Head. Time. Throw. What word can precede all of us?

I am but a little stick, yet magic follows when I’m flicked.

I come from a bull or a steer. You can buy a dried version of me at the pet store as a chew toy for your dog.

I have metal arms, but I cannot hold a thing, I block your path until you scan or hear a ding. I guard the busy stations where the daily crowds arrive, I spin around in circles to let you pass inside. I only take you one by one, no matter how you file.

If you cut me, you'll be crying and crying and crying