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Re: rotating space station



I believe it falls behind. In the rotating coordinate system, two
"apparent" forces are acting. One is the centrifugal force. The other is
the Coriolis force. (Aside: I tend to think the "coriolis force
demonstrations are misleading - they are actually coriolis plus
centrifugal force demonstrations)

So, I agree with you in this respect. However...

Is this different from what would happen on earth? Actually, the answer
is no. Suppose you throw the ball up in the air at the equator. The ball
should land behind you, I believe. One way to think about it this: R is
the ball's distance from the earth's axis of rotation. As the ball goes
up, R increases and omega decreases (conservation of angular momentum) and
thus falls behind. On the way back down, R returns to what it was and
omega returns to what it was but the ball never gets an opportunity to
"catch up" to where it was when it was thrown.

The difference between throwing a ball on earth and throwing the ball on
the space station is that on the space station delta R is larger compared
to R.

----------------------------------------------------------
| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
----------------------------------------------------------

On Thu, 28 Sep 2000, Carl E. Mungan wrote:

Serway "Principles of Physics" 2nd ed. Chapter 5 Question 6:

Consider a rotating space station spinning with just the right speed
such that the centripetal acceleration on the inner surface is g.
Thus astronauts standing on this inner surface would feel pressed to
the surface as if they were pressed into the floor because of Earth's
gravitational force. Suppose an astronaut in this station holds a
ball above her head and "drops" it to the floor. Will the ball fall
just like it would on the Earth?

Detailed (excuse my sarcasm) answer given in the Solutions Manual: Yes.

I think that answer is wrong. From the point of view of an inertial
observer, the "dropped" ball will continue horizontally at a constant
speed equal to the tangential speed of the space station until it
hits the floor. Meanwhile the space station rotates and hence the
component of the astronaut's velocity in the original horizontal
direction decreases. Thus it seems to me that the ball should hit the
floor ahead of the astronaut, and not right at her feet like on Earth.

Am I being stupid? Carl
--
Dr. Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Annapolis, MD 21402-5026 mailto:mungan@usna.edu
http://physics.usna.edu/physics/faculty/mungan/