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First, I should make it clear that this isn't a question about angular momentum (unless I may have completely missed something). It is my understanding that a nebula must have some inherent initial spin before collapse to form a solar system (and if it doesn't have that spin, only a star is produced). Then, basically, Conservation of Angular Momentum takes hold (and this is where the rotation is more noticeable), thus producing the accretion disc around the star, then planetary bodies, etc.

Now, what determines the initial rotation of a nebula before collapse? Why is it that some nebulae do not have an initial rotation before they collapse?

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While there is always Some element of spin (it would be very difficult to have an absolutely non-rotating body, or cluster of bodies) if it is very low, we can treat it as effectively zero, as there are various drag effects as the nebula coalesces.

The reason most objects (whether they are nebula or not) do end up rotating is from the very effect you note - as you move in towards the centre, rotation effects increase due to the Conservation of Angular Momentum, and these outweigh drag effects in a lot of cases.

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Why would it be very difficult to have a non-rotating body? Also, in thinking about it today, I came up with a potential solution to my own question. If all the particles in the cloud have a temperature (which is almost certain, since no known records of absolute zero exist), then they all have a motion, and therefore a vector quantity. Thus when the nebula reaches its critical mass (or density/volume), the vector sum of the particles gives it the angle of rotation (conserved during the collapse) and therefore noticeable spin. Is this the case? If not, where have I gone wrong? – Nate Feb 28 '12 at 4:19
I think you have partially answered your own question. There are all sorts of motion from very large to very small scale. The probability of the sum of these resulting in a net zero rotation is low. – Rory Alsop Feb 28 '12 at 8:36

As @Rory said, there will always be some spin, but it can vary from very little to very much.

The primary source of spin in nebulae (also for galaxies), is torque from the local environment. Nearby nebulae, clouds, stars, etc can exert a net torque on the nebula (or galaxy) giving it angular momentum. This is the primary source of spin for nebulae.

After inflation, there were random over-densities of angular momentum in different regions---just like there were over-densities of mass, etc. This effect is primarily important for larger objects (e.g. galaxy clusters), and I don't think it has any roll on nebulae... but I'm not positive.

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