Effect of Earth's Rotation on Time According to Wikipedia:

Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century ago, slowly increasing the rate at which UTC is adjusted by leap seconds.

The angular velocity of Earth is reducing (although not very much). That means our speed with respect to the earth's axis is dropping down. According to Einstein's special relativity, time goes slower for faster particles (Time Dilation). As our speed is decreasing day by day, time goes faster and faster. I mean that in future angular velocity is less than the present. If time is going fast, we'll reach that future point of less angular velocity faster (making time to go still faster). That means this is a cyclic process making time to go faster and faster (recursion).
Is this explanation correct? Will this affect Earth and us (like day and night duration)?

 A: For the speed at which the earth rotates, relativistic time dilation would be pretty much unnoticeable.  For the satellites in the GPS system, it does have to be taken into account in order to predict accurate positions on  the earth.
A: Let's not take into account the decrease in the pace of time caused by the gravity on (and in) Earth. As the Earth's rotation reduces with time the rotation will eventually come to a halt (even though this can be when time reaches infinity). Yes, if the earth's rotation reduces time will go faster for particles on Earth (and inside the Earth but at different rates depending on which point we choose) for all their momentary velocities decrease (these instantaneous velocities of a rotating spherical mass are by the way the cause of frame dragging).
This will have as a result that the coming to a halt of rotation will occur sooner than in the case if time didn't go faster by the diminishing velocities of the Earth's particles.
If the Earth's rotation is getting less, the time is not going faster and faster. It will go faster as the Earth's rotation decreases, but the rate of change in time decreases as the Earth's rotation approaches zero. When the rotation is zero, the Earth particles move through time at a maximum rate (again, ignoring gravity).
This means there is no cyclic process making time go faster and faster. The Earth's rotation will decrease a very little faster though, but this is too slow to make a noticeable difference for the duration of night and day. Night, as well as day, take the same amount of time in a rotating Earth and a non-rotating Earth (unless the Earth were spinning with an angular velocity close to the speed of light, in which case night and day wouldn't be visible and the Earth would be torn apart).
