[zeroca]

Why the Earth rotates around its axis? Does it have internal-combustion engine (which works without a fuel) built into its center, or does its rotating conflict with the rule of conservation of energy?

[AntonioLao]

the conservation of angular momentum keeps the earth rotating around its axis. But because of the inhomogeneous mass distribution, the rotation does wobble to some extent. Still the earth's rotation can be modeled by a gyroscope with all the valid physics behind it. Another thing, since this rotation is in empty space, there is no frictional force to slow it down.

[zeroca]

Dear Mr. (if I’m not mistaken) AntonioLao
In our particular case it doesn’t matter that the rotation does wobble to some extent because of the inhomogeneous mass distribution.
The final part of your answer is from school physics, as I recall, but the real question behind my question above is - why the earth started to revolve on its axis? Why the angular speed of the earth increased from initial velocity of zero up to the value it has presently? Don’t say that the initial velocity equaled to present one. It wouldn’t be the convincing explanation. What forced the Earth to start rotating? Don’t say that it happened because there wasn’t any frictional force to prevent its speeding up; it wouldn’t be as well a convincing explanation, because I can say for instance that absence of frictional force isn’t obstacle for its staying quiet.
So I assert that there must have been the real reason (the force) of impact, which made it rotate. Please remind me: don’t all planets do the same? And can we accept the rotating of planets as something generally peculiar to the whole universe, and that it demands explanation?

[AntonioLao]

about 4.5 billions years ago, when the planets were still being formed out the many planetesimals collisions, the incremental angular momenta from all the planetesimals were added together creating a point called the center of mass. So that the total angular momentum is the vector sum of all these elemental momenta. But once the change in mass is stabilized without anymore further collisions, the total angular momentum became conserved and has been for the past 4.5 billions years. The rotational rate might be slowing down due to constant accumulation of micrometeorites, increasing the mass of the earth gradually and very, very slowly in the millions of years.

Not only planets rotate on an axis, but the sun, neutron stars, black holes, galaxies, comets, asteroids, and even subatomic particles all possess angular momentum. In the case of elementary particles, the angular momentum is called spin and this property is quantized. It has only two values, say spin-up or spin-down.

[zeroca]

Hello Mr. AntonioLao!

Presently it’s not important for us exactly when was the moment of beginning, so let’s omit it.

I almost fully agree with your reply except for the assertion that planets were formed out of planetesimal collisions, and the principal reason for rotating was (or is) exactly it. But let’s put off its consideration for a later time, if you don’t mind.

We agree that generally rotation means the existence of angular momentum. It’s the same as existence of a centrifugal force, which is applied to the center of rotating body vertically to the axis of rotation.

Earth’s rotation can be modeled by a gyroscope, but it can be analyzed by choosing any rotating system, for instance
1. Electrical centrifuge;
2. Rotating bicycle wheel (which’s fixed on the wall with its pivot);
3. Whirligig
And compare it with the Earth’s rotation to show principal discrepancies (marked with cardinal) and resemblances (marked with ordinal numbers).

I. ---- The case of el. centrifuge rotation is stationary (if it’s switched on for long) as it is in case of the Earth, but
1. The former is located on Earth’s surface (“within gravitational field of the Earth"), the latter is located in an “empty space”, and also
2. We can’t detect any outer influence (force), which could be considered as a locomotive force of Earth’s rotation (like an electricity in case of el. centrifuge), and also
3. The rotational axis of the Earth isn’t fixed, as in the cases of el. centrifuge and fixed bicycle wheel.

1. The case of rotation of bicycle wheel is an example of fading, attenuating rotating system, as well as the case of whirligig, but
2. Both of them are located within “gravitational field of the Earth” in contrast to the Earth, which’s located in an “empty space”, and also
II. ----The rotational axis of the whirligig isn’t fixed, as that of the Earth’s,

So, let’s firstly choose the whirligig and let’s made it rotate:
1. The rubbing between the top of whirligig and the ground’s surface serves as a frictional force, which slows rotation down, and also
2. The adjacent air to the whirligig serves as a frictional force against rotation, and we can prove it with a simplest experiment.

But for some reason the air, adjacent to the Earth doesn’t serve as a frictional force to slow down its rotation (despite the heterogeneity of its surface) and it didn’t happen for the period of 4.5 billions years. What’s the reason?
O. K.
Let’s take a helicopter and try to fly up into the air vertically from the surface of the Earth at the distance of 1-2 km in a good weather, and hang in this position. The force of attraction to the Earth equals to the raising one and this is the reason the helicopter remains hung immovably, but notice that it rotates along with the Earth at a speed of Earth’s rotation, so the helicopter has the same angular momentum as the Earth and it means that the air, or rather 1. The space adjacent to the Earth rotates as well together with the Earth and it means that planet isn’t only the globe alone, which rotates in an empty homogenous space, but planet is the unity of the globe and the adjacent space which’s organically bind to it (the adjacent space spreads up to some distance radially from the center of the Earth) and just this space contains the locomotive force of permanent angular momentum of planet’s revolving on its axis.

But how it happens, let’s speak another time.

[AntonioLao]

Originally Posted by zeroca 3. The rotational axis of the Earth isn’t fixed

for all practical purposes, the earth's rotational axis is fixed pointing at Polaris, the north star. But the precession of the axis caused by an external torque, in many thousands of years from now, the north star can be a different star or just an arbitrary point in space.

for a simple two-body motion (sun-earth) neglecting perturbation, the earth's motion is only affected by the gravitational field of the sun.

while 3-body motion (sun-earth-moon), the complexity of ocean tides must be considered. Still all these do not affect the motion of earth's axis directly in immediate noticeable effects. Even the phenomenon of magnetic reversals do not affect the motion of the axis.

all these imply that the 5 fundamental conservation laws can be applied independently of each other.

1. the conservation of energy
2. the conservation of mass
3. the conservation of linear momentum
4. the conservation of angular momentum
5. the conservation of charge (electric, weak, color)

there are other conservation laws such such baryon numbers, lepton numbers, strangeness, etc.