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## Main Question or Discussion Point

So, I've been reading on GR and I've come across this.

Awhile ago I read a smaller book on relativity that ended with a neat thought experiment: take a disk, lay out the circumference with many small rods, and start spinning it at relativistic speeds. Because of SR length contraction, each of the rods seems shorter, therefore the circumference of the circle as measured by you, the inertial observer, would seem to be less than 2πr. As odd as it is, I've been able to visualize it pretty well thanks to embedding diagrams like what I have linked below, where in (b) the radial distance is greater than what the circumference would imply for flat euclidean space.

So, overall, it seems as though this should make sense, except the equation the book's offered is throwing me off. It's:

[itex]C=2πr(1+\frac{ω^{2}r^{2}}{2c^{2}}) > 2πr[/itex]

However, instead of implying that the circumference is

[itex]\frac{ω^{2}r^{2}}{2c^{2}}[/itex]

A negative term?

Awhile ago I read a smaller book on relativity that ended with a neat thought experiment: take a disk, lay out the circumference with many small rods, and start spinning it at relativistic speeds. Because of SR length contraction, each of the rods seems shorter, therefore the circumference of the circle as measured by you, the inertial observer, would seem to be less than 2πr. As odd as it is, I've been able to visualize it pretty well thanks to embedding diagrams like what I have linked below, where in (b) the radial distance is greater than what the circumference would imply for flat euclidean space.

So, overall, it seems as though this should make sense, except the equation the book's offered is throwing me off. It's:

[itex]C=2πr(1+\frac{ω^{2}r^{2}}{2c^{2}}) > 2πr[/itex]

However, instead of implying that the circumference is

*less*than what you'd expect with a given radial distance, this equation seems to imply that the circumference is*more*. Is that the case, or am I understanding this equation incorrectly? Is[itex]\frac{ω^{2}r^{2}}{2c^{2}}[/itex]

A negative term?