How Fast Can A Disc Spin?

[johnferk]

I've always wondered how fast a disc of a given size could spin. The question actually isn't all that absurd.

 

Though experiment -

 

Consider a disc with a radius of "X" meters with a rotational velocity of "Y" revolutions/sec. The absolute maximum spin rate would occur when the linear velocity at the edge of the disc gets close to C (299792458 m/sec).

 

For a disc rotating at 1000 rps (my carpentry router rotates at about this speed)the radius would only need to be 4.8 kilometers to achieve a linear velocity slightly greater than C at the edge of the disc.

 

For a disc rotating at 100E6 rps, the radius will only need to be 0.5 meters.

 

Does it really make any difference- probably not - I've just always been fascinated by thinking what would happen as you proceeded out from the center of a rotating disc until you encounter a C limitation. What happens exactly at the transition point of the disc.

 

On the other hand, it might actually be a relevant question. Consider - the fastest known rotating pulsar (PSR J1748-2446ad)has a radius of about 10 miles (16.4 kilometers) and a rotational speed estimated at 760 rps. That gives a linear velocity at the surface of PSR of ~0.254C which is beginning to get serious. At the other extreme. graphene flakes have been pushed to rotate at 60 million rps. Assuming the radius of a carbon atom is ~7.5e-11 m you would need a globe 0.7 m in radius to hit C.

[CraigD]

What a wonderful thought experiment! :) :thumbs_up

 

I've always wondered how fast a disc of a given size could spin. The question actually isn't all that absurd.

 

Though experiment -

 

Consider a disc with a radius of "X" meters with a rotational velocity of "Y" revolutions/sec. The absolute maximum spin rate would occur when the linear velocity at the edge of the disc gets close to C (299792458 m/sec).

I agree.

 

Some fun wrinkles in this thought experiment occur when you consider what the mass of the disc due to Special Relativistic mass dilation. As the speed of edge of the disk get close to c, its mass approaches infinity. At some speed short of that, then, the Schwarzschild radius of it exceeded its radius, and the disk is a black hole.

 

Care to assume an example thickness and density for the disk, and calculate the speed at which this happens as a function of the disk’s radius, jwkref? (or, of course, any other reader of this thread?)

 

If you can do it by exact calculation, rather than using some numeric approximation method, you’re a better mathematical physicist than I – not that hard an achievement, but still one that’d awe me! :)

[joekgamer]

This is very interesting. I wonder what the difference(s) would be between a solid disk and a hollow "wagon wheel".

[phision]

For a disc rotating at 1000 rps (my carpentry router rotates at about this speed)the radius would only need to be 4.8 kilometers to achieve a linear velocity slightly greater than C at the edge of the disc.

 

Are you sure that your router rotates at 1000rps(revolutions per second) and not 1000rpm(revolutions per minute)?

I'm not sure but even if your router does do 1000rps, I'm think it would be described as 60,000rpm.

[johnferk]

Yes - the maximum speed on my router is 58,000 rpm. It is a seriously dangerous piece of hardware that requires a great deal of respect. Reason I seldom use it freehand and generally keep it firmly mounted to the router table :D

[Eclogite]

That is an order of magnitude greater than I would have imagined, so I have learned something today. I am not sure if it is of any use other than adding another item to my list of things to avoid.

[CraigD]

Yeah, as a general rule electric motors, especially brushless ones, can innately reach very high rotation rates. Many can damage themselves if run unloaded, so they’re commonly built much stronger than needed for their intended use, to protect against accidental unloaded runnings. High-end commercial brushless electric motor with such over-engineering typically has a max speed around 250,000 RPM.

 

Last I read, the fastest electric motors are based on prototypes built at ETH Zurich in 2008, reached a speed of 1,000,000 RPM! (see this ScienceDaily article) I see that promises to bring these motors to market proved true – see Celerotron’s CM-1-1000. Rated for at 1,000,000 RPM (these motors appear to be precisely digitally controlled), Celetron’s literature states they can safely exceed this rate if needed.

 

There’s been a lot of press lately about Dyson vacuum cleaners using “digital electric motors”, some that spin their air impellers at 88,000 RPM, others at 104,000.

