Ancient people since the early Greeks have known that the earth was in constant rotational motion as evidenced by the occurrence of day and night time. Since then, earth's rotation became a common and household information; its unlocking though, took generations of deep and inquisitive thinkers with the ancient Greeks in the forefront.
Unfortunately, Greece and the rest of the ancient continental Europe where most of the now modern science actually begun still grope in darkness at deciphering the cause of the earth's rotation grounded on empirical scientific data.
Indeed, countless of scientific workers - Aristotle, Plato and even Galileo did not lived enlightened of this dilemma of the earth's rotation. All they knew was that the earth completed one rotation in an interval of twenty four hours. But science is a process of chronological contributions that the discovery of one is often dependent on previous discoveries. Galileo arriving many centuries later than the Greeks performed experiments not for the purpose to put a solution to the problem the earth's rotational motion, but his works nevertheless provided hints to all later like-minded individuals where to start their scientific research . Towering among them, was Sir Isaac Newton who was born interestingly in the same year Galileo died.
Equipped with the information of Galileo's work, Sir Isaac Newton found one of the grandest laws of nature, what is now known as Newton's First law of Motion in Physics. It says that any body will forever remain in motion once it is in motion and remains at rest once at rest unless acted upon by an external force. Succeeding experiments later confirmed the unquestionable validity of this scientific fact and must have something to do with the perpetual motion of the earth. Scientists were indeed correct right after having discovered the conservation of angular momentum, a consequence or mere rotational counterpart of Newton's First law of Motion. That is, all bodies in rotational motion will rotate in perpetuation so long as no outside factors that can disturb their rotational motion.
In the case of the earth, it was been rotating since its birth due to its being a previous part of the initially rotating cloud of interstellar dusts from which the entire solar system subsequently formed. In the billion of years of the earth's existence no astronomical event had ever occurred that can alter earth's rotation. Thus, its perpetual rotation, in complete obedience to the conservation of angular momentum.