# Spinning disk and relativity **URL:** \ **Category:** Factual Questions\ **Created:** [May 27, 2003, 11:06am UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738 "2003-05-27T11:06:22Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![NardoPolo](https://avatars.discourse-cdn.com/v4/letter/n/ecae2f/32.png) [@NardoPolo](https://boards.straightdope.com/u/NardoPolo)\ **Post date:** [May 27, 2003, 11:06am UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738/1 "2003-05-27T11:06:22Z")
Say I’m looking down on a spinning disk. From my perspective it’s spinning clockwise, and the edge of the disk is moving at .5c. What would I see? On one hand, when you spin a disk it looks the same. On the other hand, the circumference should appear to be shortened. But the diameter should still be the same. 😕 ---
**Author:** ![refusal](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@refusal](https://boards.straightdope.com/u/refusal)\ **Post date:** [May 27, 2003, 11:32am UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738/2 "2003-05-27T11:32:25Z")
In the theory of special relativity it is impossible to accelerate a rigid body whilst maintaining its rigidity (this creates paradoxes): thus you cannot spin a rigid disk from a speed of 0 to a relativistic speed. The disk will inevitably deform. As NardoPolo says, according to special relativity, the radius will remain the same, but the circumference will shrink. See [this page](http://galileo.phys.virginia.edu/~vc/743/answer/disk/disk.html) and [this page](http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html) for a little more detail. The actual solution brings in rather complex calculations involving general relativity, which I don’t have to hand and can’t find online (and I’m not sure if anyone has done). ---
**Author:** ![refusal](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@refusal](https://boards.straightdope.com/u/refusal)\ **Post date:** [May 27, 2003, 11:34am UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738/3 "2003-05-27T11:34:17Z")
Addendum: I said “according to special relativity, the radius will remain the same, but the circumference will shrink.” This is due to a limitation in the special theory of relativity, and does not describe the actual behaviour. ---
**Author:** ![rsa](https://avatars.discourse-cdn.com/v4/letter/r/839c29/32.png) [@rsa](https://boards.straightdope.com/u/rsa)\ **Post date:** [May 27, 2003, 3:18pm UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738/4 "2003-05-27T15:18:55Z")
You can view an applet of a spinning wheel here: [http://physics.berea.edu/~king/Teaching/ModPhys/Relativity/animations.htm#length](http://physics.berea.edu/~king/Teaching/ModPhys/Relativity/animations.htm#length) A non-relativistic wheel on the left is compared to a wheel spinning at 87% the speed of light on the right side of the page. Below that is an applet showing a spacetime wheel diagram. As already pointed out, there are no rigid materials. Information on the position and movement of different areas on a physical object can only be transmitted at less than the speed of light. ---
**Author:** ![NardoPolo](https://avatars.discourse-cdn.com/v4/letter/n/ecae2f/32.png) [@NardoPolo](https://boards.straightdope.com/u/NardoPolo)\ **Post date:** [May 28, 2003, 11:07am UTC](https://boards.straightdope.com/t/spinning-disk-and-relativity/177738/5 "2003-05-28T11:07:46Z")
Fine, so it’s not rigid. Which way would it flex? The rim of the wheel would compress (circumferentially), but so would the distance around the circumference itself. If we took a 10º wedge out of the disk, the remaining 350º would compress. But so would the 10º section of nothing. **Refusal** your second link is helpful. I especially liked the statements: > [@](#): > > The circumference contracts but the radius doesn’t. But in the original rest frame, the circumference is a circle, sitting in a spatial slice (t=constant) of ordinary flat Minkowski spacetime. In other words, we would have a “non\_Euclidean circle” sitting in ordinary Euclidean space. This is a contradiction. Yet I’m still scratching my head. What is the contradiction?