Wouldn't gravity have an effect on any measurements if it were aligned vertically? I'm just sayin'...
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Boy a whole bunch of great posts!
Ok... aostling, that was exactly what I was looking for originally. I'm fairly certain I've seen that before in a strength of materials book but right now, I don't have access to any books. They are all buried on the bottom of a bunch of college related paraphenalia, like clothes and food
The issue here is not the acceleration but the velocity. That was why I was opting for a larger diameter wheel rotating slower. The larger the diameter, the closer it approximates linear velocity. However, a few inches will make little difference in this case so I expect a smaller, faster "flywheel" is more feasible.
Thanks for the real world examples. I should have thought about the lawnmower blade at least. That was an obvious example for someone who's worked on many a lawnmower!
Cameron  Yep, thats exactly what I intend to do. At the specified speed, I will see a difference between two precision oscillators only one order of magnitude greater than the error. Incidentally, it will take something like 5 years at that speed to notice a difference of one second Luckily, I don't have to look for one second differences. This is why higher speed is better, the shift will be much more pronounced at higher speeds.
I tried integrating, as you did Cameron. A(rho)r is really just the total mass, so it becomes MRw^2 for the entire assembly. I got some rather absurd numbers. I calculated a force of 341,000 N. Perhaps I made a mistake in my arithmetic or my conversions somewhere. I'll do it again today and see what I get. I was working on about 4 hours of sleep yesterday, so its entirely possible!
I'm studying physics, btw. My area of interest is in high energy physics and its been a few years since I've crunched numbers for mechanics. I tested out of mechanical and intro level E&M courses so the last time I had those was in high school. I remember how to approach problems and the basics, like centripedal force, for instance, but ... well I'm no engineer Without a book I don't remember all the equations for stress, strain, moments, etc. Thats why I tried integrating, that seems like the most straightforward and "physical" approach.
Alright, well I gotsta go work! Later this evening I'll crunch some more numbers.
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Oop I forgot! Evan and everyone else who brought up the issues of safety and aerodynamics:
Maybe it is because I'm studying to be a physicist and we have a habit of reaching for a vacuum pump at the slightest provocation, but I intend to operate the physical part of the apparatus in vacuum. My plan was to use a compressed gas container of some sort, maybe an LP tank or an old aircompressor tank to make the enclosure. This would provide safety from flying shrapnel and allow me to draw a reasonable vacuum. The vacuum pump would be on the entire time so I expect some orings on the "drive shaft" would be sufficient to create a partial vacuum that would dramatically reduce the aerodynamic concerns.
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Fasttrack,
I'm an engineer but the wrong kind for your problem. I did have to take special relativity however. I'm almost sure I did something boneheaded in the derivation I posted. It seems like you have to integrate twice, once from the center to get the force required to keep each point moving in a circle and again to figure out the maximum stress at the hub. I haven't thought this through really thoroughly however.
I'm to the point where I have to look everything up too. I think Aostling and his solution are ahead of the game in that he's an aerospace engineer with the reference library on the shelf for dealing with these problems the easy way.
Actually doing the integrals and getting the answer will make your presentation to the physics faculty a lot more impressive. The trick is to make sure you get the same answer as the engineering book Congrats on thinking up a really interesting demo!
If I can be of any help, please don't hesitate to post.
Cameron
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I have this nagging feeling that the acceleration produced in a rotating system will produce relative motion that averages to zero. It doesn't satisfy the classic Einstein thought experiment in which linear acceleration is indistinguishable from gravitation. Determining that one is in a rotating system would be trivial. Since the acceleration vector is constantly changing I would expect there to be no net difference. It isn't the same as satellites orbiting the earth as they are in free fall around the curved space of the gravity well and are not accelerated at all.
I don't think the solution to the twins paradox will save this either as it depends on asymmetry of accelerations to produce the differential time dilation.
I may be wrong. For the sake of your experiment I hope so.Free software for calculating bolt circles and similar: Click Here
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Actually Evan, that is the main ... umm "experimental" part of this crazy plan.
Special relativity only holds for inertial refernce frames. Of course, space is really not flat at all so thats where General Relativity comes in. Luckily I'm taking a class devoted specifically to general relativity next semester, but it is my current understanding that special relativity holds for "local" areas that approximates flat or euclidean space.
I expect that you will be right, however. Even with a relatively large diameter flywheel... it is still very very small
edit: Thanks Cameron! I'll most likely have many more questions.
