This could be fun...
Let's see how quickly the Earth would have to rotate, in order for the surface to reach near-light speed. (Not taking in account for equitorial expansion)
Earth Diameter = 127,563,000M
Earth Circumference = 127,563,000M * Pi = 400,750,984M
Speed of Light in a Vacuum = 299,792,458 M/sec.
For fun, we'll take 1M/sec; I'd like to stay below the cosmic speed limit.
And finally, 400,750,984M / (299,792,458M/sec) would tell us that the earth would have to complete 1 revolution in 1.337 "Standard" Earth seconds.
If in fact this were possible, our Earth would complete 64,634 revolutions per 24 "Standard" Earth hours.
"Standard" Earth seconds/hours is just my fancy way of saying, a second, as we know it today.
-SF