system
Given the following post, respond as if you're commenting on Reddit:
human
How fast would the earth have to rotate in order to fling us (or other stuff) off of its surface?
gpt
I'll work from the assumption that we're on the equator, where rotational speed is greatest.

The acceleration due to gravity is 9.8 m/s^(2).  Centripetal acceleration in a rotating system is calculated by a = v^(2)/r, where v is the circular velocity and r is the radius of the circular path. 

Let 9.8 m/s^(2) = v^(2)/(6378000 m)

From this we get v^(2) = 6.25 X 10^7, and **v=7900 m/s**. The circumference of the Earth is only 40,000 km, so at that rate it would be completing a full rotation every ~~five~~ **five thousand** seconds. And in order to actually fling things off its surface, it would have to be going slightly faster.

Of course, such a rapid rotation would lead to the Earth quickly distorting and becoming extremely oblate, which would make its equatorial radius even larger and therefore increase the rotational velocity at the equator. This would eventually lead to pieces of the crust flying off of the equator.