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From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a singular thing but really a bunch of particles bouncing against each other, but can still be described by ideal gas laws as if it were a singular object. What is the flaw in my thinking?

atwood22 4y ago
That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.
- mwint 4y ago
  Lay person’s attempt at an explanation: Centripetal force, but no work is done because the motion of the spinning object is perpendicular to the force continually changing the linear motion to follow the circular course?
- uoaei 4y ago
  There are forces holding atoms together, such that the conglomerate constitutes a solid object whose geometry is stable in time. Those forces are strong, and are often sufficient to keep a solid object in the same shape even if rotating at high speeds. Sometimes they are not, in which case the solid object is deformed as the individual atoms are "flung outward" by the (ultimately linear) momentum, which overcomes the attractive force that binds atoms into molecules/lattices/whatever.
  - derefr 4y ago
    Thought experiment: if you have an elastic band floating in space, and you nudge it repeatedly to get it rotating faster and faster, will it stretch out (the way a timing belt would if run too fast) or will it stay slack? In its own reference frame, is the band being put under tension — and so experiencing elastic deformation — from the momentum of the particles within it?
    - yongjik 4y ago
      Yes it will stretch out.
- Schroedingersat 4y ago
  Changing linear momentum does require a force (but not necessarily work), as does changing angular momentum. In orbits it's gravity, in particle interactions it's the electromagnetic force.
- mlsu 4y ago
  Well, if it completes a full rotation, the applied force over the time of the full rotation is zero (hence, work is zero). So yes, the momentum is linear, but it all pencils out by the direction, right? That's my understanding of this, but I'm far from a physics expert.
Schroedingersat 4y ago
It's very decidedly not an abstraction on linear momentum. It's a conserved quantity just like any other. Light has angular momentum even when travelling in a straight line. Anything with spin does even when stopped. In physics there is a concept known as symmetry. Any way you can swap around your variables without influencing the answers corresponds to a way in which the laws of physics are symmetric (or a way someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved). Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.
- kadoban 4y ago
  Is that the _same_ angular momentum, or just the same term used for something different? My understanding is that "spin" isn't really anything necessarily spinning and it's more just an analogy for a property of subatomic particles that doesn't exactly correspond to a concept at the macro level.
  - Schroedingersat 4y ago
    It has almost the same relationship to angular momentum (and tangentially magnetic fields) as charge on an electron has to charge in a capacitor or an electric fields. > My understanding is that "spin" isn't really anything necessarily spinning Yeah, this is kind of the point. A bunch of non-spinning things like particles, or more abstractly an EM field can have angular momentum. This is the same quantity that is conserved in things that are spinning.
    - kadoban 4y ago
      > This is the same quantity that is conserved in things that are spinning. In what sense is it the same? If we called them completely different names, what would be different or more complex?
      - Schroedingersat 4y ago
kergonath 4y ago
From a layman’s perspective, if something spins, you need to apply a force to it to stop spinning, otherwise it will just keep spinning. Hence, conservation of angular momentum. If you change the mass distribution, it will spin faster or slower, just like ice skaters (this is probably the most striking example), but the angular momentum is still conserved, regardless their linear momentum. There is no fundamental difference between this and what happens at the atomic scale. The not layman’s answer is Noether’s theorem: the invariance of the laws of physics after a rotation of the frame of reference implies conservation of angular momentum.
- andreareina 4y ago
  Which implies that it's separate from linear momentum (the conservation of which is implied by invariance after linear translations).
  - kergonath 4y ago
    Indeed!
- mrow84 4y ago
  Your layman’s answer still doesn’t quite do it for me - if you had two masses in space, joined together by a wire, and you span them around their combined centre of mass, angular momentum would remain conserved even if we wound the wire in or payed it out. If I cut the wire, though, wouldn’t the masses immediately shoot off (roughly) in whatever direction they were travelling at the time? That is my interpretation of the “everything seems linear” perspective colordrops offered - it seems like you only get the apparent rotation because of all the other forces holding things together. edit: I accept that the non-layman’s answer may hold, I just find the intuition a bit off.
  - drdeca 4y ago
    Angular momentum would still be conserved when you cut the wire though? Also, couldn’t you just as well frame all the linear momentum in terms of angular momentum? ... hm, I guess one question is, how would we describe a world where one is conserved but not the other, and visa versa, So e.g. a physics invariant under rotation around each point but not under translations, or visa versa... Well, it seems like being invariant under rotation around any point, should maybe imply invariance under translations as well.. But, if we are talking about just rotations around a particular point, then a good example is a model of an atom where we consider the nucleus to be the fixed origin, and with the electrons to just be in a rotationally symmetric potential well, and in that model angular momentum is quite important, while linear momentum isn’t quite so important?
andreareina 4y ago
This isn't explanatory, but should at least demonstrate that it is separate: electrons are point-like particles and thus have no internal substructure to rotate, yet they behave as though they have angular momentum. This "intrinsic angular momentum" is the electron's spin.
alecst 4y ago
Ok so you want the flaw in your reasoning. Imagine a hula hoop. It’s spinning, but otherwise not moving. Mentally divide it up into lots of little chunks. Each chunk has a little bit of linear momentum. 1. Is each chunk’s linear momentum constant in time? No, because its direction of motion is changing. Hm, that’s unfortunate. 2. What about if you do R x p, the radius of the loop crossed with the momentum of that little chunk. That gives you a quantity for each chunk that’s unchanging. That’s called the angular momentum of that chunk. If you add the angular momentum for all the chunks, you get the total angular momentum. So you see that angular momentum works just like linear momentum. You take a conserved quantity for a single chunk and add up over all the chunks. You’re free to think of all the little particles and their linear momentum, but that isn’t so useful, since summing the linear momenta gives you zero, whereas summing R x p gives you something to reason about.
sacrosancty 4y ago
In support of your idea, engineers routinely use FEA simulation software that models dynamic systems without any explicit representation of angular momentum or rotational inertia. Only linear displacement/velocity/acceleration, "translational" mass, and elasticity. Such software can still model rotating systems and all the complex effects that come with rotation. So at least classically, I don't think angular momentum is a fundamentally essential concept.

