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So tomorrow for some unknown reason Earth starts spinning significantly faster.

How fast could it spin before life on earth dies.

What would be the extinction factor?

Super storms, the planet disintegrates, everything on the surface gets thrown into space, etc.

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Sudden speedup implies sudden catastrophe.

Lets assume a sudden doubling of rotational speed. You suddenly have 1000 miles per hour winds at the equator at the atmosphere is now moving far too slow to keep up. Same problem with the oceans no longer matching the nearby Earth.

Energy required to perform this speedup is beyond incredible. Earth has a rotational energy of about 2.138e29 Joules, to double the speed would require 6.414e29 J - this is about 65% of the binding energy of the planet Mercury, a bit more than 100,000 years worth of solar energy hitting the earth. Even at 99% efficiency, the waste heat will cook the Earth far beyond survivability.

OK, hand of God time (reverse Joshua effect). Still quite a bit of destruction as the new speed requires the earth to become more oblate., i.e., the polar diameter will decrease and the equatorial diameter will increase. Major earthquakes and volcanic eruptions globally, climate impact will be huge (nuclear winter times 100 perhaps). It will take many millennia to reach a new balance. Still, life should not be completely extinguished and eventually you reach a new equilibrium.

At higher speeds, you would have more transitional problem, but you start having even bigger problem such as notably reduced atmospheric pressure at the poles. And the earth start losing atmosphere at a more rapid rate. Just how fast you all die off depends on the new speed.

If you reach 10 times the rotational speed, you are all dead fairly quickly as the atmosphere would be lost pretty quickly, followed by the oceans boiling off. Not instantaneous death, over the course of a normal lifespan Earth would become mostly dead.

At 16 times the rotational speed, the atmosphere would be gone in minutes as the rotational velocity has exceeded the speed needed to enter orbit, i.e., things on the surface near the equator would simply start orbiting earth.

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Before I say anything else, I feel this question is far too vague for a proper answer.

'Like Earth' in what way? mass? atmospheric composition? distance to what type of primary?

Please elaborate, and remember that the question of 'support life' is hand in hand with 'evolve life'. Planetary spins don't often ( ever) increase to the point where it would become an issue for native life.

I'd like to recommend an article from "WIRED" magazine a few years ago that addresses precisely this kind of subject, along with some well explained Physics, I think you'll find the answer you're looking for. Read more at WIRED and Rotational speed

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    $\begingroup$ Better as a comment than an answer. $\endgroup$ – Mwr247 Jul 8 '16 at 19:51
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    $\begingroup$ Avoid explaining via a link, as links can move or be removed, and it leaves the answer hollow. Try quoting a particularly helpful passage from the linked resource in your answer. $\endgroup$ – Ranger Jul 8 '16 at 20:24

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