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I Why does atmosphere rotate w/ constant angular velocity?

  1. Jun 18, 2016 #1
    Hey guys. I've seen this question asked on a few different forums, and I understand the basic gist of the answer but I am not yet satisfied with what I have read. People seem to have varying degrees of understanding of this, and I am the type of person that wants to understand things 100% and so I am hoping that someone out there can answer this question in pretty good detail.

    This is the type of question that flat earthers bring up pretty often, and I am definitely not one but I like to be able to really know things when I say it to them so that I can break it down to some level where they will understand it. Anyway...

    The earth spins (I am using the word earth to denote the planet itself, although the atmosphere is also considered part of earth) and the atmosphere spins with it at the same angular velocity. We know this because if the angular velocity were not constant, then you could launch a hot air balloon straight up, and the air at high altitude would be spinning faster or slower than the earth, and therefore you could travel around this way but this is clearly not the case. So I understand that the earth and the atmosphere both spin with the same angular velocity (360 degrees in 24 hours, so about 15 degrees per hour.)

    What I don't understand is why the atmosphere spins with the same angular velocity, (instead of the same tangential velocity) as the earth. Maybe it's difficult for me to grasp because humans have much more intuitive understanding of linear behavior than angular behavior, but I understand it like this:

    The earth spins, and the surface of the earth pulls the bottom layer of atmosphere (say, air at a height from h=0 to h=500 feet or something) along with it. This is because of friction between the earth and the air, and because of Newton's Third law, since the air exerts negligible friction on the earth (compared to the earth's mass), the air is forced to speed up until its angular velocity matches that of the earth. This is all good so far. Here's where is stops making sense to me though. Now, the atmosphere above the bottom layer (let's say 500 feet to 1000 feet) is pulled by the bottom layer of atmosphere until it reaches the same angular velocity. Therefore, the atmosphere in this second layer is moving faster (tangentially, and therefore with greater linear velocity) than the bottom layer of atmosphere. This means that the bottom layer of atmosphere causes the layer above it to move faster than it is moving itself. If the bottom layer moves at a constant velocity, how can it cause something which it is pulling to move faster than it?

    For example, at the equator, the surface of the earth moves at about 1000 mph. This pulls the atmosphere immediately above it to the same speed. But the atmosphere 500 feet above the surface of the earth will have the same angular velocity and therefore a higher tangential velocity due to the greater distance from the center of the earth, so let's say it's going 1050 mph. The higher up in the atmosphere we go, the faster the air is moving tangentially, because it has the same angular velocity. What I don't understand is how an object moving at 1000 mph can pull another object to a speed of 1050 mph.

    I understand that at the far edge of the atmosphere, where it butts up against outer space, there is no friction on the outer edge, so there is nothing that should slow it down. If you compare this to a doughboy pool (that's what we called the as kids), in a round pool 3 feet deep, you and a few of your friends would run in a circle, making a whirlpool in the water that would continue to pull you along with it once you stopped moving. This whirlpool would only last a few seconds, since the friction from the pool edge would slow it down. Our atmosphere is different, since there is no outer edge to slow it down, and the earth spinning in the middle is like a motor that continues to pull it at all times.

    I feel like I understand 80% of this problem, and I'm just missing the 20%. I know that the upper atmosphere being pulled by the lower atmosphere must be the same reason that each 'layer' of the earth gets pulled by the layer immediately below it. Yet, the earth all moves at the same angular velocity, and so the layers don't spread apart as the outer layers move faster or slower than the middle layers (the surface of the equator is the fastest moving point on earth, while the point inside the earth halfway to the center from the equator will move with the same angular velocity but tangential speed of half that of the surface, from s = r * theta.

    I don't know if my question makes sense, but I know that I don't fully understand it and it has something to do with the difference between angular and tangential (linear) velocity. Can someone please help me find the missing piece?
     
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  3. Jun 18, 2016 #2

    A.T.

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    Same angular velocity implies same tangential velocity for any given radius.
     
  4. Jun 18, 2016 #3
    Hey AT, I appreciate you trying to answer, but a couple things...

    First, your statement is only true in 2-dimensions and obviously the sphere of earth and the spherical shell of the atmosphere are both 3-dimensional objects. The tangential velocity would be a function of both radius and the latitude in 3 dimensions.

    Also in the original post I said

    This imples that tangential velocity is related to angular velocity through the radius, so yeah of course the tangential velocity will be the same for two objects at the same radius and same angular velocity. You could also take the derivative of the equation at the end, giving ds/dt = r * d(theta)/dt. So for a fixed r, ds/dt must be equal to d(theta)/dt for all r. My question is about how the top layer of a fluid (such as the atmosphere) could spin with higher tangential velocity than that of the bottom layer, which is at the surface of the earth.

    [Mentors' note: insults unrelated to the discussion have been removed]
     
    Last edited by a moderator: Jun 18, 2016
  5. Jun 18, 2016 #4

    etudiant

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    The earth's atmosphere is pretty thin, 90% of its mass is below 10 miles, versus a 4000 mile earth radius. So 2D is not a bad approximation, but of course that neglects a whole lot of factors, of which 3D movement is one, but add temperature and physical swings such as clouds and winds.
    Friction drag presumably got the motion started, but then it gets complicated very quickly.
    Jupiter would probably be a better illustration of the problem, we think it is atmosphere a long ways down, so why it keeps spinning with all the dissipative opportunities that provides is a good topic.
     
