Why do planets rotate?
Why do the planets rotate? What force cause them to rotate?
There is no force that causes the planets to rotate. Most of the rotation comes about from the conservation of angular momentum. Angular momentum is given by L=m*w*r2 where m is the mass, w is the angular velocity in radians per second, and r is the radius of the circular motion. Due to conservation of angular momentum, if the radius of the orbit decreases, then its angular velocity must increase (as the mass is constant).
All planetary and stellar systems are born from the collapse of dense interstellar clouds. The clouds may originally be very large (even thousands of light years across). Consider a portion of the cloud the collapses from a size of a light year or so to the size of the solar system. That is a huge change in the size of the system. So, the very slight rotation that the cloud has in the beginning is increased dramatically when the collapse takes place. In fact, this is one of the barriers in star formation: there is excess angular momentum and there has to be a way of losing angular momentum before you can form a star.
Anyway, the bottom line is that stars like the Sun spin from the original angular momentum that was there in the solar nebula from which it formed. Not only that, all orbital motion of the planets (including the spin) is due to this orginal angular momentum.
You are saying that original angular momentum of the cloud causes orbital motions and rotations of the planets(mostly). But in the case of orbital motions we have gravitational force that gives us some restrictions of movement(Kepler laws,for example).
What I am saying is that there will be no planets if there was no initial angular momentum in the primordial solar nebula. If a nebula with absolutely no rotation collapses, then there will only be a central non-rotating star and there will not be any planets. Planets form out of a protostellar disk, which itself forms only because of the initial angular momentum of the cloud. The dynamics of a rotating body is of course controlled by forces like gravity. Kepler's laws are a direct consequence of gravity.
Are there some laws also in the case of rotations?
The only thing that has to be kept in mind in rotation is that it results in a centrifugal acceleration that points radially from the center of motion. Hence, there has to be some force that conteracts this acceleration; otherwise the body will fly away (in case of orbital motion) or will disintegrate (in case of spinning). In the case of orbital motion, the counteracting force is gravity; gravity causes the body to continually fall towards the center, and this exactly conteracts the force resulting from the centripetal acceleration. In the case of a spinning object, it is the self-adhesion of the body itself that keeps it together. This results in a limit for how fast an object can rotate and still keep itself together. If it rotates too fast, the outward acceleration felt by the elements in the body may be more than the force that keeps them bonded together, and if this happens, the body breaks up. Other than this, there is no real law concerning rotations. (Note that rotational motion involves conservation of angular momentum just like linear motion conserves linear momentum).