My husband and I were sitting around and wondering what would happen if the earth suddenly stopped spinning. Would we, you know, fall over? What would happen?
You would go flying at over 1,000 mph(equator), the crust would break up, all life would go extinct and Hollywood would spawn another bad science disaster movie.
That depends on where you draw the limits of the Earth. If you exclude the organisms on top of it (and the amosphere, I assume) we’d go flying, as runner pat says (though I don’t see why the crust would break up). If you include everything out to the atmosphere (which is pretty reasonable), nothing much immediately, though as far as life on Earth is concerned, the yearlong days would fuck most everything up soon enough.
See 0:44 and following in this video. 
We’d fry immediately, since all that energy bound up in the rotation of the earth has to go somewhere. IIRC, it’s actually been calculated how hot the Earth would get, but I don’t recall the temperature offhand.
Well, that rather depends on what model of earth slowing we’re using, doesn’t it? If we’re positing the Earth magically stopping, I see no problem with the energy magically being channeled into the sun, or being turned into a death ray aimed at Venus, or just disappearing.
FYI: If you’d like a fanciful, YA take on the scenario, someone just sold a novel based on that premise. (Well, the premise of the earth’s rotation slowing, not just stopping suddenly.)
If the world magically stopped spinning and everything else was good, the cats would be wanting dinner constantly. MOM!!! The light says its dinnertime, wash the bowls we used 10 minutes again and do it again. MEOWMEOWMEOW!!!
So…the world would start spinning again because of all the fat cats in the dinnertime part and the skinny cats who didn’t get constant dinners would unbalance the world enough to get it spinning again.
Do the oceans stop too, or just the land?
This linkexplains it in detail.
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By the principle of conservation of angular momentum, the earth would have to move out farther from the sun. How much farther, I don’t know. If by stopping rotation you mean one side always faces the center of the galaxy, then the days and nights would be half a year long.
The only plausible way for the Earth to stop spinning would be if an object at least as large as the Moon hit one side of the Earth at the right angle and speed to cancel all the Earth’s angular momentum. If that happened, suddenly going at about 1,000 mph relative to the Earth’s surface would be the least of your worries.
Have a look at the last m,inute or so of the film version of H.G. Wells’ The Man Who Could Work Miracles. Or read the story:
Right, so falling over is a definite possibility. 
You could skin your knee :eek: