At ground level g is 9.8m/s^2.suppose the Earth started to increase it's angular velocity. How long would a day be when people on the equator were just 'thrown off' ? why is the expression 'thrown off' a bad one?
better to say when they would be weightless.
centripetal acceleration = v^2/R = omega^2 R
when is that the same as g = 9.8 ?
omega^2 R = 9.8
R = 6.38*10^6 meters
so
omega^2 = 9.8 / 6.38*10^6
omega = 10^-3 sqrt (9.8/6.38) = 10^-3 * 1.24 radians/second
how long to go 2 pi radians then?
2 pi = 10^-3 * 1.24 t
t = 6.28 * 10^3 / 1.24 = 5.06 * 10^3 seconds
divide by 3600 to get hours
5.06 /3.6 = 1.4 hours in this new day