Could tall buildings in very heavily populated cities affect earth's rotation

Question

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?

Answer 1

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 $10^{15}$.