# What would happen if ? (imaginary earth)

1. Oct 13, 2009

### jonjacson

...the angular speed of the earth would be increased around ten times?.

I mean if w, that now is 7,27 * 10-5 rad/s would be 6,05 *10-4 rad/s.

¿what would happen to a quiet body at the equator?¿and at the pole?.

Make some easy calculations and you will see it, let's comment the physics in that imaginary planet.

2. Oct 13, 2009

### mgb_phys

Centrifugal force at the equator is only around 0.03 m/s^2 (0.3% of g) so increasing this to 0.3 m/s^2 wouldn't have much effect (compared to g=9.8)
It would make the Earth bulge a little more and would have some complex effects on tides

3. Oct 13, 2009

### arildno

The weather patterns ought to undergo significant changes as well, not only the tides.

In particular, the changes in Coriolis-type effects would be way more significant than the changes radial acceleration-effects.

This is because radial acceleration effects will be swamped by the big gravitational force anyway, whereas in the other directions, there are, in general, no particularly strong forces whose effects would swamp the coriolis effect.

4. Oct 14, 2009

### jonjacson

Yes you are right, I made a mistake, but I think you too, because centrifugal force is not linear with w, Fc=mw2R , so if you increase ten times w, Fc is increased 100 times.

I made the calculations another time and the result to make equal the centrigual force and the gravity at the equator is: 1,24 *10-3 rad/s , wich make more sense.

I simply use this equality:

GMm/R2 = mw2R , and w= square root( 4 *pi *density/3)

¿do you agree?

Assuming that w does not change with time we would have(azimuthal force equals to 0) :

-translation force remains the same, it is not function of w

-centrifugal is the most different force, because depends on the square of w

-coriolis is linear with w

If you would live at the equator ¿could you walk like the astronauts into their naves?

It would be curious the difference between living at the poles or living at the equator ¿what do you think?

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And talking about the tides, I can't see why they would change, tides are a comparattive effect due to gravity , it's not the force that matters , it's the difference in force.

The shape of the earth would change due to the centrifugal force , but ¿can you explain why tides would change?.

I am so sorry for the mistake, I only wanted to make equal centrigual and gravitational force at the equator, and see the implications on the ficticious forces.

Last edited: Oct 14, 2009
5. Oct 15, 2009

### Cleonis

As mgb-phys pointed out: an earthlike planet that spins faster than the Earth would have a more pronounced equatorial bulge.

Your quick 'n dirty calculation may not be very far off, but factoring in the equatorial bulge would take it to the next level.

There are approximative expressions for the amount of bulge as a function of rotation rate, and expressions for the gravitational potential of a bulging planet.

I don't know whether a celestial body with such as rotation rate that effective gravity at the equator is zero or nearly zero will be stable. As I recall there have been theoretical explorations. Of course such a high rotation rate will never actually occur. I think a proto-planetary disk that spins relatively fast will simply never contract to a planet.

Cleonis