[johnferk]

That's interest.

 

OK at 10e6 rpm (16666 rps) you only need a disc that is 3 kilometers radius for the linear velocity to exceed C. To build that is within the realm of today's technology since the disc does not need to be solid.

 

In fact, I'd envision not a disc but a rigid rod (akin to a steel pipe) fixed at its rotational center.

 

Think about a carbon nanotube 6.5 kilometers in length and then start it spinning.

[CraigD]

For a disc rotating at 1000 rps (my carpentry router rotates at about this speed)the radius would only need to be 4.8 kilometers to achieve a linear velocity slightly greater than C at the edge of the disc.

I didn’t notice this before, but you seem to have made a factor of 10 error in this calculation.

 

Linear speed [math]s = s_a r[/math], so to have [math]s = c[/math] and [math]s_a = 6283 [/math] (about 1000 RPs), you’d need [math]r = \frac{299792458}{6283} \dot= 47714 \,\text{m}[/math], about 48 km.

 

Think about a carbon nanotube 6.5 kilometers in length and then start it spinning.

I don’t think you could build such a thing using conventional materials.

 

Centripetal acceleration [math]a_c[/math] is given by

 

[math]a_c = \frac{s^2}{r} = s_a^2 r[/math]

 

where [math]s_a[/math] is angular speed and [math]r[/math] is radius.

 

For your r=3250 m rod it’s ends at s = 0.5 c, [math]s_a = \frac{s}{r} \dot= 46122[/math], about 440,000 RPM, [math]a_c \dot= 6.9 \times 10^{12}[/math], almost 700 billion gees, many times greater than the acceleration under which any material would fly apart.

 

Assuming the forces from such acceleration could be managed by some super-advanced engineering...

 

This is very interesting. I wonder what the difference(s) would be between a solid disk and a hollow "wagon wheel".

As mass dilation is asymptotic ([math]\frac{c}{\sqrt{c^2-v^2}}[/math]), a most-mass-in-its-rim “wagon wheel” wouldn’t be much different than a solid disk, I think, because only the outer rim would experience the greatest mass dilation, making the inner parts less significant.

 

In fact, I'd envision not a disc but a rigid rod (akin to a steel pipe) fixed at its rotational center.

A rod instead of a disk would add a new wrinkle to the system, as according to General Relativity, the machine would be a gravity wave generator.

 

I’ve had to cobble the formulae around a lot, but I think the power of the 0.5 c tip speed rod (assuming most of its mass is at its tips) would be about

 

[math]P = 421 \left( \frac{m}{10^{20} \,\text{kg}} \right)^4 \,\text{W}[/math]

 

Fwhere [math]m[/math] is the mass of one of the tips

 

For human size masses, this power would be tiny. For a couple of pretty big (say 10¹⁹ kg) asteroids, it’s be 0.04 W.

Edited April 26, 2015 by CraigD
fixed broken math tags

[johnferk]

I'm notorious for making "order of magnitude" mistakes, so it is highly likely I am wrong and your are right. My calculations are below.

 

Regardless :rolleyes: to explore what happens, you don't really need a disc. 48 kilometers of 1/4 inch copper pipe would do the trick (although that would not be rigid enough to survive).

 

It is less a matter of whether it is technically feasible right now in time, as opposed to what would be the experimental prediction "if you could build it."

 

 

++++++++++++++++++++++++++++++

I calculated things this way using as a model the example given at the end of this mail:

 

rps X 2pi = radians/sec (angular velocity)

 

angular velocity X radius (meters) = m/sec (linear velocity)

 

so

 

 

revolutions per second 2 pi angular velocity (radians/sec)

 

1.00E+03 X 6.28 = 6280

 

 

 

 

 

angular velocity (radian/sec) radius in meters linear velocity (m/sec)

 

6280 X 5.00E+04 = 314000000 meters/sec

 

299792458 (C in meter/sec)

 

1.0473912589 ratio

 

 

************************************************************************************************

 

What am I missing I can't see my error as I used this model to make the calculations

 

 

http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_triganglinvelocity.xml

 

A Ferris Wheel rotates 3 times each minute. The passengers sit in seats that are 25 feet from the center of the wheel. What is the angular velocity of the wheel in degrees per minute and radians per minute? What is the linear velocity of the passengers in the seats?

