Some clarifications --

wrote:
Tom Roberts wrote:
wrote:
...which I posed as an ordinary corkscrew rotating along its
axis, and I made the claim that the corkscrew must be straight
in some frame. As Todd corrected me, this could only happen
if the corkscrew had a very long "pitch", or a very high rate
of rotation, or both.

A normal corkscrew won't do, you need one of fixed pitch, and it must
lie on a cone with apex at its point where it is driven to rotate. That
is, it is a helix with linearly varying radius, having zero radius at
its point (where it is driven).

Thanks, Tom, this is very interesting.

As you can see later in my post, I do reach the conclusion
that my scenario wouldn't fly, owing to too much stress
(without compensating strain) requiring the speed of sound

i.e. if we gave it enough strain to keep its Young's
modulus within theoretically allowed limits, it wouldn't
stay helical

to exceed c in the material. Was this a correct statement,
albeit one I didn't attempt to justify by calculation? In
other words, what is it that forces the conical shape.

Also, I while do see why your conical helix would have to

while I do

spin mounted on some exceedingly massive base (to provide
the momentum necessary for a stable axis) I don't see why
it would have to be *driven* -- apart from the question of
gravitational radiation, of course. Is there some other
reason for energy to be lost here?



But assuming we could construct such a corkscrew, there is
still a problem in the moving frame: we would have a perfectly
straight rod pulling itself along in a helical path by its
own bootstraps, as it were, in violation of our momentum
conservation laws.

No. The driving force in the initial frame will have tangential
components that must conserve momentum; they will make momentum be
conserved in any other frame, including the one in which the corkscrew
is a straight rod (angled relative to the axis around which it rotates,
of course, and driven from the point it intersects the axis).

That much I see.

Actually, what I see is that given a sufficiently massive
mounting (and a forgiving bearing) you can spin an angled
bar by one end so that it describes a cone, without violating
any conservation laws. But once it's spun up, this does not
require any tangential component of force within the bar or
the mounting, as far as I can see.


Thanks again for any further info you might suggest.

Particularly any modern references on this sort of thing,
as Tolman is, for all its virtues, old.