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That's easy! It takes a day to revolve, so just convert that value to radians per second and divide the speed of light by it.
We must make our units consistent, so we'll use meters and seconds, since we know that the speed of light is about 3(10^8) m/s.
So, 2pi radians divided by 24 hours, is about 0.000007272 radians per second.
If wr = c, then r = c / w = 3(10^8) / 7.272(10^-5) = 4.125(10^12).
So, the Earth would need a diameter of about 8.2506(10^12) meters! That's an awfully big planet but, then again, planets don't revolve too fast, so this was not entirely unexpected...
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