Mistborn: The Hero of Ages said:
Vin with the power of Preservation spins the planet around in an incredibly short timeframe, and the Sun is noted to drop below the horizon in less than a second. Using this formula for help.Mistborn: The Hero of Ages said:
Using the values of the Earth for this. The circumference of the Earth is 40075km, and half of that is 20037.5km, or 50% of the circumference of the planet. This calculator gives us a result of 3.1415926535898 radians from that percentage. The mass of the Earth is 5.97219e24kg and its surface area is 5.1 X 10^8 km^2 (or 5.1e14m^2).
E = 1/2Iw^2
= 1/2 (5.97219e24 X 5.1e14) X 3.1415926535898^2
= 1.50305039e40 joules
= 3.5923766491395793855 tenatons
That's energy. What about speed? Timeframe is less than a second, but we'll go with a second.
T = 20037.5km/1s
= 20037500/340.29
= Mach 58883.5993
I'm not sure how accurate the rotational kinetic energy method is, so let's also try the normal formula for kinetic energy.
KE = (0.5)mv^2
= (0.5) X 1.19892134e39 X 20037500^2
= 286.54907743785850471 ninatons
Final Results
Vin rotates the planet (energy - low end) = 286.549 ninatons
Vin rotates the planet (energy - high end) = 3.592 tenatons
Vin rotates the planet (speed) = Mach 58883.599