# Conservation of Angular Mometum for a Car/Earth System

• alkaspeltzar
In summary: It's not an isolated system like the bullet / door example. The Earth is not isolated from the car / conveyor belt system.So if you figure out where the engine gets the energy to spin up the rear wheels, you'll see where the energy goes to spin up the front wheels and the conveyor belt.In summary, the car's conservation of angular momentum with the Earth can be seen through the forces of the car pushing back and the Earth moving back and rotating, resulting in the car accelerating forward. The friction force on the front non-driving wheel also contributes to the conservation of angular momentum, as it provides the necessary torque to rotate the wheel. The overall force on the car is equal to the force on the Earth
alkaspeltzar
See attached. You can see how the car as a whole conserves angular momentum with earth. Car pushes back, Earth moves back and rotates, car accelerates forward.
https://www.animations.physics.unsw.edu.au/jw/momentum.html

However, the ground puts a friction force on the front non-driving wheel, which gives it AM about its axle. IF you look at the overall force on the car, it is Force(Drive) -Force(friction), same as earth, as Earth gets a rearward Force but the friction from front wheel pushes forward.

If i was to look at the torque about the center of the Earth via the car, it is the same as the earth. But what and where do we include the wheel and its angular momentum? What am i missing? How does the angular momentum come into play so that the Earth and car are equal

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about the center of the Earth
The force to accelerate and rotate the non-driven wheels in the absence of friction is provided by the driving wheels. That takes care of the complete angular momentum balance about the centre of the earth. Note that friction to make the non-driven wheels rotate does not do any work.

It's a tough job to derive angular momentum of the non-driven wheels about the centre of the earth. But it can be done (##L\equiv \int \vec r\times d\vec p ##) ##\ \ ## Nice exercise !

PS my car is a front-wheel drive

BvU said:
The force to accelerate and rotate the non-driven wheels in the absence of friction is provided by the driving wheels. That takes care of the complete angular momentum balance about the centre of the earth. Note that friction to make the non-driven wheels rotate does not do any work.

It's a tough job to derive angular momentum of the non-driven wheels about the centre of the earth. But it can be done (##L\equiv \int \vec r\times d\vec p ##) ##\ \ ## Nice exercise !

PS my car is a front-wheel drive
Why do you say in absence of friction? Isn't the car pushing forward, the friction from the ground what creates the torque about the non driven front wheel?

Also how does the rotation and Ang momentum of the front wheel balance with the earth...sorry I didn't follow

When you say angular momentum of the front wheels, you have an axis in mind. What axis ? And do you want to consider the angular momentum of he earh around that axis ?

BvU said:
When you say angular momentum of the front wheels, you have an axis in mind. What axis ? And do you want to consider the angular momentum of he earh around that axis ?
I was considering the angular momentum of the wheels with respect to their axles. Is that my mistake, I'm mixing up axis of rotation? I keep seeing Ang momentum at the wheels relative to the axles then seeing ang. Momentum of the Earth on wondering why it doesn't add together.

I asked questions the other day about a bullet striking a door. In the end it was clear how both either gained or lost Ang. Momentum. With a cars front wheels, I see how the wheel gains Ang. momentum about the axle, but I'm having a hard time seeing where it came from such that it is conserved

Conservation is wrt one single axis. Pick one.

BvU said:
Conservation is wrt one single axis. Pick one.
Okay I get it. So if choose the axis of the wheel, how is AM conserved? Torque from ground causes AM, but how did ground lose it? Like when a bullet hits a door with a hingez the door gains it, bullet loses it.

Hehe , in post #2 I picked the other axis and showed an expression for the AM of the wheel wrt Earth axis.

It's bedtime here (1:30)

alkaspeltzar said:
Okay I get it. So if choose the axis of the wheel, how is AM conserved? Torque from ground causes AM, but how did ground lose it? Like when a bullet hits a door with a hingez the door gains it, bullet loses it.
Maybe the whole Earth / car system is adding too much confusion for you. Instead, think of a simplified system with a car held down on a conveyor belt in space away from the Earth. That's obviously an isolated system, so the linear and angular momentum have to be conserved.

If the car is rear-wheel drive (assuming it's an electric car and can run in the vacuum of space), as the rear wheels start to drive the mass of the conveyor belt, that also spins up the front wheels. The energy for the moving conveyor belt and the front wheels comes from the motor driving the rear wheels. It doesn't come from anywhere else. Does that help?

berkeman said:
Maybe the whole Earth / car system is adding too much confusion for you. Instead, think of a simplified system with a car held down on a conveyor belt in space away from the Earth. That's obviously an isolated system, so the linear and angular momentum have to be conserved.

If the car is rear-wheel drive (assuming it's an electric car and can run in the vacuum of space), as the rear wheels start to drive the mass of the conveyor belt, that also spins up the front wheels. The energy for the moving conveyor belt and the front wheels comes from the motor driving the rear wheels. It doesn't come from anywhere else. Does that help?

View attachment 270301
I guess maybe that helps. But as I said above with my bullet and door example, you can see where Ang momentum goes. As the tires roll on the treadmill, and gains AM, where is it being lost?

alkaspeltzar said:
I guess maybe that helps. But as I said above with my bullet and door example, you can see where Ang momentum goes. As the tires roll on the treadmill, and gains AM, where is it being lost?
Nowhere. The energy to spin up those front wheels comes from the engine driving the rear wheels, which drives the belt and the front wheels. The sum of the AM of the rear wheels, the belt and the back wheels is zero because it's an isolated system.

