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"How Fast Would the Earth Have to Spin to Fling People Off?"


goalkeeper0

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While exploring this lovely APlusPhysics site, I came across an article titled, "How Fast Would the Earth Have to Spin to Fling People Off?"

I never thought about this question, but now wonder why I didn't. Oh wait, it's because the idea seems incredibly silly and impossible. Well, someone actually came up with an equation to answer this question.

Here is the physics thought process:

[ATTACH=CONFIG]644[/ATTACH]

Ffake=an added force used to fix the accelerating reference frame

Really, just two forces exist:

Fground= normal force and Fgravity=mg

[ATTACH=CONFIG]645[/ATTACH]

If you want to solve using other locations on earth other than equator:

[ATTACH=CONFIG]646[/ATTACH]

[ATTACH=CONFIG]647[/ATTACH]

So....Since changes in longitude impact this problem, every person on the world would not fling off at the same minimum rotational speed of the Earth. Those at the equator would fly off most easily. Luckily, we are not near the equator as seen by the weather today. At the equator the Earth's rotational speed must be 0.0124 rad/sec for people to tangentially fling off. The actual rotational speed of the Earth is 0.0000727 rad/sec. We should have nothing to worry about.

source: http://www.wired.com/wiredscience/2013/03/neil-degrasse-tyson-still-complains-about-the-daily-shows-globe/

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At the equator the Earth's rotational speed must be 0.0124 rad/sec for people to tangentially fling off. The actual rotational speed of the Earth is 0.0000727 rad/sec. We should have nothing to worry about.
Haha, good thing! You had me worried for a second there ;) Nice post!
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