Quoted:
Why is that. I would assume that the shorter the barrel the less time that the bullet is in the barrel. Less time in the barrel would equal less spin on the bullet which could affect the stability?
In a 14.5" 1/7 you will get 2 full turns on a bullet. In a 14.5" 1/9 you will get about 1.75 turns. Is this logic correct?
I am by no means an engineer.
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The barrel length will have no affect on stabilization unless the length is something ridiculously short for an AR 15, like 1 or 2 inches (which I don't think is even possible using a gas system). The bullet enters immediate twist after leaving the throat and is pretty much spinning at the same rate then as it will when it leaves the barrel. Barrel length will affect MV, however, which can affect your practical range, but stability should be no problem.
Accuracy can also suffer with shorter barrels, but not because of stability from a lack of rotation. Longer barrels not only give the bullet more time to "settle down" and fly straighter, but also lengthen your sight radius.
Hope this helps. I had the same misunderstandings when I was looking into buying my AR15.