The earth's rotation slows down over time

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What is the leap second?

Our calendar and our (civil) time calculation are based on the movement of the earth. One orbit around the sun is one year, one period of rotation one day. One day corresponds to 86400 seconds. If you divide the mean day length by 86400 you get the world time second. However, the SI second (from the international system of units) is defined by the resonance frequency of the cesium atom and determined with atomic clocks. The difference between world time and atomic time is approx. 0.75 seconds per year. One reason for the difference is the tides caused by the moon. That means that the "clock of the earth" lags behind the atomic clocks. More detailed explanations can be found on the website of the Physikalisch-Technische Bundesanstalt: http://www.ptb.de/cms/index.php?id=1818.
If the differences between atomic time and universal time add up to one second, a leap second is inserted. This is done in such a way that the last minute of the day concerned lasts a second longer. However, when the next leap second is needed is not known, as various other effects affect the rotation of the earth. Actually, after the last time in 1999, 2006 and 2008, they had expected to have to add a leap second again in 2010, but this was not the case. An explanation can be found here: http://www.spiegel.de/wissenschaft/natur/0,1518,736851,00.html.

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Does the length of the day change?

Yes. The day length LOD (engl., Length of Day) varies constantly. In the long term, due to the tidal friction in the earth-moon system, the earth's rotation speed will steadily decrease, i.e. the length of the day will steadily increase. In the long term, this is 2 milliseconds per century for the length of the day. For the period from 1623 to 2000 there is a representation of the variation in day length at http://hpiers.obspm.fr/eop-pc/earthor/ut1lod/lod-1623.html. This clearly shows that the day length increases over long periods of time. For the period from 1962 to today you can find a graphic at http://datacenter.iers.org/eop/-/somos/5Rgv/plotname/213/EOPC04_08_62-NOW_IAU1980-LOD.jpg. This clearly shows that there have always been major fluctuations in the mean day length. The seasonal fluctuations are mainly caused by changes in the atmosphere (relocation of high pressure areas, changes in jet streams). Other changes are also possible due to El Nino events. But changes in the length of the day are also caused by the effects of the earth's core, which is connected to the earth's mantle by a core-mantle coupling.

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Will the earth stop spinning at some point?

Or to put it another way: When will the earth - like the moon already - perform a bound rotation, i.e. when will the length of the month and the length of the day coincide so that the earth always faces the moon on the same side?
According to http://en.wikipedia.org/wiki/Orbit_of_the_Moon this would be ready in about 50 billion years, but then the month length would be 47 days today because the moon has moved away from the earth. The cause of this development is the tidal friction in the earth-moon system, which has also led to the moon already executing a bound rotation, that is, it takes as long for one rotation as for one rotation around the earth and therefore always the same side for us turns to.
The slowing down of the earth's rotation is currently 2 milliseconds per 100 years. Since the second was defined in such a way that the mean day length 100 years ago was exactly 24 hours = 86400 seconds, the mean day length today is 24 hours and 2 milliseconds. However, this only applies to the very long-term average, because there are also regular and irregular fluctuations in the length of the day for other reasons by several milliseconds.
The above value of 50 billion years is only fictitious, because the conditions in the solar system will change fundamentally much sooner. In about 5 billion years, the sun will turn into a red giant and expand many times over to the size of the earth's orbit today. The earth is not swallowed up, but goes into a "higher" orbit because the sun is losing mass at the same time. But even before that, in about 2 billion years, the earth's oceans will evaporate due to increased solar radiation. In any case, before the earth stops turning, there will be no more people on earth.

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Does the earth spin faster when the leaves fall?

The earth actually rotates faster or slower depending on the season, which has to do with mass displacement (atmosphere, water, interior of the earth). But does it actually spin faster in winter when the leaves have fallen from the trees? No - it's the other way around - the earth rotates faster in summer, not in winter. But why is that so? Periodic shifts of air masses contribute to these seasonal effects.
It is true that the leaves on the trees increase the earth's moment of inertia in northern summer (pirouette effect) and there are more trees in the northern hemisphere than in the southern hemisphere. However, this certainly existing influence is completely superimposed by larger opposing effects. The length of the day is shortest in northern summer, which is equivalent to saying that the earth then rotates faster.
This becomes very clear in the graphic http://www.iers.org/IERS/EN/Science/EarthRotation/LODgps.html. The change in day length for the period 1995 to 1998 is given here, whereby summer and winter can be distinguished very well.
The fall of the leaves theoretically has an influence on the rotation of the earth. According to calculations by Prof. Peter Brosche (University of Bonn, specialist in the theory of the earth's rotation), the change in the length of the day due to falling leaves is no more than about 10 nanoseconds. That is several orders of magnitude below what can be measured (approx. Tenths of a millisecond). The foliage masses are much smaller than the masses that are constantly moving in the atmosphere, oceans, etc. and that have a really measurable impact.

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If all motor vehicles in the world start parallel to the equator in one direction at the same moment - how is the rotation of our earth influenced?

The rotation speed of the earth would change due to the physical law of the conservation of angular momentum. If the cars start to the east, the turn becomes slower, if they start west, it becomes faster. Except for the poles, this also applies to all other places on earth. However, the effect is greatest at the equator. How big the effect would actually be can also be roughly calculated
Assume there are around 700 million motor vehicles. Each car weighs between 700 kg and a ton. Then the total mass is 6 * 1011 kg. The earth has a mass of almost 6 * 1024 kg. the ratio is 1:1013. A day has almost 108 Milliseconds. If you let the cars drive on the straight at Michael Schumacher's speed, the maximum effect is around 10-5 Milliseconds. Unfortunately, this is not measurable. But the effect is there.
One can imagine the enormous masses in the atmosphere - because one can measure their effect on the earth's rotation.

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