Ghost Force(?) & Angular Momentum

In summary: I don't see how I missed it before! :-)Thank you very much!In summary, the conservation of angular momentum explains the change in angular speed of celestial objects as they orbit the sun, without the need for an external force or torque. This is due to the change in the moment of inertia, which can result in an angular acceleration even with zero external torque. This concept is fundamental in classical mechanics and can be further explored through Lagrangian/Hamiltonian mechanics.
  • #1
yasar1967
73
0
From Kepler's second law as well as conservation of angular momentum, we know that Earth (any many other celestial objects) move faster when they get near the sun during their orbit and get slower when they are far away. This is a "change" in the angular speed so the derivative of it is a constant(if it's not a function). But this change must bring an angular acceleration α which in return brings us a torque due to the fact that

Torque= I x α = r x F

What is this force and where does it come from?
Sun's gravity is a central force and can act only parallel to the displacement vector from sun-to-earth thus it can't have any torque effect at all.

What force cause this acceleration of Earth during these phases?
 
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  • #2
There is no "force". This is the result of the conservation of angular momentum. It is the same effect that you get when you are spinning and bring your arms in. There's no external force or torque of any kind there.

Zz.
 
  • #3
How would you explain the mathematical consequence then? a change in the angular speed thus an angular acceleration YET no force and no torque??
 
  • #4
yasar1967 said:
How would you explain the mathematical consequence then? a change in the angular speed thus an angular acceleration YET no force and no torque??

Mathematical consequence? What mathmatical consequence?

The conservation laws of our universe are not mathematically derived. It has no consequences to mathematics. The mathematical description of the conservation of angular momentum is pretty obvious, which I don't think is what you're asking.

Zz.
 
  • #5
Thank you :)
What mathematics say that if there's a change in angular speed there MUST be an acceleration. If there's an acceleration there MUST be a force.
Yet you are saying that "that must not be" that's not how universe works.
Am I following you?
 
  • #6
yasar1967 said:
Thank you :)
What mathematics say that if there's a change in angular speed there MUST be an acceleration. If there's an acceleration there MUST be a force.
Yet you are saying that "that must not be" that's not how universe works.
Am I following you?

Notice that when I wrote my response, I wrote the word "force" in quotes. I assumed that you know about external forces and torques that are missing from the system. This is the reason why the angular momentum of the system is conserved.

There is also something that you are missing. In classical mechanics, the "conservation laws" actually is the most fundamental aspect of the dynamics of any system. The "forces" are actually not that fundamental, and in fact, in the Lagrangian/Hamiltonian mechanics, forces don't even exist! This is because ALL you are actually detected are the two fundamental variables : the cannonical momentum and the cannonical coordinate positions.

So I don't quite understand the "obsession" with "forces" here in a system that really do not need such a thing when the application of a conservation law is sufficient and, in fact, simpler.

Zz.
 
  • #7
It's not an obsession, if you're to think about it in classical terms you're prone to find a force to cause such acceleration.
But I guess this is where classical physics ends and "beyond" begins.
I'll think about a "forceless" universe and read Lagrangian/Hamiltonian mechanics.

Thank you, you opened my mind.
 
  • #8
yasar1967 said:
It's not an obsession, if you're to think about it in classical terms you're prone to find a force to cause such acceleration.
But I guess this is where classical physics ends and "beyond" begins.
I'll think about a "forceless" universe and read Lagrangian/Hamiltonian mechanics.

Thank you, you opened my mind.

Classical physics does not end at angular momentum (in this context). Far from it. Perhaps http://www.lightandmatter.com/html_books/7cp/ch03/ch03.html [Broken] can contribute to your understanding of angular momentum.
 
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  • #9
yasar1967 said:
From Kepler's second law as well as conservation of angular momentum, we know that Earth (any many other celestial objects) move faster when they get near the sun during their orbit and get slower when they are far away. This is a "change" in the angular speed so the derivative of it is a constant(if it's not a function). But this change must bring an angular acceleration α which in return brings us a torque due to the fact that

Torque= I x α = r x F

What is this force and where does it come from?
Sun's gravity is a central force and can act only parallel to the displacement vector from sun-to-earth thus it can't have any torque effect at all.

What force cause this acceleration of Earth during these phases?

What happens is that the moment of inertia changes. And when that happens, [tex]\tau = I\alpha[/tex] is no longer good enough. We need to consider the more fundamental relationship [tex]\tau = \frac{dL}{dt}[/tex]. Since the angular momentum is given by [tex]L = I\omega[/tex], we can see that, in cases where I changes, torque is given by [tex]\tau = I\alpha + \frac{dI}{dt}\omega[/tex]. This means that there can be an angular acceleration without any external torque. You just need I to vary in time while the object is rotating; and, that's exactly what's happening here.
 
  • #10
Parlyne said:
What happens is that the moment of inertia changes. And when that happens, [tex]\tau = I\alpha[/tex] is no longer good enough. We need to consider the more fundamental relationship [tex]\tau = \frac{dL}{dt}[/tex]. Since the angular momentum is given by [tex]L = I\omega[/tex], we can see that, in cases where I changes, torque is given by [tex]\tau = I\alpha + \frac{dI}{dt}\omega[/tex]. This means that there can be an angular acceleration without any external torque. You just need I to vary in time while the object is rotating; and, that's exactly what's happening here.

Ah, the perfect explanation! Since [itex]I=r^2m[/itex], zero external torque (in Parlyne's equation) implies [itex]\alpha = - \frac {2 \omega} {r} \frac {d r} {d t} [/itex], or in other words, unless there is a torque the planet has to decelerate (in terms of angular velocity) while-ever it is getting further from the sun ([itex]\frac {d r} {d t}[/itex] is +ve), and conversely a skater must spin faster if she draws in her arms.
 
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  • #11
Crystal clear... thank you!
 
  • #12
Why can't we just say that the force here is gravity? If the orbit isn't circular, the object isn't traveling tangentiallly to the gravitational potential, so there is a force component in the direction of motion.
 

1. What is the concept of Ghost Force in physics?

The concept of Ghost Force refers to a hypothetical force that has been proposed to explain the phenomenon of angular momentum in rotating systems. It is believed to be a non-contact force that acts between objects, causing them to experience a torque and thus change their angular momentum.

2. How is Ghost Force related to angular momentum?

Ghost Force is thought to be responsible for the conservation of angular momentum in systems where no external torque is present. It is believed to be a hidden force that acts between objects in a rotating system, causing them to experience a torque and thus maintain their angular momentum.

3. Is Ghost Force a proven concept in physics?

No, Ghost Force is still a theoretical concept and has not been proven or observed in any experiments. It is a proposed explanation for the conservation of angular momentum in certain systems, but more research and evidence is needed to confirm its existence.

4. Can Ghost Force be detected or measured?

As of now, there are no known methods to detect or measure Ghost Force. Since it is a hypothetical force, its existence and properties are still under debate and investigation by scientists.

5. What are some potential applications of understanding Ghost Force?

If Ghost Force is proven to exist and its properties are better understood, it could have implications in various fields such as astrophysics, where it could help explain the motion of celestial bodies, or in technology, where it could be utilized in designing more efficient and stable rotating systems.

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