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Why do planets rotate and revolve in the universe?

rotating earth

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We have a question and answer similar to this particularly the last 2 paragraphs by ManishEarth is an answer to your question. –  user8 Sep 29 '13 at 10:50

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As the planets evolve during their protoplanetary stage and accrete materials from the protoplanetary disks, which are gravitationally collapsing interstellar dust and gases, these accreted particles retain some of the angular momentum from the materials they form from and being in constant motion.

    accretion period of the protoplanetary disk

      Generated image (virtual fly-by) from a simulation of the accretion period of the protoplanetary disk, showing preservation of
      angular momentum in the orbit around a Jupiter-size planet, as it clears its neighborhood. (Source: Frédéric Masset)

One nice description for this angular momentum preservation, and why the planets appear to rotate faster than their surrounding protoplanetary disk goes like this:

Conservation of angular momentum explains why an ice skater spins more rapidly as she pulls her arms in. As her arms come closer to her axis of rotation, her [rotation] speed increases and her angular momentum remains the same. Similarly, her rotation slows when she extends her arms at the conclusion of the spin.

Source: Scientific American article on Why and how do planets rotate? (George Spagna)

So it could be described as this axial rotation of planets resulting in conservation of the angular momentum of the materials in the protoplanetary disk, forming during the accretion period of the planetary system as the protoplanets gain in weight, and preserve this angular momentum due to inertia of their radial velocity.

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