| Topic: |
Science > Physics |
| User: |
"Ken S. Tucker" |
| Date: |
10 Feb 2006 04:55:50 AM |
| Object: |
Spinning cube question |
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
TIA
Ken S. Tucker
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
10 Feb 2006 12:35:06 PM |
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"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:1139568950.013237.42100@g43g2000cwa.googlegroups.com...
| Is it possible to a spin a cube so that at each corner of the
| cube it experiences the same outward centrifugal force,
| directed from the middle of the cube to the 8 corners?
| TIA
| Ken S. Tucker
Take a perfect cube.
stick a pole through one of the flat centers
through to the other flat center.
Spin the pole, the cube spins with it.
all 8 corners will experience the same centrifugal force.
:)
Tada!
too easy?
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| User: "Sam Wormley" |
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| Title: Re: Spinning cube question |
10 Feb 2006 08:35:47 AM |
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Ken S. Tucker wrote:
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
TIA
Ken S. Tucker
Rotation about an axis through the center of opposite faces.
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| User: "Puppet_Sock" |
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| Title: Re: Spinning cube question |
10 Feb 2006 10:00:34 AM |
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Sam Wormley wrote:
Ken S. Tucker wrote:
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
Why do you ask? What is it you are attempting to get at?
Have you read a Pellucidar book or something?
Rotation about an axis through the center of opposite faces.
Note that this will produce a vector directed radially from the axis,
not from the centre of the cube. It will be the same magnitude for
each corner, just not directed from the middle of the cube. That is
it will be directed, for any given corner, it will be directed from the
centre of the face that corner is on that the axis goes through.
Socks
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| User: "Sam Wormley" |
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| Title: Re: Spinning cube question |
10 Feb 2006 11:02:26 AM |
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Puppet_Sock wrote:
Sam Wormley wrote:
Ken S. Tucker wrote:
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
Why do you ask? What is it you are attempting to get at?
Have you read a Pellucidar book or something?
Rotation about an axis through the center of opposite faces.
Note that this will produce a vector directed radially from the axis,
not from the centre of the cube. It will be the same magnitude for
each corner, just not directed from the middle of the cube. That is
it will be directed, for any given corner, it will be directed from the
centre of the face that corner is on that the axis goes through.
Socks
True, I don't disagree. The outward radial component from the
cube center through the cube vertices will be of equal magnitude.
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| User: "Bruce Scott TOK" |
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| Title: Re: Spinning cube question |
10 Feb 2006 06:25:35 AM |
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Ken Tucker wrote:
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
From an axis from which the corners are equidistant, yes. From the
center (I assume you mean the vector force is directed from the center),
no.
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "Ken S. Tucker" |
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| Title: Re: Spinning cube question |
10 Feb 2006 01:56:32 PM |
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Bruce Scott TOK wrote:
Ken Tucker wrote:
Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the middle of the cube to the 8 corners?
From an axis from which the corners are equidistant, yes. From the
center (I assume you mean the vector force is directed from the center),
no.
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
Thank you Bruce, I'll rephrase the question with Bruce's
suggestion....
"Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the *center* of the cube to the 8 corners? "
Puppet Sock asks "why the question?".
I'm studying spinors, to better understand modern physics,
particularily applied when asked to comment on an article.
I resort to imagination and use models sitting around my
office, like dice, paper airplanes etc.
Let me use airplane terminology as everyone has access
to model something like that, (assume my airplane has
the same length Y as wing span X and rudder height Z,
6 equal axes extended from the origin).
I'm facing North to start.
1st) I'll Yaw the airplane 180 degrees, no Roll or Pitch.
Now I'm facing South.
Easily the wings have an equal Centrifugal Force (CF)
(the CF is always directed from the origin) as
the fuselage, during that manuever, but none on the
rudder.
2nd) I'll Yaw the airplane 180, and Roll 180.
Now I'm facing South but I'm upside down.
During that manuever the CF will again be equal on the
wings and fuselage, but also on the rudder as it now
experienced a 180. (The tricky thing is that the wings
are in the same orientation as before the manuever).
But by using 90 increments the CF along X Y and Z
are apparently equal.
Now I get out a cube, and place the origin in the center
of the cube, and set the X Y Z axes perpendicular to the
centers of the 6 faces of the cube.
I now have demonstrated a maneuver how the center of
the 6 faces can have an equal CF, i.e. symmetrical.
I presume - by symmetry - each of the 8 corners also
has an equal CF, (in disagreement with Bruce :-(.
What I don't yet have is mathematical proof - one way
or the other. If anyone has one give me a hint.
