Re: Threaded shaft length contraction paradox/contradiction?
- From: David <dseppala@xxxxxxxxxxxxx>
- Date: Sun, 15 Apr 2007 20:48:20 -0500
On 15 Apr 2007 06:03:10 -0700, "Phil" <cms_pg@xxxxxxxxxxxxx> wrote:
On Apr 15, 4:47 am, David <dsepp...@xxxxxxxxxxxxx> wrote:Although Dirk calls one of my postings from awhile back some sort of
Can anyone explain how to apply Einstein's notions of space and time
to the following length contraction problem?
Let there be a long threaded shaft along the x-axis, or in other words
a very long threaded bolt aligned along the x-axis. In the rest frame
of this shaft, let there be 1000 threads per meter along the shaft.
Let there be a nut of length L on this shaft that also has 1000
threads per meter. Initially, let both the shaft and nut be at rest.
Now start spinning the nut. Because of the nut's spin, the nut
travels down the shaft at some velocity V.
As measured in the rest frame of the shaft, per Einstein, the nut
should span a length less than L, but that would mean the 1000 threads
of the nut span less than 1000 threads of the shaft. Or as measured
in the frame that has zero velocity with respect to the nut's motion
along the length of the shaft, the 1000 threads of the nut span a
length on the shaft that has more than 1000 threads. I don't see how
either of these is possible.
If I attempt to make some sort of argument about the nut being
stretched or compressed so that both the nut and shaft always
simultaneously span the same number of threads, then I don't see how
to apply Einstein's notions of simultaneous events in the two moving
frames. If I simply count the number of threads on the nut and then
mark two points of the shaft that span the same number of threads, if
both frames agree that the nut simultaneously spans these two points,
then Einstein's notion of simultaneous events for these two frames
doesn't work.
Thanks,
David Seppala
David,
Nuts and bolts are made loose enough in their fit to spin freely.
Simply isn't possible to spin the nut fast enough for it to get too
tight to spin in the context of SR.
fumble, for relativistic effects to be measureable I pointed out you
can either have high velocities or very long lengths. If we make the
shaft extremely long and the nut extremely long the relativistic
effects will be measureable with very low velocities - hence the nut
doesn't have to spin very fast for it to spin in the context of SR.
David
Fact is, the thread turn rates.
don't have to be the same in order for a nut to thread a shaft. The
key is the turn rates, the lentgh of the nut, and the looseness of the
fit.
- References:
- Prev by Date: Re: Threaded shaft length contraction paradox/contradiction?
- Next by Date: Re: Threaded shaft length contraction paradox/contradiction?
- Previous by thread: Re: Threaded shaft length contraction paradox/contradiction?
- Next by thread: Re: Threaded shaft length contraction paradox/contradiction?
- Index(es):
Relevant Pages
|
