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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?

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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