TIA
Ken S. Tucker
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| User: "Puppet_Sock" |
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| Title: Re: Spinning cube question |
10 Feb 2006 03:22:27 PM |
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Ken S. Tucker wrote:
[snip]
"Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the *center* of the cube to the 8 corners? "
As has been pointed out, no. You wanted a proof.
Any rotation must define an axis. The centrifugal force
vector at a corner of the cube defines a line that passes
from the corner to that axis, and is perpendicular to that
axis. It is not possible for the eight corners of a cube to
have perpendiculars to a line that intersect that line at the
same point. It is possible to get four at a time, but not all
eight. Thus it is not possible to spin a cube such that the
centrifugal force vectors at the corners are all directed from
the centre of the cube to the corners.
You see, to get points aligned the way you require, you'd
need them in a plane. You also need that plane to include
the centre of the cube, and for them to be arranged at
the corners of a regular polygon so they are equally
distant from the centre. Though they don't have to occupy
all the corners of that regular polygon.
The corners of a cube are not in a plane.
Puppet Sock asks "why the question?".
I'm studying spinors, to better understand modern physics,
particularily applied when asked to comment on an article.
What makes you think that a cube has something to do with
spinors?
[snip complicated example with air craft]
I now have demonstrated a maneuver how the center of
the 6 faces can have an equal CF, i.e. symmetrical.
No you have not. Just as the eight corners can't have
perpendiculars to a line that meet in a single point,
so too the six face centres can't. Only points in a plane
can have this property. So, no single rotation can produce
equal centrifugal force in the centre point of the six faces.
I presume - by symmetry - each of the 8 corners also
has an equal CF, (in disagreement with Bruce :-(.
What I don't yet have is mathematical proof - one way
or the other. If anyone has one give me a hint.
Now you have. A rather easy to produce one.
Socks
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
10 Feb 2006 03:31:12 PM |
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|
"Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
news:1139606547.218846.224320@g44g2000cwa.googlegroups.com...
| Ken S. Tucker wrote:
| [snip]
| > "Is it possible to a spin a cube so that at each corner of the
| > cube it experiences the same outward centrifugal force,
| > directed from the *center* of the cube to the 8 corners? "
|
| As has been pointed out, no. You wanted a proof.
|
| Any rotation must define an axis.
How about if the rotation is occuring along all 3 planes?
east to west spin,
north to south spin,
and up to down spin,
all occuring at the same rate of spin?
:)
3 rotations all occuring on a different axis that meet
at one point.
:)
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| User: "Gregory L. Hansen" |
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| Title: Re: Spinning cube question |
12 Feb 2006 07:52:46 PM |
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In article <TvidnXje97GDm3DenZ2dnUVZ_tmdnZ2d@comcast.com>,
Spaceman <Realspace@comcast.not> wrote:
"Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
news:1139606547.218846.224320@g44g2000cwa.googlegroups.com...
| Ken S. Tucker wrote:
| [snip]
| > "Is it possible to a spin a cube so that at each corner of the
| > cube it experiences the same outward centrifugal force,
| > directed from the *center* of the cube to the 8 corners? "
|
| As has been pointed out, no. You wanted a proof.
|
| Any rotation must define an axis.
How about if the rotation is occuring along all 3 planes?
east to west spin,
north to south spin,
and up to down spin,
all occuring at the same rate of spin?
:)
3 rotations all occuring on a different axis that meet
at one point.
:)
Rotate the axis of rotation. All eight corners still can't get the same
centrifugal force at each point in time, but they can all get some.
--
"The hardest conviction to get into the mind of the beginner is that the
education he is receiving in college is not a medical course but a life
course for which the work of a few years under teachers is but a
preparation." -- Sir William Osler
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
12 Feb 2006 08:08:04 PM |
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"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:dsoope$888$1@rainier.uits.indiana.edu...
| Rotate the axis of rotation. All eight corners still can't get the same
| centrifugal force at each point in time, but they can all get some.
Ok,
agreed.
:)
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| User: "Ken S. Tucker" |
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| Title: Re: Spinning cube question |
13 Feb 2006 12:58:40 AM |
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Spaceman wrote:
"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:dsoope$888$1@rainier.uits.indiana.edu...
| Rotate the axis of rotation. All eight corners still can't get the same
| centrifugal force at each point in time, but they can all get some.
Ok,
agreed.
:)
Using satellites (sats) we can get a cube with equal centrifugal
forces at each corner...momentarily.
Imagine this, 4 sats are in circular orbit aligned with the equator
90 degrees separate, and 4 sats are in a North-South plane
again 90 degrees separate. The sats will form a cube alignment
every 1/4 revolution.