Tony  I'd like to run it in excess of 24 hours. That will be dictated partially by the amount of heat generated in the bearings and what kind of virbations I notice (i.e. do I feel confident enough to leave it run without someone watching it...)
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Fasttrack,
From the form of the lorentz transform for time, I am assuming that your experiment will work under this rationale:
While linear dimensions are only dialated in the direction of motion, time isn't a linear dimension and therefore must be uniformly dialated by a motion in any direction. If there aren't oddball affects from the acceleration of motion in a circle, I think it will work though my memory is much to hazy to remember caveats in the theory.
I remember from my special relativity class a decade or so ago using Helliwell's book (and having Helliwell as prof) that the experiment has been shown to work with atomic clocks and airplanes. Airplanes travel in approximately circular motion around the earth and they got a dialation result by flying an atomic clock on an airplane for a long distance and comparing it with one that was not flown.
It has been ages since I thought at all about this but memorizing the Lorentz transform was mandatory for passing that class. Engineers, physicists, mathematicians, and biologists alike had to take it.
After we passed, we got t shirts that had a picture of a brain with the caption "this is your brain" followed by a picture of a vertical line captioned "This is your brain at 0.999999c: Any questions?"
Regards,
Cameron
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Maachinery's Handbook
Originally posted by dpThis appears to be something a bicycle does all the time. I must be missing something.
But, a look at Machinery's Handbook is well worth the effort as it is a goldmine in these sorts of things. There's too much for me to scan and post today else I'd do it.
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telephone exchanges as was used a spinning gyro type back up [power], they were spun up and topped up by a drive motor/ mag clutch, if grid power failed the mag clutch would latch a dynamo and the spin would generate power for the telephone system, apparently several rotors exploded due to creep, all the maths worked out but,...bang, put down to the analysis of the steel, seggregation creep and non metalic inclusions.
solution was to stick them under great big concrete covers.
moral is even if it satisfys all the numbers be careful of spinning energy storage, flywheels do have a habit of disintegrating, the numbers and maths can be found in loads of places but 'the theory of machines' black is as good as any.
all the best
mark
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While linear dimensions are only dialated in the direction of motion, time isn't a linear dimension and therefore must be uniformly dialated by a motion in any direction. If there aren't oddball affects from the acceleration of motion in a circle, I think it will work though my memory is much to hazy to remember caveats in the theory.
As for the clocks around the world experiment, what it measured is not just the effect of accelerating the clock in a moving airplane.
Hafele and Kiting experiment [9] strongly support the
existence of a Universal Inertial frame. In this experiment four cesium beam
atomic clocks were flown around the world twice, once eastward and once
westward to test the theory of relativity. The time difference between the flying
clock and the clock, which stayed on the earth's surface, was compared. The
flying clock lost 59  + 10 nanosecond during the eastward direction and gained
273  + 7 nanoseconds during the westward trip. If we analyze a airplane flight in
around the world trip it is seen that most of the time the airplane fly in uniform
velocity .In order to fly in circular, track the airplane seldom make an angular correction of
it's flying direction, this and the time the airplane change it's height
because of elevation forces are the only time the airplane experience radial
acceleration, which is negligible compare to the flight period.
The result can only be explained by taking into account the universal inertial
frame. The earth has a rotational velocity, in the eastward direction flight the
velocity of the plane is positively added to the earth velocity and increased the
velocity of the clock on the airplane relative to the universal inertial frame and the
clock lose time relative to the clock which stayed on the surface .In the westward
trip the airplane velocity added negatively to the earth velocity this decrease the
velocity of the clocks on plane relative to the universal inertial frame and the clocks
gained time relative to the clock which stayed on the surface .
This paper, although poorly translated is very on topic.
http://arxiv.org/pdf/physics/0105008Last edited by Evan; 05182008, 02:53 AM.Free software for calculating bolt circles and similar: Click Here
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As does much of both quantum mechanics and relativity theory. Neither are intuitive.
It's like this:
Airplane flies east or west and stays on the same side of the Earth relative to the sun since it is flying at the approximately same velocity as the Earth is rotating. The result is that the velocity of the aircraft is adding or subtracting from the movement of the Earth through space. The problem with relativity is figuring out what something is relative to.
Do a search on the "slow moving clock problem" in relativity.Last edited by Evan; 05182008, 03:19 PM.Free software for calculating bolt circles and similar: Click Here
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