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Re: rotating space station



Did you factor in the fact that the 'horizontal' speed of the ball will be
less than the tangential speed of the floor since it is closer to the center
of rotation? The rotational velocities of the ball and floor are the
same--not the linear velocities.

Rick

----- Original Message -----
From: "Carl E. Mungan" <mungan@USNA.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, September 28, 2000 5:37 PM
Subject: rotating space station


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/