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| User: "Puppet_Sock" |
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| Title: Re: Spinning cube question |
11 Feb 2006 08:44:15 PM |
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Spaceman wrote:
"Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
news:1139606547.218846.224320@g44g2000cwa.googlegroups.com...
| Ken S. Tucker wrote:
| [snip]
| > "Is it possible to a spin a cube so that at each corner of the
| > cube it experiences the same outward centrifugal force,
| > directed from the *center* of the cube to the 8 corners? "
|
| As has been pointed out, no. You wanted a proof.
|
| Any rotation must define an axis.
How about if the rotation is occuring along all 3 planes?
east to west spin,
north to south spin,
and up to down spin,
all occuring at the same rate of spin?
:)
3 rotations all occuring on a different axis that meet
at one point.
:)
Sigh. Rotations form a group. The combination of any two
rotations is another rotation. The combination of any number
of rotations is a rotation. Your situation will be identical to
a rotation around a single axis. Any rotation picks out an axis.
Socks
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
11 Feb 2006 08:51:58 PM |
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"Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
news:1139712255.096451.238250@g47g2000cwa.googlegroups.com...
| Spaceman wrote:
| > "Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
| > news:1139606547.218846.224320@g44g2000cwa.googlegroups.com...
| > | Ken S. Tucker wrote:
| > | [snip]
| > | > "Is it possible to a spin a cube so that at each corner of the
| > | > cube it experiences the same outward centrifugal force,
| > | > directed from the *center* of the cube to the 8 corners? "
| > |
| > | As has been pointed out, no. You wanted a proof.
| > |
| > | Any rotation must define an axis.
| >
| > How about if the rotation is occuring along all 3 planes?
| > east to west spin,
| > north to south spin,
| > and up to down spin,
| > all occuring at the same rate of spin?
| > :)
| > 3 rotations all occuring on a different axis that meet
| > at one point.
| > :)
|
| Sigh. Rotations form a group. The combination of any two
| rotations is another rotation. The combination of any number
| of rotations is a rotation. Your situation will be identical to
| a rotation around a single axis. Any rotation picks out an axis.
Really?
Have you ever run a 3D simulation of such or
are you just playing on paper?
:)
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| User: "Eric Gisse" |
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| Title: Re: Spinning cube question |
11 Feb 2006 09:04:42 PM |
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Spaceman wrote:
[snip]
Really?
Yes, really. If you were actually interested in mathematics you would
have learned this long ago.
Have you ever run a 3D simulation of such or
are you just playing on paper?
:)
You can work it out on paper with some linear algebra.
http://mathforum.org/library/drmath/view/51887.html
I, however, have absolutely no expectation that you will be able to
understand it.
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
11 Feb 2006 09:21:41 PM |
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"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1139713482.382392.108060@z14g2000cwz.googlegroups.com...
| Yes, really. If you were actually interested in mathematics you would
| have learned this long ago.
Funny,
does not look the same as the one axis spin does.
I think you should check your ratio of math to reality.
:)
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| User: "Eric Gisse" |
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| Title: Re: Spinning cube question |
12 Feb 2006 12:41:48 AM |
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Spaceman wrote:
"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1139713482.382392.108060@z14g2000cwz.googlegroups.com...
| Yes, really. If you were actually interested in mathematics you would
| have learned this long ago.
Funny,
does not look the same as the one axis spin does.
I think you should check your ratio of math to reality.
:)
As I expected, you didn't understand.
Though to be fair it is just a cursory introduction that actually
assumes the mathematical background to understand linear algebra. I
could point you to the book that taught me what I know about linear
algebra, but as I said, I doubt you would understand.
.
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| User: "Spaceman" |
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| Title: Re: Spinning cube question |
12 Feb 2006 10:50:09 AM |
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"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1139726508.528195.326670@g44g2000cwa.googlegroups.com...
|
| Spaceman wrote:
| > "Eric Gisse" <jowr.pi@gmail.com> wrote in message
| > news:1139713482.382392.108060@z14g2000cwz.googlegroups.com...
| > | Yes, really. If you were actually interested in mathematics you would
| > | have learned this long ago.
| >
| > Funny,
| > does not look the same as the one axis spin does.
| > I think you should check your ratio of math to reality.
| > :)
|
| As I expected, you didn't understand.
As I expected, you never deal with the real itself, and are
competely lost in abstract land.
Take one corner only,
You are stating that the corners are going to follow the same
path with one axis, as they would with two or three.
That is funny!
Too bad you don't "see" why it is.
LOL
.
