If the Earth were to suddenly stop spinning, it would be the high winds, rather than gravity, that would immediately remove all traces of life from the Earth's surface. Thankfully, there is virtually no chance of the Earth's seizure of rotation.
If the Earth were to suddenly decelerate from its current rotational speed of 1,000 MPH to 0 MPH, Earth's atmosphere would not stop with it. For everyone and everything on the ground relative to the air, this means that all of the surrounding air would instantly transform into 1,000 MPH winds. At these speeds, the winds would sweep up all life and destroy all cities on the planet within just one hour.