Angular velocity and c: Is this a paradox? Can you explain it?

In summary, Dale claims that no matter what size the disc is, its angular velocity will be constrained such that v at the very edge will be < c. This is because solid bodies aren't held together by magic; they're held together by internal intermolecular forces. As the velocity increases it takes more and more energy to continue to accelerate the disc, and eventually it will shatter.
  • #1
diligence
144
0
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?
 
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  • #2
diligence said:
Is there a constraint on how large the disc can be?
Yes.
 
  • #3
DaleSpam said:
Yes.

ok, then what is it? ~5million meters is not very far in the grand scheme of things.
 
  • #5
DaleSpam said:
r<c/w

that's not exactly a size constraint, more like an angular velocity constraint. i don't see any reason why it's theoretically impossible to build a disc of arbitrarily large size.

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
diligence said:
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 ?
Yes.
 
  • #7
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
ZikZak said:
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.

Also, remember that as the velocity increases it takes more and more energy to continue to accelerate the disc. You could not physically get it to c because that would take infinite energy.
 
  • #9
ZikZak said:
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.

well i guess there certainly is a size constraint, in that the part of the disc that is too large will just fly apart.

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

1. What is angular velocity and how is it different from linear velocity?

Angular velocity is a measure of the rate at which an object is rotating around a fixed axis. It is different from linear velocity, which measures the rate of change in position of an object in a straight line. Angular velocity is calculated in radians per second, while linear velocity is measured in meters per second.

2. What factors affect angular velocity?

The main factor that affects angular velocity is the distance from the axis of rotation. The farther an object is from the axis, the greater its angular velocity will be. Other factors include the mass of the object and the torque applied to it.

3. What is the relationship between angular velocity and centripetal force?

Angular velocity and centripetal force are directly proportional to each other. This means that as the angular velocity of an object increases, so does the centripetal force required to keep it moving in a circular path.

4. Is angular velocity a constant value?

No, angular velocity is not a constant value. It can change depending on the speed and direction of rotation, as well as any external forces acting upon the rotating object. This is in contrast to linear velocity, which is constant for an object moving at a constant speed in a straight line.

5. Is there a paradox between angular velocity and the speed of light (c)?

No, there is no paradox between angular velocity and the speed of light. Angular velocity is a measure of rotational motion, while the speed of light is a measure of the speed of electromagnetic radiation. While both values involve velocity, they are measuring different types of motion and are not directly related to each other.

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