If one was asked to list the natural factors causing variations on the global temperature of the Earth over timescales from months to millennia I think most would write down such things as the oceans, atmosphere, sun, Earth’s orbit and their associated timescales. How many would, I wonder, include changes in the rotation of the Earth as an influence in changing global temperature. Certainly not the IPCC. In AR4, their 2007 review of the science of climate change, it doesn’t receive a mention. Yet it might be an influence, and an important one at that.
We have very accurate and precise measurements of the Earth’s rotation. Very long baseline interferometric techniques with radio telescopes observing celestial point sources can determine the length of day to 0.02 ms which is equivalent to less than 1 cm at the equator. Before radio data optical observations can be used, though at reduced accuracy.
The Earth’s length of day varies over a range of timescales and is thought to be due to interactions (angular momentum exchange) between the solid Earth and the atmosphere (the oceans have a much smaller effect) as well as, on longer timescales, interactions between the mantle and the core. However the observed decadal variation, approx. 4 ms, is too large to be explained by atmospheric interactions (typically 1 ms) and too swift to be due to anything inside the Earth.