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Is it a good idea to put spin on projectiles? I know it wouldn't make much difference with stones or BBs, but what about arrows, etc? This would surely increase accuracy.
Well, there's spin, and then there's spin ... it all depends on the direction relative to the projectile's motion. Ideally, the spin should be transverse (both laterally and vertically) to the line of forward motion, in order for it's gyroscopic effect to be most beneficial to maintaining it's flight path. The greater the distance travelled, and the greater the spin, the more effect the spin will have ... which is why the difference between gun barrels that are rifled, rather than smooth bore, is very pronounced. Conversely, the shorter the distance, and less the spin, the less effect it will have.

On arrows, particularly for medium and longer range shooting (but not for short range), spin is helpful - which is why some people pay extra for "helical", rather than straight, fletchings. I have helical fletchings on the arrows for my longbow.

Here's a diagram I found for you:
 

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It would make a difference on stones and BBs and you don't want it; not with slingshots at least.

Spin is only wanted on projectiles that are either also drag stabilised, and/or are launched in a stable way (such as down a barrel, or guide), and/or where the spin can be imparted in a very predictable way.
 

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A big part of the stability imparted by spin is based on the fact that projectiles are imperfect. Projectiles that are not uniform will vary their direction due to air and gravity. Spinning them sort of "averages out" the error over 360 degrees of rotation and makes it self canceling.
frosty2
 

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A big part of the stability imparted by spin is based on the fact that projectiles are imperfect. Projectiles that are not uniform will vary their direction due to air and gravity. Spinning them sort of "averages out" the error over 360 degrees of rotation and makes it self canceling.
frosty2
Canceling out sounds right, almost algebraic in nature.
 
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