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This is a very good question that may not have an ultimate answer, but there is an explanation. The reason a planet rotates is due to its origins from the nebula from which it formed. This nebula had to be rotating. You probably have heard about the gyroscope and how it works- conservation of angular momentum. Angular momentum is determined by the rate of rotation and the mass of the object and its distribution as a function of distance from the axis of rotation. This is the principle behind an ice-skater spinning up when the arms are brought close to the body, or slowing down when the arms are extended. Except for dissipation and action of other torques, angular momentum is held constant. Thus the rotation of the gases and dust from which a planet formed causes the planet to keep on rotating, to conserve the initial angular momentum.

The planet's rotation is of course changed by events both inside and outside of the planet. For example, it has been recently shown that the use of dams has changed the distribution of stored water on earth at different latitudes, sufficiently to change the length of the day! The difference is small, but has been detectable.

But, why is the angular momentum conserved? And why was the nebula rotating if the universe began in a big bang?

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