centrifugal force vs gravity

[claymore]

if the earths rotational period started to increase ,could it get to a point where centrifugal force and gravity at the equator were in equilibrium and every thing on the surface had zero weight. Taking it a bit further, if centrifugal force overcame gravity and started to propel off the surface anything that wasn`t anchored down , would gravity take over and drag it all back as soon as it had left the surface?

[jake-the-peg]

Yes and no.

(We'll ignore the fact that technically there's no such thing as centrifugal force because it's a helpful illusion and that you mean speed increase - increasing the period slows the rotation)

Firstly the "centrifugal force" is given by mv�/r where m is the mass of the body v it's velocity and r the radius.

Gravitational force is given by GMm/r� where M and m are the two massesand G the Gravitational constant

put theses 2 together for weightlessness and you get

v = squareroot(GM/r)

Plugging in the numbers gives me a velocity of about 8Km/s to do this.

That means the Earth would rotate in about 5 seconds.

Now would everything fly off?

Well it's only things connected to the Earth that would be moving at that speed things that weren't nailed down would have a pretty rough ride!

No I'm not a geologist but I'd suspect the whole strocture of the Earth's crust would break up without enough gravity to hold it together

There are things in the univese that do rotate at this speed. Pulsars for example do rotate at anything up to 700 times a second!

http://www.newscientist.com/article/mg18925355 .300-superfast-pulsar-breaks-the-rules.html

But these are neutron stars and the whole atomic structure of them has broken down so much that only quantum mechanics stops them fom vanishing as a black hole.

They are so dense that a teaspoon of neutron star material weighs as much as a hundred million elephants

[claymore]

Thanks Jake, does that mean that if the earth was spinning twice as fast as it is now ,apart from having twelve hour days ,we wouldn`t notice any difference?

[mibn2cweus]

Escape velocity from the Earth�s surface is about
11.1 kilometres/second. The Earth�s equatorial circumference (where its surface rotates at the greatest speed) is about 40000 kilometres.

The Earth�s daily rotation rate already causes it to bulge slightly at the Equator. Ignoring other contributing factors, such as the Earth's motion around the Sun . . . If the Earth rotated once per hour (40000/11.1=3600seconds) the Equator would reach escape velocity and the Earth would be flattened to a disc eventually extending to the edge of the universe.