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| User: "The Ghost In The Machine" |
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| Title: Re: Spinning cube question |
12 Feb 2006 03:00:16 PM |
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In sci.physics, Spaceman
<Realspace@comcast.not>
wrote
on Sun, 12 Feb 2006 11:50:09 -0500
<SrWdnYTPZcmh-nLenZ2dnUVZ_t2dnZ2d@comcast.com>:
"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1139726508.528195.326670@g44g2000cwa.googlegroups.com...
|
| Spaceman wrote:
| > "Eric Gisse" <jowr.pi@gmail.com> wrote in message
| > news:1139713482.382392.108060@z14g2000cwz.googlegroups.com...
| > | Yes, really. If you were actually interested in mathematics you would
| > | have learned this long ago.
| >
| > Funny,
| > does not look the same as the one axis spin does.
| > I think you should check your ratio of math to reality.
| > :)
|
| As I expected, you didn't understand.
As I expected, you never deal with the real itself, and are
competely lost in abstract land.
Take one corner only,
You are stating that the corners are going to follow the same
path with one axis, as they would with two or three.
That is funny!
Too bad you don't "see" why it is.
LOL
OK, lessee.
The original question's answer is obviously that it is
not possible; the best one can do here is an axis through
each face center. The magnitude of the centripetal force
would be the same on all 8 corners but the direction of
said force would be towards each face center (there are
two such, intersecting with the axis; the other four faces
are not relevant here), not the cube center.
Any other axis results in an asymmetry.
A better answer might include the actual construction of
the cube (my answer after all assumes that the edges do not
factor into the calculation). If one assumes a wireframe
cube there's no method by which to attach a face-centered
axis without more rods. There are at least two ways to
attach those rods to the axis: one can directly attach
rods of length sqrt(2)/2 to each face vertex, or one can
attach rods of length 1/2 to the center of each face edge.
The forces on each vertex will be slightly different
because of flexing -- not that a wireframe cube is all
that rigid anyway; if one really wants a rigid cube one
needs some sort of cross-bracing, such as that seen on
many cantilevered bridges.
http://en.wikipedia.org/wiki/Cantilever_bridge
http://www.nycroads.com/crossings/queensboro/
--
#191,
It's still legal to go .sigless.
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| User: "Ken S. Tucker" |
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| Title: Re: Spinning cube question |
11 Feb 2006 01:12:53 PM |
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Puppet_Sock wrote:
Ken S. Tucker wrote:
[snip]
"Is it possible to a spin a cube so that at each corner of the
cube it experiences the same outward centrifugal force,
directed from the *center* of the cube to the 8 corners? "
As has been pointed out, no.
Well's it's equal when the spin is zero, is an easy one ;-).
You wanted a proof.
Any rotation must define an axis.
Ok, but that axis can be a variable in direction
and magnitude, for example precession.
The centrifugal force
vector at a corner of the cube defines a line that passes
from the corner to that axis, and is perpendicular to that
axis. It is not possible for the eight corners of a cube to
have perpendiculars to a line that intersect that line at the
same point. It is possible to get four at a time, but not all
eight. Thus it is not possible to spin a cube such that the
centrifugal force vectors at the corners are all directed from
the centre of the cube to the corners.
You see, to get points aligned the way you require, you'd
need them in a plane. You also need that plane to include
the centre of the cube, and for them to be arranged at
the corners of a regular polygon so they are equally
distant from the centre. Though they don't have to occupy
all the corners of that regular polygon.
The corners of a cube are not in a plane.
Puppet Sock asks "why the question?".
I'm studying spinors, to better understand modern physics,
particularily applied when asked to comment on an article.
What makes you think that a cube has something to do with
spinors?
Consider the tensor (Like Maxwells Eqs),
A_12,3 + A_23,1 + A_31,2 =0
thats 3D. Classically that's part of the description
of an EM-wave.
[snip complicated example with air craft]
I now have demonstrated a maneuver how the center of
the 6 faces can have an equal CF, i.e. symmetrical.
No you have not.
Just as the eight corners can't have
perpendiculars to a line that meet in a single point,
so too the six face centres can't. Only points in a plane
can have this property. So, no single rotation can produce
equal centrifugal force in the centre point of the six faces.
I presume - by symmetry - each of the 8 corners also
has an equal CF, (in disagreement with Bruce :-(.
What I don't yet have is mathematical proof - one way
or the other. If anyone has one give me a hint.
Now you have. A rather easy to produce one.
Socks
Intuitively I agree, but my intuition might be simple.
Consider a mass located at the center of the cube
produces a equal g-force on the corners.
Thanks
I'll study it further.
Ken
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