 

The answer to this is 471 ft/min according to the textbook

 

If I plug these into the formula I used above (substituting rpm for rps and feet for meters), I come up with the same answer as the textbook.

 

 

revolutions per min 2 pi radins/min

 

3.00E+00 S 6.28 = 18.84

 

 

 

angular velocity (radian/min) radius in feet linear velocity (feet/min)

 

18.84 X 2.50E+01 = 471 feet/min

[DFINITLYDISTRUBD]

There is no physical contact when reading a CDs/DVDs so playing them doesn't generate any wear on the disc.

Meta Burn

first off there is in fact wear occurring when you play a cd (unless your cd player just happens to spin the disc in a vacuum

 

Secondly: Seriously?! If I were you and intended to actually stay an active member I'd ditch the adverts.

[sigurdV]

first off there is in fact wear occurring when you play a cd (unless your cd player just happens to spin the disc in a vacuum

 

Secondly: Seriously?! If I were you and intended to actually stay an active member I'd ditch the adverts.

Answered ure question :)

[DFINITLYDISTRUBD]

WOW! that's some router!!! Fastest electric tool I own tops out at 15,000 RPM no load speed I know some Dremel type tools hit in the mid twenties... The only tool I own that even makes it to 30+k RPM are my air powered die grinders...are you sure it makes 60k rpm?

 

As to the fastest you can spin a disk...depends on what it's made of, how big it is, how well it's balanced, the medium it's spinning in, how the surface interacts with the medium, and lastly how much money you are willing to put into it.....and oh yeah, how you wish to determine the speed Rpm or Mph/Kph at the rim...with the latter you could either have a very small disk spinning at ungodly Rpm only to have a rediculously slow Mph/Kph (or min. or sec.) or a really big disk with an extremely low Rpm but very high speed at the rim.

 

Sorry just had to stick my nose into this one. I have often wondered what the limit is as well...I've often considered the limit to probably be about the same as the MPH of planetary orbits....I don't know for sure (but I intend to try and find out somehow) but I have a gut feeling that the MPH for all of the planets in our solar system is about the same and it's probably about as fast as things can spin without flying apart....mind you this is just a hunch and I make no claims as to it's accuracy.

[lawcat]

fastest rpm in universe? probably in the order of 10^44 rpm, which is c/plank's length (meters per sec/meters x 60s/minute).

 

 

 

On Earth, electrically, for constant speed

 

RPM = 120 x Frequency/number of poles

 

Take minimum number of poles at 2, and maximum switching frequency of a magnetic field (inuction motor) at 10^12 (using a digital switch to switch the field on off).

 

RPM = 6 x 10^13. (this would be a tiny tiny induction motor)

[Turtle]

since the idea seems to be to approach the speed of light on the rim and not necessarily a high rpm, i did a search for the "largest flywheel" and found this bit. they don't seem to give a size or rpm though. :shrug: anyway, as has already been said, theoretical limits of "speed" aside, the practical mechanical limits seem to prohibit coming anywhere near the speed of light.

 

Beacon Power spins up world's largest flywheel plant

...The flywheel facility, billed as the largest in the world, is designed to regulate the supply of energy across the grid.

 

Using carbon fibre cylinders suspended by magnets in a vacuum, the flywheels can store electrical power as kinetic energy for short periods of time. This makes them appropriate for regulating fluctuations in demand over very short periods.

...

[phision]

The maximum speed a solid disc(circular) can spin, is when the rim has a speed equal to that of light( the universal speed limit).

∴(therefore), the maximum number of rotations, a disc of radius R would be able to make is equal to, the speed of light © divided by 2πR.

 

However due to the relativistic mass involved the structural integrity of the disc would be compromised long before this speed was reached!

 

[belovelife]

could this be done in the salt flats with a magnetic rail , using the quantum hole thing, with liquid nitrogen cooled elements?