atwood22 4y ago

That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.

mwint 4y ago
Lay person’s attempt at an explanation: Centripetal force, but no work is done because the motion of the spinning object is perpendicular to the force continually changing the linear motion to follow the circular course?
uoaei 4y ago
There are forces holding atoms together, such that the conglomerate constitutes a solid object whose geometry is stable in time. Those forces are strong, and are often sufficient to keep a solid object in the same shape even if rotating at high speeds. Sometimes they are not, in which case the solid object is deformed as the individual atoms are "flung outward" by the (ultimately linear) momentum, which overcomes the attractive force that binds atoms into molecules/lattices/whatever.
- derefr 4y ago
  Thought experiment: if you have an elastic band floating in space, and you nudge it repeatedly to get it rotating faster and faster, will it stretch out (the way a timing belt would if run too fast) or will it stay slack? In its own reference frame, is the band being put under tension — and so experiencing elastic deformation — from the momentum of the particles within it?
  - yongjik 4y ago
    Yes it will stretch out.
Schroedingersat 4y ago
Changing linear momentum does require a force (but not necessarily work), as does changing angular momentum. In orbits it's gravity, in particle interactions it's the electromagnetic force.
mlsu 4y ago
Well, if it completes a full rotation, the applied force over the time of the full rotation is zero (hence, work is zero). So yes, the momentum is linear, but it all pencils out by the direction, right? That's my understanding of this, but I'm far from a physics expert.