  6. Jun 18, 2016 #5
    Thanks etudiant, jupiter is a good analog to the situation. Honestly I don't know if the surface rotates at the same angular velocity as the interior of the planet, like ours does, but I assume it would. I guess the problem I have is only understanding things partway. I have always felt this way, and usually want to understand a problem from the big picture all the way down to the smallest components. That's why I decided to become an engineer, haha.

    Anyway, I still don't understand how, if friction drag is pulling the adjacent air which is moving slower than the faster-moving air, the air at higher altitudes must get pulled to a faster tangential speed than the air below it (ie, the air being pulled ends up moving faster than the air which is pulling it).

    Maybe the answer is this... in a fluid, like air, the particles are not all moving at the same speed (the same way that the temperature of a substance is actually an average temperature of the molecules, as the individual temperatures vary quite a bit if I remember correctly.) So in the air at the lower altitudes, which is being pulled by friction force from the earth, some of those molecules are moving slower than average and some are moving faster than average. The molecules that are moving faster than average will continue to collide with the molecules in the higher-altitude air until the higher-altitude air reaches the same angular velocity, which is a sort of equilibrium relationship between all altitudes of the air and the tangential velocities of the individual air molecules.

    That would be my best guess at the situation. The earth as a whole spins at the same angular velocity because earth as a whole is held together by gravity and can be simplified as one free-body object. Again, not sure if this is the best way to look at it but I'm going to keep asking different forums until someone hits the answer on the bullseye to where I understand it a million percent.


    Which means, yes, I want to understand it times 10,000 o0)
     
  7. Jun 18, 2016 #6

    Drakkith

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    Because it's not moving linearly, it's moving in a circular motion. If a part of the atmosphere closer to the surface pulls on an adjacent layer that's just a bit further out, in order to keep up with the inside layer the outside layer has to move faster. If it doesn't move faster, then its angular velocity is less than the inside layer, and thus there's still friction. So the only way to reach a point where friction is no longer acting on the outside layer is for it to move at the same angular velocity as the inside layer. It must do this, otherwise the inside layer will just keep pulling on it until it does.

    Also note that the atmosphere was formed with the rest of the Earth, and has already been rotating the entire time anyways. There was a never a point where the atmosphere was stationary and the Earth had to accelerate it up to speed.
     
  8. Jun 19, 2016 #7
    Drakkith thank you for your reply. I guess what it comes down to is that the motion of the atmosphere cannot be thought of in terms of being linear, because it makes sense when you say

    but it only makes sense if we think about it as circular motion. I feel that the air particles and other particles in the atmosphere would each be moving in a straight line, as they do inside a balloon, for example, but I guess this is the exact leap that I don't truly understand. I can repeat it and I understand the concept of it, it just doesn't sit right with me intuitively for some reason. Either way, thank you for your reply and everyone else who answered too.
     
  9. Jun 19, 2016 #8

    Drakkith

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    Of course. If the motion isn't circular motion, then my explanation doesn't apply.

    You can't really think of this in terms of how individual air molecules behave. It's a result of the collective behavior of many particles.
     
  10. Jun 19, 2016 #9

    FactChecker

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    I think you have over-estimated the increase in velocity at the higher atmosphere. The radius of the earth is about 21,000,000 feet so the radius at 21,000 feet is only 0.1% higher. That would only add about 1 mph at 21K feet. With everything else that is happening in the atmosphere, maybe there is no overall increase in speed but it is not noticeable.
     
  11. Jun 19, 2016 #10

    D H

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    Venus is another good example. Surface winds on Venus are rather small compared to those on Earth. Things however get rather weird in Venus's upper atmosphere, which rotates much, much faster than does Venus itself.

    We see this to a limited extent in the Earth's atmosphere. Like Venus, the Earth's upper atmosphere (i.e., above the stratosphere) rotates a bit faster than does the Earth. This is generally attributed to the upper atmosphere's diurnal bulge. Unlike Venus, the super-rotation of the upper atmosphere is rather small, perhaps 10 to 20 percent faster than the rotation rate of the Earth as a solid body.

    Venus's rotation rate is so very slow that the concept of a diurnal bulge (as an explanatory mechanism) doesn't quite make sense. If you want to make a tiny dent in science, explaining Venus's weird atmosphere might be a good place to start. You'll need to fully understand atmospheric dynamics to do so, and if you gain this knowledge, this will put you on a footing with a number of very good scientists who are trying to explain Venus's weird rotation rate.
     
  12. Jun 19, 2016 #11
    FactChecker - good catch. I knew that the increase in tangential speed wouldn't be huge, but I didn't expect it would be as low as 1 mph. Even if the upper atmosphere didn't spin at the same rate as the lower, it might not be noticeable if the difference between thrm is that low.

