Another Rotating Cylinder Problem - explain from moving frame view
- From: David <dseppala@xxxxxxxxxxxxx>
- Date: Fri, 14 Apr 2006 13:02:39 GMT
Can anyone explain this rotating disk problem from the point of view
of a moving observer?
In the rest frame let there be two rotating disks of diameter D
perpendicular to the x axis. Let the distance between the disks be L.
Let there be a rotating cylinder of the same diameter and length
connecting these two disk. Let the disks be massive and made out of
steel and let the cylinder be made out of wax. Let the cylinder and
disks rotate at one revolution per second.
Let there be a frame moving along the x axis relative to this rest
frame with some V. Let L and V be such that simultaneous events
measured in the moving frame at each disk (separation L) are measured
as a half- second time interval in the rest frame. At time t0 as
measured in the moving frame a thin straight wire is simultaneously
attached to the two disks at the top position of each disk and along
the top of the wax cylinder. This is a straight line in the moving
frame, but spirals around the cylinder making a half revolution as
viewed in the rest frame.
Now very slowly the tension of this wire is increased - the wire is
stretched. This means the wire is very slowly approaching a straight
line as viewed in the rest frame. As the tension is increased this
wire cuts through the wax cylinder. Eventually the wire becomes a
straight line and any further stretching of the wire does not change
its shape.
As viewed in the moving frame the wire is a straight wire on the
surface of the cylinder rotating with the cylinder before we start
stretching the wire. Now as the wire is stretched the center point of
this wire eventually touches the center of the rotating cylinder (the
x-axis) as the wire slices through the wax. Can anyone explain as
viewed in the moving frame why the center of this straight wire cuts
the wax all the way through to x-axis as the wire is stretched?
If you post an explanation, does the same explanation work when the
straight wire is simultaneously attached as measured in the rest frame
and then the wire is slowly stretched? That is, the wire is stretched
and stretched but it never cuts into the wax eventhough it spirals
around the cylinder as viewed in the moving frame.
This physics result of SR seems non-sensical to me.
Thanks,
David Seppala
.
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