Depends on how the angular momentum (that manifests itself as Earth's rotation) would be absorbed. If, magically, it's absorbed smoothly and evenly, then not much dramatic happens initially (a small change in your weight and some earthquakes as response to the missing centrifugal forces), but the Earth climate and weather would change dramatically within about 100 hours (mind you that the day==year), the day side heating and drying up and the night side freezing.
If, on the other hand, the angular momentum is absorbed only at certain points, for example if some cosmic giant stops rotation with its finger, then all other structures would need to decelerate from the rotation, likely destroying most human constructions, causing massive flooding of the continents, crumbling of mountains, huge earthquakes, instant death to most non-microbic life forms.
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