Note: The "puke machine" ride is often called the "Gravitron." Not to be confused with the hypothesized "Graviton." ImJustAnotherOkie wrote "Gravitron." Ergo, I was having a little fun.
UNIFORM CIRCULAR MOTION
Applying this to The Gravitron Puke Machine example I gave in my last comment:
Simply put, the pencil is accelerated in the circle along with you. When you hold the pencil out, it is still attached to your arm. Therefore, you are still imparting inertia to the pencil while still confining it to a circular path (albiet, a smaller circular path than what you, yourself are experiencing). Side note: I guess I could get more precise with my terms, but "inertia" is close enough and keeps it simple.
When you let go of the pencil (after positioning your hand with your fingers pointed towards you), it still has its imparted inertia and wants to travel in a straight line at an approximate right angle relative to the center of the puke machine. (Think of the pencil as being "flung" out from its orbit).
You, however, are still travelling in that circular path while the pencil is now travelling in a straight line tangental to the arc from which it left.
Your confined circular motion allows you to intercept the pencil as it is "flung" along that tangental straight line.
From your perspective, the pencil fell back towards you.
If you don't believe me, try it yourself. I did it at Six Flags with a gumball or something when I was younger.
No graviton needed...but, you WILL need The Gravitron Puke Machine!
:)
Cheers!