Sup Broskies,
Listen, I’ve really been bottling my mind on this one. Let’s say I have a hot air balloon and I stay up in the air, in the same piece of sky, for 24 hours. Would I travel around the world?
Thanks,
Joey from New Jersey.
In the same sense that you do that by standing on the ground, yes.
In a balloon, you are bouyant, so you move with the air. The air is generally rotating along with the earth, so if there was no wind or moving air masses, no matter how long you stayed up, you’d remain over the same spot on the earth.
There usually is wind, both localized gusts and the large moving air masses. So you would go anywhere the air goes, which would not be around the world in 24 hours.
Would that be regular or diet?
And if I’m correctly interpreting the OP . . . if that were the case, we’d be experiencing huge winds all the time, more-or-less 1,000 mph at the equator.
If the world worked as the OP seems to believe it does, you could jump into the air for a second and find yourself half a kilometre away when you came down*. 
*at the Equator
You already have velocity in the direction the earth is rotating of the same speed. So when you “hover” you still have a pretty fast velocity which matches the earth’s rotation. To literally stay in the same spot so that the earth rotates below you, you’d need to be creating an equal velocity in the opposite direction to the rotation of the earth - which is pretty fast. Fast enough, in fact, to circumnavigate the earth in 24 hours - I’ve not heard of a balloon which can achieve those speeds.
Think of it on a smaller scale as like being on a merry-go-round - you are rotating at the same speed as the ride. To hold still relative to the ground (as opposed to the ride) you’d have to run around it in the opposite way it’s rotating at the same speed it’s rotating.
Or like being on an escalator or moving walkway.
If you jump “straight up” you only appear to be going straight up to you relative to the moving surface below you (earth, merry-go-round, escalator or whatever); you are actually moving horizontally also at the same velocity you were when “stationary” on that surface. Which is the same speed that the surface itself is moving at.
Think about it. The earth moves at about 1000 mph (at the equator, 700 mph or so at the upper east coast) and if the atmosphere stayed in place there would be a huge amount of friction. The molecules in the atmosphere would raise hell with trees and anything that wasn’t bolted down. Birds would have extraordinary migratory issues and flies, mosquitoes, and bees would all be endlessly circling the earth.
Gravity and momentum have pretty much given us what we experience today, with our mild weather patterns compared to what you envision.
Also, if that was the case we wouldn’t need airplanes to get to Australia.
There was a conceptual art piece about standing still at the North Pole
Inertia is a wonderful thing.
You’re spinning 0-1,000 miles per hour around the Earth, depending on lattitude.
The Earth is orbiting the Sun at roughly 66,000 miles per hour.
The Sun is orbiting the center of the Milky Way at approximately 483,000 miles per hour, so we’re whizzing around our galaxy at roughly 134 miles per second.
The Milky Way is moving through the Universe at a speed which is hard to estimate, but is significantly faster than our orbit of the Milky Way.
So if you could overcome the referential intertia of the object you’re standing on simply by floating above it, within seconds you’d be well outside of the atmosphere and we’d all be killed by the act of jumping into the air.
I think this explains it best.
If you could jump into the air for a second you wouldn’t find yourself half a kilometre away when you came down, you’d find yourslef playing for the Lakers: that’s a 48" vertical leap you got there, son! 
All the previous posts are true*, of course, but I find it most useful to think about it thus:
The important thing is, what were you doing just before you jumped? (Or, just before the balloon took off?)
Answer: You were stuck to one spot on the Earth (by gravity – that is, attraction toward the Earth’s center.) Anything you do after that has to use* that *as your starting point.
So, if you insist on using the axis of the Earth’s rotation as your frame of reference, which is what you insist on doing, even though there’s no particularly good reason to do so in this case (keeping in mind that, in the most general sense, any frame of reference is as “true” as any other), then yes, your movement, both before and after the jump/launch, will be at 1000 mph or whatever.
Similarly, if you trace the path of someone walking down the aisle of a jet airplane from the perspective of standing on a spot on the ground, the tracing will resemble the tracing of the jet itself almost exactly. Yet the person walking in the jet senses nothing but their own, walking-speed movement.
(*Although you have to be careful to not over-emphasize the “stuck in the air column” part of it, as one poster did. It’s better to think of it as both the balloon and the air column as more or less stuck to the Earth’s surface because, again, they both started out stuck to it. Not completely, of course – on a continental scale, air molecules – prevailing winds – really do move in a direction influenced by the Earth’s rotation, but friction and gravity – the “partial stickiness” to the Earth’s surface – means that the air masses typically move around twenty or thirty miles an hour, not five hundred or a thousand.)
Somebody already answered that you would be going the same speed as the Earth. But my question would be, wouldn’t the balloon eventually slow down and stop in comparison to the earth below? It doesn’t but I don’t know why.
My father was an airline pilot and he had a co-worker who had a hot air balloon. I found the man to be a total ass prick. His basket had some kind of leather lining at the top, so this idiot decided that one had to wear leather gloves up to the elbows to touch his precious gondola. There is a lot of work involved. Since the pilot of the balloon cannot drive it forward, a car had to follow us around. My father got pissed at me because I did not want to go, Caddyshack was on TV. Unfortunately for him, he had the only boy who cared not one whit about being off the ground.
The balloon comes to a stop relative to the surrounding air.
It takes force to change the velocity of an object. For a balloon, the only significant force is friction/pressure from surrounding air. If it’s moving relative to the surrounding air, this force tries to stop it (relative to the air).
Because the balloon is in the air, and the air is still frictionally and gravitationally “stuck” to the surface. It flows around a little, which we call “wind,” but air pretty much stays attached to the ground.
If it did not, then we would be experiencing 1000-mph winds all the time as the Earth rotated under its motionless atmosphere.
The previous two posts answered your question just fine. I would add: Why do you insist on privileging the axis of rotation of the Earth? It’s only slightly more logical to use that as your frame of reference, as it is to, say, use the motion of the Earth around the Sun, or the motion of the Milky Way Galaxy through the Local Group. Does the balloon “slow down” relative to either of *those *“motions”? Not at all.
The question the OP asks is only very slightly more “logical” than asking, “when I jump in the air on the side of the Earth which happens to be facing away from the direction of the Earth’s path orbiting the Sun, why am I not whisked up into space, waving the Earth goodbye as it continues on its path without me?”
Well, that’s just it. It isn’t without you. It’s with you, because you started out part of it. Stuck to it. So any “motion” the Earth experiences relative to any other object – the Sun, the center of the Milky Way Galaxy, etc. – will be equally experience by me as well, regardless of whether I’m jumping or just standing.
I’d make you wear leather gloves if you wanted to touch MY precious gondola.
This detail makes me smile.
I think most people don’t intuitively grasp that the earth’s atmosphere is rotating with it, suspended in space. Once they think about it, of course it makes sense, but many of us envision the rotating globe without also envisioning the clouds with it. It’s the fault of those old newsreel intros.