Earth's rotation can vary within a small range by rearranging the distribution of mass (changing the Moment of inertia). That's why on ice ages the day was a few seconds longer, because large amounts of water that used to be on the ocean was piled in large ice sheets, so like in the classic example of a rotating ice skater, by moving mass (ice on Earth or the arms of the skater) away from the rotation axis, slows down the rotation speed.
The only other way for the Earth to significantly change its rotation speed is by losing angular momentumangular momentum, and any imaginable event that could change significantly Earth's angular momentum over a period of 15 years would be so catastrophic that the change in rotation speed would be secondary. Such event would have to be something like the collision with a massive asteroid, the fly-by of planet-size celestial body, or the ejection of large amounts of mass by the explosion of gigantic natural nuclear reactors (all things that might have happened very early in Earth's history).
As an anecdotal note, the fact that this number is quite close to the critical velocity, have made some people think that the explosion of a natural nuclear reactor could have been enough to give the extra kick to eject the whole Moon from the surface. Something that would explain why the composition of the Moon is so remarkably similar to that of Earth by recent analysis, challenging the theory of formation by a collision with "Theia" a hypothetical Mars-sized body. Although, there are other recent theories with an alternative solution to this problem, such as the synestia theory.
Finally, it would be wrong to restrict all possible changes of rotation speed only to surface processes or interactions to other celestial bodies. It could also be possible that mass redistribution in the Earth's interior could affect rotation speed. Events like the iron catastrophe would have increased the rotation speed, and other mass redistribution events could have happened or might be happening, but this is just speculation. Studying such processes is extremely difficult, we know very little about the dynamics of the Earth interior, and it will be extremely hard to prove or falsify theories concerning such internal mass redistribution events. This answers and and others in the same question have some ideas of how the angular velocity of a planet could change.