    DH - that is very interesting. I know that He us has all kinds of violent weather conditions like acid rain and volcanism, but I didn't know about the strange behavior of the upper atmosphere. I'm going to have to have a look at that (although I may not put much of a dent in science just yet, lol)

    And Drakkith - again I appreciate your reply. To be honest, I do not intuitively understand what is precisely causes the circular motion of the atmosphere. Assuming it is significant (1 mph wouldn't be), my understanding is still that friction drag would cause whatever slow-moving particles were rotating to speed up due to collisions of the tiny particles. And since air and other constituents of the atmosphere are tiny particles, is it not accurate to think about it in those terms? Anyway these tiny collisions would cause all levels of the atmosphere to rotate with the same angular velocity, although it is undeniable that this means that the upper atmosphere is moving faster (in linear terms) than the lower.

    I am not trying to frustrate you, and I apogize for running in circles. I learned about circular motion in my mechanics class and it makes perfect sense for things like ferris wheels, motors, windmills and car tires. Those are all rigid objects which are connected physically and can be treated as isolated free body objects (in oversimplified terms.) This still seems inherently different to me than a fluid suspended above a globe, where the nature of the movement of the individual particles should be linear, because they actually travel along linear paths, not circular ones. They might follow a circular path on average, but if you look closer, the particles are actually moving in tiny linear paths until they bump into other molecules. Is that wrong? Please correct me if it is.

    I do appreciate each response about this and I guess my question would be, if thr motion of atmospheric molecules is linear, why does that result in the atmosphere as a whole moving in circular motion?

    I understand if you guys give up on this thread, haha. All serious replies are welcome.
     
  13. Jun 19, 2016 #12
    I like to think of the atmosphere as if the Earth was completely covered with water.
     
  14. Jun 19, 2016 #13

    FactChecker

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    Gravity pulls every molecule toward Earth.
     
  15. Jun 19, 2016 #14

    Drakkith

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    Not quite linear. Gravity is pulling them down, so they will move in a very, very shallow curved path in between collisions.
     
  16. Jun 19, 2016 #15

    A.T.

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    By radius I obviously meant the distance from the rotation axis.

    If the layers don't have the same angular velocity, then you have relative motion between the layers, and friction which opposes it.
     
  17. Jun 19, 2016 #16

    CWatters

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    In the OP you say that the earth pulls the bottom layer of the atmosphere around. It doesn't need to do any "pulling" as there is nothing trying to stop the atmosphere rotating. You might as well say that the atmosphere is pulling the planet around.
     
  18. Jun 19, 2016 #17
    I do not know much about the history of the Earth but as I understand it, at one time the Earth was molten and condensed to a solid. Then the crust developed (I am not sure how, so I have to be vague. Anyway the atmosphere came from the Earth in some manner. As far as I know the atmosphere did not come directly from outer space. If the atmosphere did come from meteors etc, then maybe the atmosphere developed over time, enough time to have acquired the Earth angular velocity. . To make a long story short, the atmosphere as generated from the Earth (which I assumed was rotating). Consequently, the atmosphere has roughly the same angular (and linear) velocity as the Earth. By the way, the Earth once rotated a lot faster. Whatever processes slowed the Earth down also slowed the atmosphere down, whether the atmosphere was generated before the slowdown or not
     
  19. Jun 20, 2016 #18

    Drakkith

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    The atmosphere was formed through several different processes. Initially the dust and gas of the solar nebula left over from the creation of the Sun collapsed to form the planet, which includes whatever atmosphere it had at that time. Since then there has been outgassing from the Earth's crust, emissions from living organisms, and all sorts of other processes that have generated the atmosphere we have today. Either way, you can say that the atmosphere has been rotating since the formation of the Earth, as both the initial atmosphere and essentially all the material that would eventually make up the modern atmosphere has been rotating since that time.
     
  20. Jun 20, 2016 #19
    Of all the responses, I like this one the best. Thank you Jim60, this is a very good way yo think about gases surrounding the earth as their behavior in terms of rotating with the earth is not so different from the behavior we might see if the earth were covered with water.

    Thanks to drakkith and factchecker, yes gravity from the earth exerts a gravitational force on all matter in the universe, and so obviously it will pull the gas molecules downward as they move about randomly.

    And CTwatters, I meant that the atmosphere continues to rotate around the earth with the same angular velocity because of the laminar friction between the earth and the atmosphere. Since the atmosphere formed with the earth and resulted from outgassing, it has always had the same angular momentum as the earth, but if it didn't, it would be forced by the earth to rotate at an angular velocity which was closer to that of the earth due to the much higher momentum of the earth. It's more in line with the idea of a non-rotating atmosphere around a rotating earth, where winds would be as high as 1000 mph and the atmosphere would eventually begin to spin as momentum was exchanged between the earth and the surrounding atmosphere. More like a thought experiment.

    I feel that I have a better understanding of why the atmosphere rotates along with the earth, and I appreciate all you guys' responses. Feel free to add more if you like.
     
  21. Jun 20, 2016 #20

    CWatters

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    Friction isn't necessary to make the atmosphere continue to rotate with the earth. I don't think there is anything trying to make it slow down.
     
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