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Would heavy elements from space hitting the Earth slow down the earth's rotation as the difference between the masses of the core and surface would be less?

Qmechanic
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The Earth spin because of the collisions it withstood at its early begining. One theory stipulates that it actually collided with another planet form the solar system which was going opposite direction. The collision gave birth to the moon. It also explains why the moon is always facing earth the same way.

Nevertheless, it certainly has nothing to do with the difference of mass. You may also note that heavier elements do not travel slower, they are simply require more energy to accelerate.

Finaly, elements hitting Earth from space could slow Earth rotation if they had the right collision course, but the probability for any given object to hit Earth in a way that would slow it down is virtually the same as the probability for a collision that would accelerate it.

Hadron
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Rotation generally comes from existing angular momentum in the initial cloud that increases in angular speed as the collapse into a denser body lowers the moment of inertia.

I do not understand what you mean by "lighter things travel faster in space". It is a strange statement. It is known that light thinking travels faster than heavy thoughts, but I do not think that the properties of the noosphere extend to matter in the physical universe.

However, that is certainly not the reason for the Earth spin as, according to information you could have found yourself on the internet, the core of the earth spins a bit faster (a very tiny wee bit faster) than the outer part (example).

By the way, the surface of the planet does have less density than the core. To state that it has less mass, you should first make precise how deep you consider the surface to extend.

Change at the surface of the planet due to heavy matter hitting Earth from space is however relevant. This matter does hit the planet with some speed that could increase or decrease (very minutely) the rotation speed over time if it were always acting in the same way. However, increases and decreases probably average to nothing over time. Still, by increasing the mass at the suface of the planet, it does increase the moment of inertia (the resistance to changes of rotation speed of a spinning body), and hence it slows down extremely minutely over the millions of years the Earth rotation speed (exactly for the same reasons that the initial cloud rotated faster when collapsing into a planet). Note that this is dependent only on the total mass falling on the planet (and where it falls), it is not dependent on the heaviness of each chunk, or its density.

babou
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angular momentum of particles causes the body to spin. think of ice skaters. as they pull their arms in they speed up. same goes for particles sucked in by gravity. earth's collision with the body that formed the moon may have impacted the rotation speed. but it was already spinning.