If you're already a TBI patient, rapid head movement, as Mark said, can set off any number of symptoms. As often as not, they are the product of damage in the neck, as opposed to a new TBI.

That's not to say that rapid head movements can't cause TBI. However, that has occurred in people who engage in repeated, long term, violent head banging behaviour, like some punk rock fans. That's a long way from a simple, rapid head shake.

By rotational injury, do you mean diffuse axonal injury, where the brain is sent spinning around inside the skull? It takes quite a bit of force to set off that motion. It is more likely to happen in things, like high speed MVAs.