it's moving like this, means that it is swinging around that

center rotation. It's actually, there's rotation in here

already, and therefore, angular momentum here already.

So this guy's going to come along and it's going to clip the edge of that

bumper car. It's going to catch it and twist it.

And the, the act of catching that edge and twisting that bumper car there.

A force, a frictional force, exerted at a lever arm from the center of rotation,

produces a torque, and will twist our main focus bumper car, and do the anger

impulse. So, as this guy comes along, heading

straight and true and it grabs the edge of the bumper car, we care about it's

going to exert the torque for the time and do the anger impulse on that bumper

car. So, let me see if I can pull this off.

The, what you should be looking for is this thing traveling straight, that one

not spinning, the collision. And after that, this guy should be

spinning, because the angular momentum will be transferred from this one to the,

to our main focus. Ready, get set.

There it is. Of course, I've got so much junk in the

way. Let me get this out of the way.

Come back guys. It's spinning.

Spinning. So, those kinds of collisions in bumper

cars break, I can try to, I'm going to hold this guy and really clip it hard.

[NOISE] It was spinning fast before[LAUGH] it flew off onto the floor.

But, those kinds of collisions occur in real bumper cars, and all of sudden, you

get clipped, our bumper car gets caught on the edge by a fast moving nearby

bumper car, and suddenly, whoa. You're spinning around.

That's where that comes from. It's time for a question.

This is a gyroscope, which consists of a wheel on an axle.

It's mounted in a frame that allows that wheel and axle to turn very freely,

almost without any frictional torques at all.

This particular gyroscope resides in a frame that's, that isolates it from the,

from the external world, so that it's very hard to exert any torques on this

wheel, this gyroscope wheel, about the gyroscope wheel's center of mass which is

the center rotation of this gyroscope. Now, there's a string wrapped around the

axle of this gyroscope. And the question is this.

If I pull that string while holding the frame so that axle can't move, except to

just rotate, all it can do is rotate. If I pull the string while the axle is is

held in in orientation, what will happen to the gyroscope?

When I pull that string, I will produce a torque on the gyroscope about it's center

of mass, center of rotation. And that torque will last for awhile,

good for actually a second. As a result, I will do a large angular

impulse on the gyroscope and transfer a lot of angular momentum to it.

And once I do, it'll be spinning fast. I'll show you.

Here we go. [NOISE].

It's now spinning quite fast and it has a lot of angular momentum.

And the interesting thing to show is that, as I try to move, the surrounding,

the, the frame that holds this, this gyroscope in place, it tends to keep

turning about the same axis. As long as I don't exert a torque on it,

I transfer no angular momentum about its own center of rotation and it keeps

turning as it was. Now, it's not perfect.

It's pretty close, but the frame really tries to prevent any angular impulses on

that spinning gyroscope. Nice.

[NOISE]. Now, in my bumper car arena which I'll

bring out in a moment, I have bumper cars that don't have rubber bumpers, they're

all plastic, they don't have very much friction between them.

And so, one, when one clips the other one, it doesn't transfer very much

angular momentum. So the one it hit, I can help that by

making my, my bumper cars not perfectly round, not circular like this, and many

bumper cars aren't quite circular. And when they're not circular, it isn't

just frictional forces that contribute to those torque.

It's also support forces, so I'm going to bring out my little bumper car arena, and

I'm going to put on some bumper cars that I've made not round.

So here, we have my miniature bumper car arena again and I've modified two of the

bumper cars by putting wires on them that stick out.

And, those wires will allow a passing bumper car to exert a large torque on

these modified bumper cars. So that makes them more similar to bumper

cars that have either rubber bumpers that, that give you a lot of grip or to

bumper cars that aren't circular, that, that extend outward in certain areas.

So that a passing bumper car can exert support forces on that bumper car and

produce torque in that manner. So first, to show you that that a passing

bumper car, let me pick a different color.

The green one passing the red one will catch its wire, exert the torque on the

red bumper car, about the red bumper car's center of mass, which will be our

center for this story. And it will set the red bumper car

spinning by doing an angular impulse on the red bumper car.

So I'll start with the red bumper car as motionless as I can get it.

Here it is, motionless. We're going to spinning.

There it goes, and I can do the same with the little red bumper car.

I only have little red bumper cars and I can set it spinning.

Where things get a little more interesting though, are when I have

bumper cars of different masses bumping into each other.

For example, this bumper car, the, this big red one, has a relatively large

rotational mass, and so, you have to pour a lot of angular momentum into that in

order to make its angular velocity significant.

So let me, let me smack a small, one of the little red guys into that big red

behemoth. Not much action.

The little red one carried the angular momentum at the start.

It has a small mass. And therefore, had a relatively small

rotational mass about the center of the big red one.

So, it didn't have much angular momentum to transfer.

It transferred a good fraction of what it had, but that wasn't enough to set the

big red one with its large rotational mass, spinning very fast.

On the other hand, if we go, use the little red one as a target, and, and take

the, well, now, I can use the big green one.

A big green one as the passing monster. It sets the little red one spinning

furiously, because, the big green one was carrying a lot of rotation, a lot of

angular momentum. It has a big mass, and it, and as it

moved around the center of rotation, which was the center of mass from our

little one, the green one was carrying a lot of angular momentum.

The little red one received a good fraction of that angular momentum from

the green one and that was enough to make the little red one with its tiny

rotational mass spin like crazy. So, you've seen these effects in bumper

cars if you've gone there or experienced them.

And that is, the big massive cars passing you and clipping the edge of your car can

really cause some serous anger response from your car.

Your car receives a big dose of anger by way of a big anger impulse, and suddenly,

you're whipped around in a hurry. On the other hand, passing cars that are

occupied by, say small children don't carry very much angular momentum about

your center of mass. And so, when they give you even a good

fraction of their angular momentum, doesn't have much effect on you and your

car. Your car receives a modest angular

momentum dose by way of a modest angular momentum anger impulse, and the result

is, is underwhelming. So, once again, the big massive cars

affect the little cars a lot more than the other way around.

Well, that's it for the story of angular impulses in, on the bumper car arena.

The next and final topic in which I, I want to talk about is what happens if the

bumper car arena isn't perfectly flat? How do the bumper cars move when they're,

when they're on a surface that is uneven? And that's the topic for the next video.

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