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AFAIK all the celestial objects have a spin motion around its axis. What is the reason for this? If it must rotate by some theory, what decides it's direction and speed of rotation?

Is there any object that does not rotate about its axis?

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Possible duplicates: physics.stackexchange.com/q/12140/2451 and links therein. –  Qmechanic Jul 6 '13 at 9:02
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In general yes, everything rotates. It is to do with something called angular moment. Gravity is the central force in the Universe, because it is the only one which has a significant pull over large distances. When things collapse under their own gravity in space (i.e. clouds of gas and dust), any small amount of asymmetry in the collapse will be enough start it spinning. Even if it spins by a tiny amount, as it collapses, angular momentum conservation will mean it spins more and more quickly - just like an spinning ice-skater pulling their arms into their body and spinning more quickly. This means that all coherent masses are spinning - e.g. asteroids, neutron stars, galaxies, quasars.

The Universe is a complex place so something may be slowing down (because the gravity of other objects is putting on the brakes) or some things may appear not to be rotating (e.g. the Moon rotates but at the same rate as it goes around the Earth).

Huge clouds of gas and dust tend not to be spinning as a whole because they are expanding to fill the available volume - like a bad smell in room! - and not necessarily gravitational bound together. However they might have little pockets which start are turbulent, collapse under their own gravity, spin and form stars.

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I'm not sure if you want an object that doesn't spin at all, or one that somehow doesn't spin on its axis. In the former, any structure large enough (e.g. superclusters of galaxies) that its dynamical time is longer than the age of the universe is effectively not rotating.

For chaotic spinning (often called tumbling), one example is Hyperion, a small moon of Saturn

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All celestial objects are formed from larger, more diffuse collections of matter (such as a nebula which collapses to form a star). These larger objects typically have some very small net angular momentum (spin). That total angular momentum is conserved, and as the object collapses it causes the rate of spin to accelerate in order to maintain the same degree of angular momentum. It's the same phenomenon as the spinning ice skater pulling in their arms except in this case the amount of contraction is a factor of millions so even though a proto-stellar nebula may not be rotating much the sheer size difference between a star and a nebula will result in the star rotating a considerable amount.

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