Subject: What path would an object follow falling through a rotating Earth?

This is related to the question "what would happen if you fell down a tunnel 
that went through the center of the Earth?", but that question does not account 
for the velocity you would have from the earth's rotation.  Imagine if you 
could pass through the earth with no fricition, but earth retained its mass and 
therefor its gravity.  Or, what shape would a tunnel have to be to allow a 
falling object to follow its path without banging on the walls?  It seem to me 
as though you might go into a slighty eliptical orbit inside of the earth.

Re: What path would an object follow falling through a rotating Earth?