Revolving light source and creation of angular momentum

[jartsa]

Let's say a train powered by electric third rail drives around without friction on a circular track, and light is shining out of the train windows, said light carries angular momentum, like light emitted from rotating or revolving things tend to do.

Where does that angular momentum come from? It must come from somewhere, as angular momentum can not be created. The train does not change with time.

 

[A.T.]

...said light carries angular momentum, like light emitted from rotating or revolving things tend to do.

Light has angular momentum relative to all reference points not on its path, regardless of how it was emitted.

The train does not change with time.

Then the total angular momentum of all the emitted light must be zero.

 

[Nugatory]

Let's say a train powered by electric third rail drives around without friction on a circular track...

That's not a closed system - both the track and the train's motor are applying forces to the train. You'll have to specify the problem more completely before we can determine exactly how angular momentum is transferred through the system.

 

[jartsa]

That's not a closed system - both the track and the train's motor are applying forces to the train. You'll have to specify the problem more completely before we can determine exactly how angular momentum is transferred through the system.

Angular momentum comes from the track. My question has been answered. Thank you.

Now I have another question: Why does the train not accelerate when the tracks are pushing the train into the forwards direction, like tracks do when train motors are pushing the train?

Some additional information: Whenever the speed of the train reaches 100 m/s, the driver turns the motors off. And whenever the speed of the train is lower than 99 m/s, the driver turns the motors on.

 

[A.T.]

Why does the train not accelerate

Some additional information: Whenever the speed of the train reaches 100 m/s, the driver turns the motors off. And whenever the speed of the train is lower than 99 m/s, the driver turns the motors on.

So does it accelerate or not?

 

[jartsa]

So does it accelerate or not?

In arbitrarily long time the speed does not reach 101 m/s. So acceleration is arbitrarily small.

 

[A.T.]

So acceleration is arbitrarily small.

Then so is the acceleration of the tracks.

 

[jartsa]

I have presented a special relativity problem clearly enough. It's just that you guys don't understand, for some reason.

@A.T. : When a black hole orbiting a star evaporates, the hawking radiation has the orbital angular momentum of the original black hole. Right?

When a train orbiting the center of circular tracks cools by radiating, the radiation has the orbital angular momentum of the original train. If the train has heating on, it can keep its heat energy constant, and it may be able to keep its angular momentum constant. Right?

 

[A.T.]

When a train orbiting the center of circular tracks cools by radiating, the radiation has the orbital angular momentum of the original train. If the train has heating on, it can keep its heat energy constant, and it may be able to keep its angular momentum constant. Right?

If the emitted radiation has non zero angular momentum, then the angular momentum of its otherwise isolated emitter cannot stay constant.

 

[HallsofIvy]

"Acceleration" is the rate of change of velocity. And velocity is a vector quantity. If the train is going around a circle at a constant speed then there is acceleration with the acceleration vector pointing toward the center of the circle.

 

[jartsa]

Hey maybe if I give some kind of solution to this problem, you can see what the problem is supposed to be:

The electrode on the train scoops up mass-energy, which is at rest relative to the rails, this causes a force on the electrode, the electrode pulls the train backwards, to compensate this the driver turns the motors on, which causes the wheels to push the rails, which gives the rails angular momentum, which points to opposite direction compared to the angular momentum of radiation emitted by the train, and net angular momentum emitted by the train is zero, as it should be.

"Electrode" means the thing that slides on the third rail.

 

[HallsofIvy]

The train does NOT "give the rails angular momentum". The rails, which are attached to the ground, do not move. In order to have "conservation of angular momentum, you would have to include the Earth's angular momentum.

 

[jartsa]

The train does NOT "give the rails angular momentum". The rails, which are attached to the ground, do not move. In order to have "conservation of angular momentum, you would have to include the Earth's angular momentum.

I see.

But that part about the electrode feeling a force when picking up mass-energy was not wrong?

Moderators, how about moving this thread to special and general relativity?