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slick_willy

- 21

- 2

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?