How would a game of (American) football work on a space station generating artificial gravity by using spin?

Question

Using rotation to generate artificial gravity is pretty common in sci-fi. I know the TV show "The Expanse" features it on the Mormon's vessel. I also remember a small-scale rotating space station on some 80's, could have been 70's, show from way back where he was running around the space station as it spun. I also remember it from a book from when I was a preteen. I also just realized that's what the halos are in the video game series "Halo", aren't they?

For those that don't understand what it is I am talking about, it is like the carnival ride the Gravitron (a.k.a. Starship, Starship 2000, Starship 3000, Starship 4000, Starship Area 51, Starship Gravitron, Starship Exodus, Alien Abduction, Alien Invasion, Twister, Devil's Hole, Area 51, Flight To Mars, and Enterprise per Wikipedia). This ride stands riders up in a circular, spinning room with their backs to the wall on plates that can slide up. When the room starts spinning, centrifugal force pins the riders to the sliding boards on the wall, which then lifts the rider up. Some riders will turn themselves sideways or upside-down pinned to the wall by the spin of the room.

A space station working on this principle would be MUCH bigger. And, instead of having their backs to the wall, they would have their feet to the wall, standing upright. So, I was just thinking, how would football work on one of these space stations?

What I mean is, how would passes be effected? In these spacecraft, it's my understanding that the perceived gravity lessens as you go towards the center. So, does this mean passes would go much higher? And does this mean that tiny increases in throw speed which cause balls to travel higher altitudes that would have ever increasing feedback on distance as altitude increases? Or, I think what is more likely, is that the ball will travel travel in a straight line from where it is thrown. Which, if this is correct, I think only short passes that are angled downwards would work, because passes angled upwards could only be caught if the ship is spinning so fast that the spin takes you to where the ball is landing on its straight path. At least, I THINK so.

Further, would it matter if a throw went with or against the spin of the station? I think this matters because it will give you a different initial angle of throw, but the ball will travel in a straight line after that. And, how about throws that go across the spin. I am aware of the Coriolis Effect from my time in the Army dealing with ballistics. I imagine something similar would have some effect in a rotating ship.

UPDATE: I found this StackExchange answer which I believe answers this question, I just need some clarification. So, it doesn't matter if I throw a ball with or against the spin of the station, it will always have the ball curve towards the "floor" of the craft? But, I am unclear whether it would matter or not if I am throwing with the spin of the craft versus against the spin of the craft. Because the ball would curve forward when facing the spin, I believe this means you have to throw with less force when facing the spin, versus against the spin. Also, would the ball fly at a constant speed? Because, the "gravity" would no longer be affecting the ball once you released it, unlike gravity on Earth, right?

Next, how about runs? If you were running perpendicular to the spin, would you feel it spinning, or would that motion all be constant and have no effect? What about juke moves? Would juking with or against the spin of the station matter, as in would more/less weight be applied with or against the spin of the station, or again, would your motion be constant?

Now, I imagine something that matters in all of this is how big the spinning station is. I think this matters because a small radius ship of 20 or so meters like the one on that old TV show/movie would have to spin much faster than a ship/station that was 10 or 1,000 miles in radius. Actually, I am pretty confident of it given the Mathematica presentation on the answer to that aforementioned Stack question. So, my question is, what are these effects on ships of 5, 25, 50, 100, and 1,000 miles radius? And, the angular velocity/acceleration (not sure which) would be whatever creates Earth-like gravity. Basically, would 1 g of this artificially-induced gravity behave the same as real gravity, if not, how does it differ?

Finally, my ultimate question is how big would a ship need to be for these effects to be negligible? And, by negligible for the throws, I mean the spin would effect the ball by a foot or less every 20 yards. And for the runs, I just mean that the extra pressure from the spin, if there is any, doesn't cause unbearable stress on the joints.

I hope these aren't stupid questions. And, I hope this has enough different from the question I referenced to warrant being its own question. Thanks for any help.

This question was closed because it lacked focus. I am not sure how much more focus I can give. The question boils down to this: "How would the physics of an American football game on a rotating space station differ from the physics of an American football game on Earth." I guess, the rest is just fluff that can be deleted if someone sees fit.

Answer 1

I made an analysis of Coriolis effect for a cylindric ship https://physics.stackexchange.com/a/694361/195949.

Using the results for a ball hit exactly upwards, with an initial velocity to reach 30m high, that means about 2.5s of travelling time. If we wish a deflection of $0.15m$ after reaching the maximum, what means $0.30m$ after coming back to the ground, $$0.15 = \frac{1}{3}\omega^2t^2\implies \omega = 0,27rd/s \implies T = \frac{2\pi}{\omega} = 23s$$ where $T$ is the period of revolution.

Considering that we wish $g$ for the acceleration, $$g = \omega^2R \implies R = 134m$$.

Answer 2

In 'Interstellar", the movie, you see the hitter hit a ball fully. The ball goes in a straight line and a window up on the inside of the cylinder station is hit. The ball follows a non-parabolic trajectory seen from the inside. If you hit the ball with the right horizontal velocity (wrt the inside local ground), the ball will rotate around the cylinder on constant height. If you give the ball the same speed as the speed of the rotating cylinder ($\omega R$), but opposite in direction, this will happen. Like a ball on Earth will stay on one height if you hit it with the right horizontal velocity (ignoring friction). If you let a ball go from your hands, it will have a linear speed and touch the ground a bit behind you. All objects in the air travel with constant momentum, with you accelerating wrt to them (but with constant speed. So it looks as if a free object moves in a weird gravity field. And object on the center line of the cylinder will stay put there if it has zero velocity.

Interstellar baseball

It does matter if you throw the ball against the spin direction or along it. Ic you throw it against the spin and give it a velocity that is opposite to its tangential velocity, the ball will be at rest as seen by an observer outside. This means the height of the ball will be constant wrt to the ground in the cylinder. If you throw it in the spin direction it will always hit the ground.
A ball shot upward can even accelerate upward again and arrive on the other half of the cylinder. If you give the ball a velocity so the tangential velocity is canceled and seen from outside it has a linear velocity towards the center of the cylinder then dependent on that velocity, it will hit the cylinder ground after a weird motion as seen from the inside. As you can imagine. If it has no velocity it will rotate around the center. I the velocity towards the center is small (as seen from the outside) the ball will rotate in smaller and smaller circles as seen from the inside, with the same angular velocity (so decreasing linear velocity). After going through the center, the ball will start moving on a circle with increasing radius again and hits the ground with a velocity that is the sum of its linear velocity and the tangential velocity of the ground rotating around the center. Can you imagine? Would be nice to visualize.

The bal, if thrown against the spin direction with high enough speed and an upward component wrt the ground inside, wil spiral into the center and spiral out again from it. Pretty weird! If you throw it in the same direction as the spin, it will hit the ground without spiraling the center.