Well, there would be
some relative motion between a point at the surface equator and a point at the equator of the planet's core. One degree of latitude at the equator measures 60 nautical miles - in statute miles, its a tad more than 68.7 miles, in feet, 362,760. Now, the Earth's core - the roughly 1500 mile diameter Iron-Nickel mass at the center of the Earth - has been
seismographically determined to rotate 0.4º +/- 0.1º per year faster than the surface of the planet (the rate of super rotation evidently varies by +/- 0.1º over time, with a periodicity on the order of centuries). Taking the 0.4º per year midfigure, that works out to a little less than 242 feet per year. Anyone who cares to work that out in terms of miles per hour is welcome to play with all the zeros that'd take; I ain't gonna do it. In any event, by that criteria, the nearest (although absurdly remote) half-mile-per-hour would be one half mile per hour, though a closer approximation would be more like one half mile per couple dozen millenia.
However, that point, regardless how many zeroes fall to the right of the decimal point before the first significant digit, is moot if one takes as "center of the Earth" a geometric point; reference the absolute center of rotation there would be no difference in rotational velocity if one considers that point to be an integral component of the rotating mass.
If on the other hand, one takes that point to be stationary, independent of the rotating mass, the equatorial circumference of the Earth being 24,902 miles give or take a few yards, and the rotational speed of the earth being one revolution in 24 hours give or take a few seconds a year, a point at the equator would be be rotating at 1,037.58333 miles-per-hour relative to that stationary point - to the nearest half-mile, 1,037.5 miles-per-hour.