Let’s make it simple: to get an artificial gravity of 0.5 g, you’ll need a radius of 450 meters and a double distance (900 meters) from the counterweight of the spacecraft.
For fun The link distance on the Wikipedia page is 450 meters. This would give a rotation radius of 225 meters. Using the same angular velocity, astronauts would have an artificial gravity of 0.25 g.
I mean, it’s not awful. In fact, the gravitational field on Mars is 0.38 g, so it would be almost good enough for astronauts to prepare for Mars work. But I will stick with 0.5 g of artificial gravity and a 900 meter long link.
What would it be like to slip on a rope?
Without going into too much detail, let’s think about what would happen if an astronaut climbed a cable from the spacecraft to the counterweight on the other side for some reason. Maybe life is better on the other side – who knows?
When the astronaut launches the cable (“I’m calling it” in the opposite direction to the artificial gravity), physics promises that they will feel the apparent weight of the rest of the astronauts on the spacecraft. However, as they rise in the cable, their circular radius (distance from the center of rotation) decreases, and the artificial gravity also decreases. They would continue to feel lighter until they reached the middle of the ligament, where they would feel weightless. As the journey to the other side continued, the apparent weight began to increase, but in the opposite direction, pulling toward the other counterweight of the link.
But that’s not very exciting for a film. That’s something that’s so dramatic. Suppose an astronaut starts near the center of rotation with very little artificial gravity. The link slowly rises instead of “down” if what is left is false gravity pull her down? What speed would it take to reach the end of the line? (It would be like falling to the ground, except that as it “falls” the gravitational force would increase as it went from the center to the distance. In other words, the more it falls, the greater the force on it).
As the force on the astronaut changes as it decreases, it becomes a more difficult problem. But don’t worry, there is an easy way to get a solution. It sounds like a scam, but it works. The key is to divide the movement into small chunks of time.
If we consider its motion in a span of just 0.01 seconds, it does not move very far. This means that the artificial force of gravity is mostly constant, as its circular radius is also approximately constant. However, if we assume a constant force in that short period of time, then we can use simpler kinematic equations to find the position and speed of the astronaut within 0.01 seconds. We then use his new position to find new strength and repeat the whole process again. This method is called numerical calculation.
If you want to model the movement after 1 second, you would need 100 of those 0.01 time intervals. You can do this calculation on paper, but it is easier to do a computer program. I will take an easy exit and use Python. You can see my code here, but this would look like. (Note: I made the astronaut larger in size so I could see it, and this animation works at 10 times the speed.)
To glide down the cable, it takes the astronaut about 44 seconds to glide at the final speed (in the direction of the cable) at 44 meters per second or 98 kilometers per hour. So this is it no safe thing.