Granted it is a pretty far-fetched idea but that hasn’t stopped some pretty big brains from trying to figure out just what would happen is such an event did happen.
Under the title of If The Earth Stood Still – Modeling the absence of centrifugal force the folks at ESRI used some pretty fancy modeling to find out the answer to that exact question.
If earth ceased rotating about its axis but continued revolving around the sun and its axis of rotation maintained the same inclination, the length of a year would remain the same, but a day would last as long as a year. In this fictitious scenario, the sequential disappearance of centrifugal force would cause a catastrophic change in climate and disastrous geologic adjustments (expressed as devastating earthquakes) to the transforming equipotential gravitational state.
The lack of the centrifugal effect would result in the gravity of the earth being the only significant force controlling the extent of the oceans. Prominent celestial bodies such as the moon and sun would also play a role, but because of their distance from the earth, their impact on the extent of global oceans would be negligible.
If the earth’s gravity alone was responsible for creating a new geography, the huge bulge of oceanic water—which is now about 8 km high at the equator—would migrate to where a stationary earth’s gravity would be the strongest. This bulge is attributed to the centrifugal effect of earth’s spinning with a linear speed of 1,667 km/hour at the equator. The existing equatorial water bulge also inflates the ellipsoidal shape of the globe itself.
Okay my head officially hurts now.