Rotation of the Earth

The rotation of the Earth (and its change over time) is significant because it is evidence for an old Earth, yet Young earth creationists (YECs) try to use it as evidence for a young one.

Old Earth
There are two separate lines of evidence for an Old Earth coming from the slowing rotation of the Earth.

Coral
Thwaites et al. (1982) suggests that the Earth's rotation slows by 0.005 seconds per year, every year (0.005 s/yr2). Because the rate of change of the rotation of the Earth is relatively predictable, we would predict a 22.7 hour-long day (in a year of 386.2 days) about 370 million years ago.

$$-0.005\text{ s/yr}^2 \times -370\text{ million yr} = +1,850,000\text{ s/yr} = +21.4\text{ days/yr}$$

$$(365.25 + 21.4)\text{ days/yr} = 386.66\text{ days/yr}$$

$$\frac{8766\text{ hrs/yr}}{386.66\text{ days/yr}} = 22.7\text{ hrs/day}$$

Measurements of the Earth's past rotation rates go back to work on the growth lines of rugose corals by John Wells (1963), who discovered that a year in Devonian times (radiometrically dated to ca. 370 million years ago) had around days of about 22 hours (in a year of about 400 days). This (rough) agreement between multiple dating methods (radiometric dating, coral clocks, and the Earth's rotation) suggests an old Earth.

Tidal rhythmites
More recent work suggests that the Earth's day was 21.9±0.4 hours long about 620 million years ago, a value derived from studying of Elatina and Reynella, Australia.

Again using Thwaites et al. 1982, we would predict a 21.9 hour-long day (in a year of 401 days) about 620 million years ago.

$$-0.005\text{ s/yr}^2 \times -620\text{ million yr} = +3,100,000\text{ s/yr} = +35.9\text{ days/yr}$$

$$(365.25 + 35.9)\text{ days/yr} = 401.13\text{ days/yr}$$

$$\frac{8766\text{ hrs/yr}}{401.13\text{ days/yr}} = 21.9\text{ hrs/day}$$

Again, this (rough) agreement between multiple dating methods (radiometric dating, tidal rhythmites, and the Earth's rotation) suggests an old Earth.

Chambered nautilus
Sometimes creationists will bring up the failures of using the chambered nautilus to measure number of days. As Dave Matson of Talk Origins explains:

Slower past rate
The present rate of slowing of the Earth's rotation may be off (though this, if anything, would further support an old Earth). Sonleitner 1991 wrote:

Young Earth
Creationists argue that the Earth's slowing rotation independently proves a young universe and supports proof that the moon could not have been old. Kent Hovind of Creation Science Evangelism said:

The earth's rotation is slowing down, meaning that the earth can't be older than a few million years.

Although Mark Isaak references Eicher (1976) for a 2 second/100,000 year (0.00002 s/yr) slowdown of the Earth's rotation, the more recent Thwaites et al. (1982) suggests that the Earth's rotation slows 0.005 seconds per year per year (0.005 s/yr2). Even given this faster rate of slowing, there's no trouble with a 4.6 bn year old Earth:

$$-0.005\text{ s/yr}^2 \times -4.6\text{ billion yr} = +23,000,000\text{ s/yr} = +266.20\text{ days/yr}$$

$$(365.25 + 266.20)\text{ days/yr} = 631.45\text{ days/yr}$$

$$\frac{8766\text{ hrs/yr}}{631.45\text{ days/yr}} = 14\text{ hrs/day}$$

While a 14-hour day may seem strange, it's certainly not impossible. In fact, it's exactly the conclusion that Thwaites et al 1982 come to.

Mark Isaak of TalkOrigins notes that there are several lines of evidence (even before 1980) for a faster past Earth rotation (numbered-points added):

Faster lunar recession
YECs argue that a faster Earth rotation would mean a faster Moon recession, which means a young Earth. They're wrong.

Biblical scientific errors
Some fundamentalists argue that the Bible shows scientific foreknowledge by predicting that the Earth rotates. Instead, the Bible assumes a geocentrist universe by implying that the Sun goes around the Earth, rather than the Earth rotating.