Does the sun have angular momentum? The sun was formed like this: Clouds of dust and gas were moving and so this cloud of gas and dust pulled together its particles by the gravity of these particles. Since this cloud used to move in order to conserve momentum the sun should rotate. Does the law of conservation of angular momentum hold true? The distance to the center is reduced compare to the radius of the original cloud so the velocity of the sun should increase. So does the sun revolve around its own axis? Also does the sun revolve around any other object like the earth revolves around the sun?
 A: The Sun certainly has angular momentum.  You are correct that if two objects are of the same mass, the speed of rotation of the smaller denser object must be greater than the speed of the larger more diffuse object if both are to have the same angular momentum.  The Sun is estimated to contain 99.86% of the total mass of the original nebula from which it formed, packed into a much smaller diameter.
Helioseismology has been used to probe the density, composition, and motion of the interior of the Sun.  It's estimated that the Sun's angular momentum of rotation about its axis is $S = 1.92\times 10^{41}\ kg\cdot m^2\cdot s^{-1}$.
In addition to rotating on its axis, the Sun (and the entire Solar System) revolve around the center of the Milky Way Galaxy. One revolution takes one galactic year, which equals about 225 to 250 million terrestrial years.  It's estimated that the speed of galactic revolution at our Sun's distance from the center of the galaxy is 1/1,300 the speed of light, c.
So the Sun has angular momentum from revolving around the galactic center, as well as from rotating around its own axis.  The Sun's angular momentum of revolution around galactic center is part of the entire angular momentum of the Milky Way, just as angular momentum of the planets is part of the entire angular momentum of the Solar System.
A: I think I have the answer. Lets look at it intuitively. Lets say the nebula that formed the sun had a mass of 100kg and had a velocity of 10 km/sec. So the momentum was say 1000 kg m/s. Now when the sun formed it had the same mass (Roughly 99.8 % of solar mass) as that of the nebula. So in order to conserve momentum it should have a speed of 10 km/s. Lets substitute 10 km/s with 27 days needed for one rotation. 
In other words I am saying that the nebula that formed the sun would have been moving very slowly, so slow that it takes 27 days for the sun to revolve on its axis and complete a rotation. This is so because of the law of conservation of momentum.
Correct me if I am wrong.
