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There have been a lot of sci-fi shows recently using the "rotating space station" explanation for gravity on space stations.

After watching these videos:

http://www.youtube.com/watch?v=49JwbrXcPjc&NR=1
http://www.youtube.com/watch?v=_36MiCUS1ro

I was wondering what would happen, if you were facing the direction of rotation, while standing on the "floor" of a rotating space station and tossed a ball "up". From the video it looks like the ball should land in front of you. Is this in fact what would happen and if you dropped a ball would it land behind you?

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Yes, the ball would land in front of you.

If you watch from outside the space station, the ball moves in a straight line at constant speed while you move in a circle at constant speed. That means the distance the ball takes to get from point A (where you release it) to point B (where it hits the floor) is shorter than the distance you take.

Further, since you threw the ball, it's going faster than you.

The ball is going a shorter distance at a faster speed, so it gets there ahead of you. From your point of view, the ball must curve forward in order to get ahead of you, so that's what you see.

Some time ago I made a Mathematica Demonstration where you can see the curved path the ball takes, varying the ship's radius and rotation rate as well as how hard you throw the ball. See here: http://demonstrations.wolfram.com/PathOfAProjectileInARotatingFrame/

You can read a full derivation of the equations on a doc I put on Scribd around that time.

http://www.scribd.com/doc/3880728/rotating-ship

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What you indicate appears to be the case. You want to minimize the Coriolis effect in any volume of space, which requires making the rotating station large.

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