Schroedingersat 4y ago

It's very decidedly not an abstraction on linear momentum. It's a conserved quantity just like any other. Light has angular momentum even when travelling in a straight line. Anything with spin does even when stopped. In physics there is a concept known as symmetry. Any way you can swap around your variables without influencing the answers corresponds to a way in which the laws of physics are symmetric (or a way someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved). Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.

kadoban 4y ago
Is that the _same_ angular momentum, or just the same term used for something different? My understanding is that "spin" isn't really anything necessarily spinning and it's more just an analogy for a property of subatomic particles that doesn't exactly correspond to a concept at the macro level.
- Schroedingersat 4y ago
  It has almost the same relationship to angular momentum (and tangentially magnetic fields) as charge on an electron has to charge in a capacitor or an electric fields. > My understanding is that "spin" isn't really anything necessarily spinning Yeah, this is kind of the point. A bunch of non-spinning things like particles, or more abstractly an EM field can have angular momentum. This is the same quantity that is conserved in things that are spinning.
  - kadoban 4y ago
    > This is the same quantity that is conserved in things that are spinning. In what sense is it the same? If we called them completely different names, what would be different or more complex?
    - Schroedingersat 4y ago

kergonath 4y ago

From a layman’s perspective, if something spins, you need to apply a force to it to stop spinning, otherwise it will just keep spinning. Hence, conservation of angular momentum. If you change the mass distribution, it will spin faster or slower, just like ice skaters (this is probably the most striking example), but the angular momentum is still conserved, regardless their linear momentum. There is no fundamental difference between this and what happens at the atomic scale. The not layman’s answer is Noether’s theorem: the invariance of the laws of physics after a rotation of the frame of reference implies conservation of angular momentum.

andreareina 4y ago
Which implies that it's separate from linear momentum (the conservation of which is implied by invariance after linear translations).
- kergonath 4y ago
  Indeed!
mrow84 4y ago
Your layman’s answer still doesn’t quite do it for me - if you had two masses in space, joined together by a wire, and you span them around their combined centre of mass, angular momentum would remain conserved even if we wound the wire in or payed it out. If I cut the wire, though, wouldn’t the masses immediately shoot off (roughly) in whatever direction they were travelling at the time? That is my interpretation of the “everything seems linear” perspective colordrops offered - it seems like you only get the apparent rotation because of all the other forces holding things together. edit: I accept that the non-layman’s answer may hold, I just find the intuition a bit off.
- drdeca 4y ago
  Angular momentum would still be conserved when you cut the wire though? Also, couldn’t you just as well frame all the linear momentum in terms of angular momentum? ... hm, I guess one question is, how would we describe a world where one is conserved but not the other, and visa versa, So e.g. a physics invariant under rotation around each point but not under translations, or visa versa... Well, it seems like being invariant under rotation around any point, should maybe imply invariance under translations as well.. But, if we are talking about just rotations around a particular point, then a good example is a model of an atom where we consider the nucleus to be the fixed origin, and with the electrons to just be in a rotationally symmetric potential well, and in that model angular momentum is quite important, while linear momentum isn’t quite so important?

andreareina 4y ago

This isn't explanatory, but should at least demonstrate that it is separate: electrons are point-like particles and thus have no internal substructure to rotate, yet they behave as though they have angular momentum. This "intrinsic angular momentum" is the electron's spin.

alecst 4y ago

Ok so you want the flaw in your reasoning. Imagine a hula hoop. It’s spinning, but otherwise not moving. Mentally divide it up into lots of little chunks. Each chunk has a little bit of linear momentum. 1. Is each chunk’s linear momentum constant in time? No, because its direction of motion is changing. Hm, that’s unfortunate. 2. What about if you do R x p, the radius of the loop crossed with the momentum of that little chunk. That gives you a quantity for each chunk that’s unchanging. That’s called the angular momentum of that chunk. If you add the angular momentum for all the chunks, you get the total angular momentum. So you see that angular momentum works just like linear momentum. You take a conserved quantity for a single chunk and add up over all the chunks. You’re free to think of all the little particles and their linear momentum, but that isn’t so useful, since summing the linear momenta gives you zero, whereas summing R x p gives you something to reason about.

sacrosancty 4y ago

In support of your idea, engineers routinely use FEA simulation software that models dynamic systems without any explicit representation of angular momentum or rotational inertia. Only linear displacement/velocity/acceleration, "translational" mass, and elasticity. Such software can still model rotating systems and all the complex effects that come with rotation. So at least classically, I don't think angular momentum is a fundamentally essential concept.