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?
[Physics] Does the sun have angular momentum
angular momentumsun
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The Universe starts out as a nearly perfectly smooth distribution of matter with tiny perturbations to the density and velocity distributions across it. If you pick any region of this early Universe, it almost certainly has an angular momentum, or in other words it has a slow net spinning motion. As matter collapses under gravity, angular momentum is conserved and the slow spin of a large object becomes the fast spin of a more compact object. This is analogous to spinning on a chair with your arms out then pulling them in - you spin faster.
Whether the sun "rises" in the east depends on your position on earth, and the time of the year. In northern latitudes, during the summer, the sun rises significantly North of East, and in the winter it rises in the South. For example, today's sunrise/sunset directions in Umeå Sweden, look like this (source: www.suncalc.net)
The yellow line shows the direction of sunrise, the orange line the current direction of the sun, and the red line the direction at sunset.
As you can see, the sun never gets close to being in the East...
The reason for this is the fact that the earth's axis of rotation is not perpendicular to its plane of rotation about the sun (the ecliptic). The same mechanism that causes summer and winter in the higher latitudes gives rise to this changing direction.
But as for the fundamental question: the rotation of the earth about its axis is much faster than the rotation of the earth about the sun - so the rotation of the earth is dominating the direction of the sunrise. Now if the earth stopped rotating altogether, the sunrise would be in the "Westerly direction", since the direction of both rotations (seen from say the North Star) is in the counterclockwise direction. It would just rise and set only once a year... But the year is 365.24 days, and while that is so, the sun will rise "mostly in the east".
A small addendum: because the earth's orbit is elliptical, its angular speed relative to the sun changes a little bit with the seasons. This is enough to make a sundial "off" by up to 15 minutes, depending on the time of year. This is captured in the "equation of time" and shown, for example, in this graph (from http://upload.wikimedia.org/wikipedia/commons/0/02/Tijdvereffening-equation_of_time-en.jpg):
And just for your amusement - on October 25th, the sun briefly rises in the South on Svalbard (Spitsbergen) before disappearing for the winter...
Best Answer
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.