The sling is a weapon to throw with tremendous force a stone from 20 to 400 grams up to 400 meters away. It is a (usually braided) rope or belt with a widening near the middle. There is a button at the throwing end (who you let go), and a loop on the other, longer end. When you hang (folded) him next to your body he must not touch the ground.
A longer sling will be used if a greater range is required. You turn him like a helicopter wing above your head. This is more difficult and less accurate.
To hunt for birds you can load the sling with several smaller stones.
Moving faster is less accurate.
Quickly turning is not necessary, just at the last sweep.
The Roman army built large pendulum systems to throw large boulders. The Greeks used lead bullets at the battle of Marathon.
The usefulness of a catapult (Y -shaped stick, slingshot) depends on the elasticity of the rubber that you have available. Except pebbles are ball bearings and marbles good ammunition. A forked branch can you get easily. Gummi you find e.g. in (large) elastics, fasteners for luggage carriers (bike and car) or covers (trailer), tent pegs, seal of preserving jars, bandages for sports injuries, inner tubes, boating equipment, elastic bungee, trampoline, package.
If you have found suitable stuff, keep it dark wrapped. UV is detrimental to the rubber that endures over time. If a string does not provide enough power, you use more of them. It is useful to outwit small rodents and birds at close range.
You can even shoot stones with a bow. Or arrows with a catapult too. This can be even more effective than the use of stones.
I was so ugly my mother used to feed me with a slingshot. (Rodney Dangerfield)