# Does the earth’s rotational angular velocity change?

This is what is written in The Feynman Lectures on Physics, Vol. 1 (ch.5)

We now believe that, for various reasons, some days are longer than others, some days are shorter, and on the average the period of the earth becomes a little longer as the centuries pass.

Why should some days be longer than the others? There is no “gravitational” source of external torque acting on the earth, so why does its rotational angular velocity change?

• Sep 16, 2022 at 17:25
• Can you say how 'rotational angular velocity' differs from simple 'angular velocity' please? Sep 16, 2022 at 20:22
• @RobbieGoodwin, I would consider the simple 'earth angular velocity' (without other context) to be ambiguous between rotational and orbital motion (or a sum of both). Sep 16, 2022 at 21:51
• Angular velocity changes to keep angular momentum constant, as magma flows up or down changing the density profile of the earth. Sep 17, 2022 at 0:09
• Just by raising your hand to ask this question you have slowed the angular velocity of the earth some infinitesimal amount by moving the mass of your hand further away from the axis of rotation. Perhaps it's angular momentum you're concerned about?
– Wyck
Sep 18, 2022 at 4:33

The Earth is not a single rigid body, but consists of at least five separate regions which can move relative to one another. These are the crust (which is the region that we use to measure day length), the mantle, the core, the oceans and the atmosphere. Although the total angular momentum of the Earth may not change, these regions can and do exchange angular momentum between themselves over timescales ranging from days to decades. This leads to fluctuations in the angular velocity of the crust, and hence fluctuations in the length of a day.

This Wikipedia article describes some of the mechanisms by which the different regions exchange angular momentum.

Over long periods of time, the Earth and the Moon exchange angular momentum through tidal effects, leading to a gradual but steady increase in the average length of a day. This effect is of the order of a few milliseconds per century.

• gandalf61 points out (correctly) that the Earth and the Moon are exchanging angular momentum. One consequence (as pointed out) is that the rotation of the Earth is slowing down. The other consequence is that the moon is moving away from the Earth. Sep 17, 2022 at 0:25
• +1, but you should change over timescales ranging from days to decades to over timescales ranging from less than a day to millennia. The Earth is still recovering from the last glacial period, which ended about 15000 years ago. The weight of that huge amount of ice resulted in global changes in the Earth's mass distribution. There are parts of the far north that are still undergoing post-glacial rebound. That rebound changes the Earth's inertia tensor, which in turn changes the Earth's angular velocity. Sep 18, 2022 at 7:05

To add to @gandalf61's answer: You can also look up solar time.

Due to the orbit around the Sun, the Earth has to rotate a bit more than 360° for the sun to get back to the same apparent position in the sky. Then, since the orbit around the sun is elliptical, the Earth moves around the sun at different speeds depending on it position along the orbit. Therefore the effect of the orbit on the solar day varies throughout the year.

• The earth rotates about 366.25 times per year, but we have about 365.25 days. It actually only takes the earth about 23 hours 56 minutes to rotate 360 degrees. The missing 4 minutes from a 'day' is for the sun to get back to it's highest position in the sky when viewed from Earth. If we used the positions of stars instead of the sun to measure a 'day' then a year would be 366.25 days, but the sun would only rise 365.25 times and it would be about a degree east of where it was the day before at the same 'time'. Sep 17, 2022 at 19:41

There is no “gravitational” source of external torque acting on the earth

Yes, there is. The tides are caused by the Moon's gravity. That energy has to come from somewhere. The drag caused by the tides is slowly changing the angular momentum of the Earth, and the tides from the Sun also doing so, albeit even more slowly.

Moreover, the Earth's moment of inertia is not constant. For instance, when two faults smash into each other and push up a chain of mountains, that increases the moment of inertia. Whenever something moves towards the equator, that also increases the Earth's moment of inertia. Etc. These changes in the moment of inertia can cause tiny fluctuations in the Earth's angular velocity.