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Is it possible that moving materials from one part of the earth to another area and using these materials to build tall skyscrapers in cities with dense populations could affect the rotation of the earth ever so slightly. If so would this contribute to climate change?

M. Enns
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Dee
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  • No, but check the dupe: around 10x larger buildings could be already on the border of the measurability. In no sense affect they the Earth climate, we are talking here about a 0.000 000 000 000 001 part change in the speed of the Earth rotation. – peterh Mar 18 '17 at 22:35

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Technically, yes. Angular momentum must be conserved.

Using $L=I\omega=\text{constant}$ (and we assume that the Earth is a closed system (e.g. no material enters or leaves the earth)) by rearranging the location of materials that make up the Earth, we are effectively changing the moment of inertia. For $L$ to remain constant, a change in $I$ would be compensated by a change in angular velocity $\omega$ (e.g. a change in rotation rate).

Now as far as the extent to which this would change the length of a day, the Earth's mass is $6\times10^{24}$ kg, and radius of $6.37\times10^6$m. If we approximate the Earth as a solid sphere, the moment of inertia of the Earth would be $I=\frac{2}{5}MR^2=9.738\times10^{37}kgm^2$. approximating a building of mass 400,000,000 kg on the surface of the earth as a point particle, this building has moment of inertia $I=MR^2=1.62\times10^{22}kgm^2$. The change in I for having a building on the surface of the Earth (and corresponding change in rotation rate $\omega$) would be of the order of $1$ part in $10^{15}$.

Bob
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  • Thank you for the response. Do you think over time this could ever so slightly effect climate change (shifts) – Dee Mar 18 '17 at 17:18
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    @Dee Any effect on the climate would be so tiny as to be negligible compared, for instance, with the effect of the carbon dioxide emitted during the construction of the building. Or, for that matter, from the effect of the Earth's slowing rotation due to the Moon, which is something like a millisecond per day per century I think. It's not even clear that climate has any immediate dependency on day length (obviously it will if the day gets very long or very short). If you are looking for an alternative explanation for climate change, this isn't it. –  Mar 18 '17 at 17:42
  • Sure....but keep in mind that Earth's rotation is slowing (and has been for billions of years) by ~millisecond/century due to other factors. Technically, skyscrapers affect the climate by virtue of changing the rotation of the Earth/length of a day.....but this effect practically negligible compared to other factors. Accounting for skyscrapers in this manner would be akin to accounting for the gravity of Pluto when determining angles for a ballistic problem in a first semester physics lab. – Bob Mar 18 '17 at 20:38