Since the time it takes for the earth to complete one rotation about itself (i.e., the time we call "day") is not constant, then the angular speed is also not constant, that is, there is a non-zero angular acceleration. What is the corresponding torque(s) causing this angular accelaration?
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$\begingroup$ "the time it takes for the earth to complete one rotation about itself" is not what we call a day, it is what we call a sidereal day. $\endgroup$– philipxyCommented Dec 1, 2023 at 0:19
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Earth Rotation Variations from Hours to Centuries (Dickey) has some analysis of these variations and states that they are mainly due to interactions with the atmosphere and with the earth's core.
Angular momentum transfer occurs between the solid Earth and the fluid regions (the underlying liquid metallic core and the overlying hydrosphere and atmosphere) with which it is in contact; concomitant torques are due to hydrodynamic or magnetohydrodynamic stresses acting at the fluid/solid Earth interfaces.
Changes in the inertia tensor of the solid Earth are caused not only by interfacial stresses and the gravitational attraction associated with astronomical objects and mass redistributions in the fluid regions of the Earth but also by processes that redistribute the material of the solid Earth, such as earthquakes, postglacial rebound, mantle convection, and movement of tectonic plates.
The paper states that most of the decade-long varation is due to core-mantle torques, while the shorter-term variation is mainly from interactions with the atmosphere.
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1$\begingroup$ There are also disturbing torques from the moon and the sun. The moon works both to slow the earth's rotation by means of tidal forces and also causes the direction of earth's rotation vector to shift (nutate) gradually over time as the plane of the moon's orbit precesses. Similar effects happen from the sun to a smaller degree as well $\endgroup$– TristanCommented Nov 30, 2023 at 19:26