In this very isolated system, just because the total AM is zero, that doesn't mean that the total rotation of the car+belt system is zero. The driven wheels and the front wheels spin one way, so the whole belt+car system spins the other way to conserve the AM.

berkeman said:
Nowhere. The energy to spin up those front wheels comes from the engine driving the rear wheels, which drives the belt and the front wheels. The sum of the AM of the rear wheels, the belt and the back wheels is zero because it's an isolated system.

In this very isolated system, just because the total AM is zero, that doesn't mean that the total rotation of the car+belt system is zero. The driven wheels and the front wheels spin one way, so the whole belt+car system spins the other way to conserve the AM.
And that's what the link I had above showed with the car and earth. Car one way, Earth other way, AM CONSERVED. But the front wheels are still spinning and they don't include that. SO if you look at the front wheels, yes as the whole car moves it powers them. That isn't the question. But friction drives them, creating torque, causing increase in AM, the ground/earth had to lose some right? If I take sum of AM momentum about Earth's axis, where does that include the am of the wheel?

I'm assuming rear wheel drive, front wheels are just spinning along. Where and how does their momentum balance so AM is conserved

alkaspeltzar said:
I'm assuming rear wheel drive, front wheels are just spinning along. Where and how does their momentum balance so AM is conserved
Have you accounted for the angular momentum of the Earth about the front axle?

There is a force from front tire on Earth. The line of action of that force does not intersect the axle. Therefore there is a non-zero torque on the Earth about that axis. It follows that the angular momentum of the Earth about the car's front axle changes as a result of that torque.

alkaspeltzar said:
For a car/earth system, the ang. mometum about the center of the Earth is conserved.
Is it? The center of the Earth is not an inertial point.

etotheipi
A.T. said:
Is it? The center of the Earth is not an inertial point.
Good point. We should say, instead, that the angular momentum about the earth-car barycenter is conserved.

etotheipi
alkaspeltzar said:
Car one way, Earth other way, AM CONSERVED. But the front wheels...
If you want to analyse the front wheels, you have to treat them as a separate body, not part of the car.

Just like in your previous threads, you are mixing up different ways to cut a scenario into bodies.

A.T. said:
If you want to analyse the front wheels, you have to treat them as a separate body, not part of the car.

Just like in your previous threads, you are mixing up different ways to cut a scenario into bodies.

Thats right! I have to conserve ang. momentum about an axis. So for the car and Earth around Earth's axis, that is what the website i attached is showing. If i am curious about the front wheel around its axis, then i have to treat/work on it separately.

I slowed down last night and figured there was something i was missing and figured that was it

jbriggs444 said:
Have you accounted for the angular momentum of the Earth about the front axle?

There is a force from front tire on Earth. The line of action of that force does not intersect the axle. Therefore there is a non-zero torque on the Earth about that axis. It follows that the angular momentum of the Earth about the car's front axle changes as a result of that torque.

No i didnt. I was looking at the force and torque from the car/tires about the center of the earth. As A.T. just reminded me, i have to do a conservation problems relative to the wheel's axis. So as you say, i need to include that the ground/earth is getting a torque from the tire relative to the wheel axle.

Ang. Momentum is just conceptually hard for me to get my head around. We didn't learn much about it in physics in college, other than simple interactions(spinning disks, bullet to bar etc)

Also, i realize i don't need to worry about our interactions on Earth's motions for the most part, as they are so insignificant or other forces/torque cancel them out.

alkaspeltzar said:
Thats right! I have to conserve ang. momentum about an axis. So for the car and Earth around Earth's axis, that is what the website i attached is showing. If i am curious about the front wheel around its axis, then i have to treat/work on it separately.
Angular momentum is conserved for one system about one reference axis. It is not conserved for two systems about two reference axes.

In particular, you cannot compute the angular momentum of A about the center of mass of A and the angular momentum of B about the center of mass of B and pretend that the sum is the angular momentum of A and B combined about the center of mass of A and B combined.

You can pick any axis you like. But, having picked it, you cannot change it in mid-thought. You can pick any set of components you like. But having drawn your mental boundaries around the system, you cannot change them in mid-thought.

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vanhees71

## 1. What is conservation of angular momentum?

Conservation of angular momentum is a physical law that states that the total angular momentum of a system remains constant unless acted upon by an external torque. In simpler terms, it means that the rotational motion of a system will not change unless a force is applied to it.

## 2. How does conservation of angular momentum apply to a car/Earth system?

In the case of a car/Earth system, the car's wheels exert a torque on the Earth, causing it to rotate. However, the Earth's mass is so much larger than the car's that the effect is negligible. Therefore, the Earth's rotation remains constant, and the car's rotation is also constant due to conservation of angular momentum.

## 3. Can conservation of angular momentum be violated?

No, conservation of angular momentum is a fundamental law of physics and cannot be violated. It has been observed and tested in countless experiments and has never been found to be untrue.

## 4. How does conservation of angular momentum affect the stability of a car?

Conservation of angular momentum plays a crucial role in the stability of a car. As the car moves, its wheels rotate and create angular momentum. This momentum helps keep the car balanced and prevents it from tipping over. If the car were to lose this momentum, it would become unstable and potentially tip over.

## 5. Is conservation of angular momentum related to other conservation laws?

Yes, conservation of angular momentum is related to other fundamental conservation laws, such as conservation of energy and conservation of linear momentum. These laws all stem from the principle of conservation of mass, which states that the total amount of matter in a closed system remains constant. Therefore, conservation of angular momentum is just one aspect of the broader concept of conservation of mass.

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