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Angular velocity and c: Is this a paradox? Can you explain it? 
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#1
Mar2411, 06:06 PM

P: 144

I thought of this today while studying relativity.
Imagine a very large disc spinning with an arbitrary angular velocity. Perhaps w=57 rad/s (this is the speed of a CD, got this from a random physics text, whatever, the speed is really not important).. The speed of light is c=3*10^8 m/s. Since tangential velocity v=rw, if one were to sit anywhere on the disc such that r > 5,260,000m, then you will be traveling faster than the speed of light. But this is impossible. How can you explain this? Is there a constraint on how large the disc can be? 


#2
Mar2411, 06:55 PM

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#3
Mar2411, 07:23 PM

P: 144




#4
Mar2411, 07:27 PM

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Angular velocity and c: Is this a paradox? Can you explain it?
r<c/w



#5
Mar2411, 07:45 PM

P: 144

so you claim that no matter what size the disc is, it's angular velocity will be constrained such that v at the very edge will be < c ? 


#6
Mar2411, 07:55 PM

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#7
Mar2411, 08:03 PM

P: 242

The reason is that solid bodies aren't held together by magic; they're held together by internal intermolecular forces. The internal forces required to maintain that rigidity become infinite as you spin the disk that fast. So it shatters.
Of course, any real disk will shatter long before its edge reaches c, but even a disk of pure unobtanium will shatter at that speed/radius. 


#8
Mar2411, 08:20 PM

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#9
Mar2411, 09:10 PM

P: 144

sorry for doubting you dale, and thanks for explaining it everybody else. 


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