Rotational state of the stars What's the state of stars? I'm not sure whether the stars are stationary or rotating. For instance, if they are not rotating what makes them stable?
 A: Stars form from collapsing dust clouds, and since interstellar dust clouds are quite turbulent at interstellar length scales it is almost certain that the dust cloud forming the star will have a non-zero angular momentum, and hence the star will have a non-zero angular momentum i.e. it will be rotating.
There are various ways we can measure the rotation of stars. For a small number of nearby stars we can actually resolve the disk and see features on them, so the rotation can be measured directly. For the vast majority of stars this isn't possible, but the rotation rate can be estimated from line broadening. If the star is rotating with its pole roughly at right angles to us one edge of the star is moving away from us and the other edge is moving towards us. This causes a Doppler broadening of emission lines like the Helium I lines, and this broadening can be measured. see for example this paper, or Google for many similar publications.
If a star has it's pole pointing towards us the rotation rate can't be measured. However we have measured the rotation rate of enough stars to be sure that rotation is the rule rather thsn the exception. Some of these rotation rates can be very fast indeed!
A: Given the huge reservoir of angular momentum stars are born with it is more a question of how is it that stars can get rid of most of this angular momentum to become the relatively slowly rotating objects we see?
One of the best and most comprehensive pictures of stellar rotation that we have comes from the periodic modulation of a star's light caused by dark starspots on their surfaces (analogous to sunspots). The Kepler satellite monitored about 133,000 stars for several years and a large fraction of these stars showed modulation from which rotation could be measured.
There are of course a number of selection effects at work. It is harder to find longer periods and also to find periods for stars with few or no starspots (which are probably also those with longer periods). But, given those caveats, have a look at Figure 1 from McQuillan et al. 2014 (ApJS in press).  http://arxiv.org/abs/1402.5694
This shows rotation period versus estimated mass for 34,000 stars in the Kepler field.  Basically stars can be found with rotation periods between a fraction of a day and 100 days at any mass. The fast rotators are either young (because stars lose angular momentum as they get older) or in binary systems where they "tidally lock" to their orbital periods.
Higher mass stars tend to rotate faster because they lack the main angular momentum loss mechanism found in stars with mass $<1.2M_{\odot}$ (the coupling of an ionised wind to a magnetic field generated by a subphotospheric convection zone). But the lack of dynamo-generated magnetic fields mean these stars don't have starspots and don't feature in the Kepler sample. For these stars, one can try to measure projected equatorial velocity from spectral line broadening and if one can estimate the size of the star this gives an upper limit to the rotation period.
A: Rotating, although not necessarily at a uniform rate since a star is not a rigid body. A point on the Sun at the equator makes a full rotation relative to other stars in about 24 days.  Further from the equator, the period is longer.  Pulsars can make a full rotation in less than one second.  
