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What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar systems, galaxies etc.), with no explanation as to why the spin began. I see a lot about the conservation of angular momentum, but these discussions all presume that the 'spin' already exists. What caused the spin in the first place? Shouldn’t gravity simply attract particles of dust, gas or matter together along a straight path till they collide, as a magnet does to a paper clip? The magnet does not make the paper clip revolve around it, and if I fall off of a building, I don’t spin around the earth. I fall in a straight path till I collide with the earth. What am I missing?

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Possible duplicates: physics.stackexchange.com/q/23104/2451 , physics.stackexchange.com/q/12140/2451 and links therein. –  Qmechanic Jun 20 '13 at 18:05
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4 Answers

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.

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Kyle has the right answer to what caused the spin in the first place (small perterbations in the early universe) but in answer to your other questions:

  • Gravity does attract matter along a straight path, it is the combination of linear momentum and gravitational pull that creates centrifugal force, which produces an orbit. Think about water in a bucket that you swing over your head, it stays in the bucket because of centrifugal forces, it doesn't fly away because of the pull of your arm (analagous to gravity), and it keeps spinning because of it's momentum.

  • The magnet and falling examples only appear to break the rules because of the difference in scale. Consider that the paperclip does not orbit the magnet from gravitational forces either. For any given attractive force, the speed required to produce an orbit must exactly balance the centrifugal and attractive (centripital) forces; too fast, and the orbit becomes hyperbolic, too slow, and the objects collide. In either case, it is the component of motion tangential to the attractive force that matters. For you to orbit the earth at a distance of the height of a building, you would have to be traveling at hypersonic speeds in a horizontal direction; similarly for the paperclip and magnet.

As it happens, I just finished reading a good book that walks through the change in mindset that allowed modern science to develop these concepts. You might be interested.

Example


As you can see in the article on centripital force mentioned above, the acceleration of an object in uniform circular motion is:

$ a = \frac{v^2}{r} $

Solving for $v$ gives:

$ v = \sqrt{a r} $

We know that the acceleration of gravity at the surface of the Earth is about 9.8 m/s^2 and we can look up that the radius of the Earth is about 6,000 km. Putting this together, we see that a horizontal speed that would produce a centripital force significant enough to keep an orbit at the surface of the Earth would be:

$ v = \sqrt{9.8 \frac{m}{s^2} \cdot 6,000,000 m} $

$ v \approx 7,500 \frac{m}{s} $

Given the speed of sound in dry air of 350 m/s, that means you'd have to jump off of that building at more than mach 20 horizontal to the ground to orbit.

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If you reverse your question, the answer will be obvious. You write no explanation as to why the spin began. Try to think the other way: what zero spin would mean? That would mean that two pretty random objects have their relative speed directed exactly in the same direction as the vector connecting their center of masses. Which is rather unlikely is you consider two objects with random speeds.

The magnet does not make the paper clip revolve around it just because magnetic field is not gravity and if you fall off of a building, you don’t spin around the earth just because 1) Earth is rather big compared with a building 2) you do not just fall in some random direction with some random speed but start falling with zero velocity (which is rather unlikely). If you take building somewhat larger than Earth and jump from the top in some random direction, most likely you will.

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is it not because of mass? the surface being lighter than the core would have to travel faster forcing the body to rotate. not too sure but i think everything has travelled the same distance in space but the lighter the mass the longer the route you take (spinning around heavier objects). like the naughty soldier running in circles round the marchers only covers the same distance but travells much further.

hope this makes sense.

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