SR view of rotating cylinder collision
dsep...@austin.rr.com
In a rest frame there are two rotating cylinders whose longitudinal
axes are aligned along the x-axis. These cylinders are moving along
the x-axis toward each other with velocity V. After they collide,
observers in the rest frame can determine whether the cylinders were
rotating at the same rate or at different rates when the collision
occurred by measuring the deformation of the colliding surfaces. The
surfaces can be at rest wrt the frame when these measurements are
done.
Now let the two cylinders rotate at the same rate. After they
collide, observers in this rest frame can determine that the rotation
rates of the two cylinders were equal when the collision occured.
Again, these measurements can be done when the surfaces are at rest
after the collision.
Now if we're in a frame moving along the x-axis that has zero velocity
with respect to the longitudinal axis of one of the rotating cylinders
before the collision, according to Einstein we measure that the
rotation rates of the two cylinders are not equal prior to the
collision. Can observers in this moving frame detect after the
collision that the two cylinders were rotating at different rates
before the collision as they had previously measured prior to the
collision? If so, how can they examine the same surfaces after the
collision has occurred and come to a different conclusion than the
rest frame observers. If they can't detect that there was a
difference in rotation rates, how do they reconcile that with their
measurement that the rotation rates of the two cylinders were
different prior to the collision. Assume we have ideal measurement
devices.
Thanks,
Dave Seppala
Dirk Van de moortel
<dsep...@austin.rr.com> wrote in message news:43c6d591....@news-server.austin.rr.com...
> Can anyone explain this SR problem.
>
> In a rest frame there are two rotating cylinders whose longitudinal
Ha.
David Can-Anyone-Explain-This---Yes-But-I-Am-
Not-Interested-In-Your-answer Seppala has returned
after his six months leave.
This time our autistic friend has brought his rotating cylinders
again, like on 27-Oct-2001, 13-Mar-2002, 23-Mar-2002,
19-Jul-2002, 10-Dec-2004, 8-Mar-2005, 27-Aug-2005
http://groups.google.com/groups?q=author%3Adse...@austin.rr.com+%22rotating+cylinder%22
Dirk Vdm
Martin Hogbin
Give it a rest David.
Martin Hogbin
Sue...
that the rotation rates of the two cylinders were
different prior to the collision. >>
Easy!
http://farside.ph.utexas.edu/teaching/jk1/lectures/node13.html
http://arxiv.org/abs/physics/0204034
http://web.mit.edu/8.02t/www/802TEAL3D/teal_tour.htm
Sue...
Bilge
Tom Roberts
> [...]
Your confusion is related to your implicit assumption that the cylinders
are continuous structures. Continuous structures pose numerous problems
for relativity. Note, however, that no such continuous structures have
ever been observed, and there is good reason to expect that none exist.
When one realizes that the cylinders are made up of atoms, one also
realizes that the collision of the cylinders is really a myriad set of
pairwise collisions between atoms[#]. For each such collision, it is
most naturally analyzed in the center-of-momentum frame of the two atoms
involved. All observers will agree on which frame that is, and on the
subsequent description of the collision between those two atoms. This
obviously applies to all such pairs.
[#] at least to lowest order. The argument applies to any
multiple-atom collision.
Tom Roberts tjro...@lucent.com
Todd
Let me see if I understand your question.
In frame A the cylinders move toward each other along the x-axis with equal
speeds and equal rates of rotation. They collide and stick together such
that they lose all x-component of velocity but they do not change their rate
of spin. Thus, there are no ''shearing'' forces between the surfaces of
contact during the collision. Therefore, no shear strains are created in
the cylinders. In other words, when a small region of the surface of one
cylinder collides with a small region of the surface of the other cylinder,
the forces between the regions act only parallel to the x-axis (no
shearing).
Inertial frame B moves along the x-axis with one of the cylinders (before
the collision). In this frame the cylinders do not rotate at the same rate
before the collision (due to time dilation effects). After the collision
they rotate at a common rate (which is intermediate between the initial
rates of spin of the two cylinders). Thus, when a small region of the
surface of one end of one cylinder collides with a small region of the
surface of the other cylinder, the two regions have different components of
velocity perpendicular to the x-axis just before they collide. But they end
up having equal components of velocity perpendicular to the x-axis after the
collision. Let's call these perpendicular components ''y-components of
velocity''. So it might *seem* that when the small regions collide and
stick together, the region that initially had the greater y-component of
velocity will try to ''drag along'' the region of the other cylinder that
had the smaller y-component of velocity. Thus it would *seem* that the
surfaces should exert non-zero y-components of force on each other (as well
as non-zero x-components of force). That is, they should exert shearing
forces that would create shearing strains within the cylinders.
Thus, in frame A there are no shearing strains but in frame B it would
*appear* that there would be shearing strains. However, the existence or
non-existence of shearing strains must be independent of the frame of
reference. So, there appears to be a paradox.
Is this the essence of your question?
Todd
dsep...@austin.rr.com
Yes.
David
Todd
<dsep...@austin.rr.com> wrote in message
news:43c94a1...@news-server.austin.rr.com...
It turns out that there are no shearing forces in either frame. So, both
frames agree that no shearing strains arise during the collision. The
forces of contact between the cylinders during the collision are entirely
parallel to the x-axis according to both frame A and frame B.
But then, how is it that in frame B the collision causes one cylinder to
slow down its rate of spin while the other cylinder increases its rate of
spin? In other words, in frame B, how can a force acting only in the
x-direction on a small region of surface of contact of one of the cylinders
cause this region to change its y-component of velocity (i.e., have a
nonzero y-component of acceleration)?
In Newtonian physics, a nonzero y-component of acceleration always requires
a non-zero y-component of force. But this is not so in SR. A relevant
exercise is the one that I suggested to you in an earlier thread (''SR and
rates''):
http://groups.google.com/groups?q=%22SR+and+Rates%22+Todd
Unfortunately, what I called the 'rest frame' in the exercise corresponds to
'frame A' here; and what I called 'frame A' in the exercise corresponds to
'frame B' here.
In this exercise, both frames agree that the particles experience only
forces parallel to the x-axis; yet, in one of the frames the particles
experience zero y-component of acceleration while in the other frame they
experience non-zero y-components of acceleration.
Todd