A miner sat inside a small rail car underground should move in his rail car by the movement of the ground above him, in the real world of course but in the magical world of the science way, something stops that happening. What?
So, a guy in a rail car should move underground because of the ground above him. What? Everything is moving. At that location, he is moving, the ground above him is moving, the ground below him is moving at the same speed.
Everything you've said is correct, except you're using that word again - relativity. It's obvious now that you're just misusing the word, and don't actually think that the speeds we are moving at are relativistic speeds.
I should also note that the massive planet rotating, say, 10x as fast as Earth, with the speeds at the equator being 5M mph, you need to also consider the gravity of such a large beast. We'd be surely crushed, and even more-so at the poles.
Yes, we would be crushed. I know that. Analogy fails at that point. Pretend gravity is as strong on that surface as on the surface of the Earth.
As someone else stated, relativity does not have to do with time slowing down and such. It simply means, if everything is moving at 1030 mph in one direction, then no net movement is detected. They all might as well be standing still. What I was saying with the rotation speeds, a sharp curve in rotation tries to change our natural direction of movement. Like a merry go round. You are constantly being flung out side because of the super fast rotation, but you are holding on to go in circles. If you let go, you will fly tangent to the point at which you let go.
The Earth is simply not spinning fast enough in proportion to itself to fling us off. It takes 6 house to even go a quarter way around the circle of rotation. That is figuratively like standing on a merry-go-round that spins one full rotation every 24 hours. Now, we are on a giant merry go round (Earth), but it still is rotating once every 24 hours. At one point are momentum wants us to go 1030 mph in a direction tangent to the Earths surface. In one hour, our direction will change by 15 degrees. Every minute, our direction changes by 0.25 degrees. This is hardly enough of a change to notice.
However, on something that spins once a second, as that oblivious FE guy posted, your direction changes by 180 degrees in half a second. That is extremely noticeable.
Please note: Everything I posted is in relation to someone standing on the equator.