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In this xkcd, Megan spins around to attempt to take momentum away from the Earth to slow its spinning.

I was wondering, if Megan spinned around, wouldn't this cause her relative velocity to the rest of the room to increase? Because she is accelerating back and forth, the twin paradox should apply, and she should experience less time for every second in 'room time'.

Is my reasoning correct? Compared to the effect that spinning could put on the rotation of the Earth, which effect is larger? Will Megan increase or decrease the time, from her perspective, until dawn?

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An object moving in a circle does experience time dilation, but the time dilation is solely due to its velocity and is given by the usual equation.

$$ t' = \frac{t}{\gamma} $$

If you're interested in the gory details I prove this at the end of my answer to Is gravitational time dilation different from other forms of time dilation?.

So by spinning Megan is making different parts of the body age at different rates, because the velocity of her tissue increases with distance from the axis of rotation, and hence so does the time dilation. However the amount of time dilation is utterly insignificant. She would fly apart due to the centrifugal forces long before she achieved any significant time dilation.

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  • $\begingroup$ But the decrease in momentum to the Earth is also utterly insignificant. Which of the two effect is more utterly insignificant? $\endgroup$ – ithisa Nov 24 '14 at 4:05

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