Yep, completely normal - as distressing as it is for us, it's generally just a stage they go through and grow out of as they start to become more physically capable and less frustrated. DD went through a phase of biting, and yes it was pretty embarrassing to have it written on her day sheet from childcare that she'd been channelling "Jaws" and biting the other kids.

The way you dealt with it was pretty well the same as what we'd do with DD, though I would usually also remove my direct attention from her for a little while (move away, not play with her etc) until she'd settled down a bit - just gave her a chance to calm down and re-focus plus gave the message that biting wasn't acceptable.