In zero gravity - I'm floating inside a torus as they spin it up, do I float do the "ground"? Imagine this scenario - I'm in a space station with one of those huge torus shaped constructions, that you spin to simulate gravity through centripetal force. But it's turned off right now, so I'm floating in the air.



When happens when they turn it on and it starts spinning?
I can imagine what would happen if I was grabbing on to something. I'd be pulled around, and the angular velocity would drag me to the outer part of the torus. But if I'm just floating there, with no friction to the ground to catch me, do I stay put, with the thing just whizzing past me?
Yes...

In the scenario you describe, you (and the air) will remain at rest, while the torus speeds up.  One hopes there are no radial partitions, or, if there are, one comes along to pick you up fairly early in the session.

Unfortunately, the rotating torus will impart its velocity to the air in contact with all the irregularities in the wall/floor/ceiling.  This would then be transferred to the rest of the air.  Floating there, you would experience a very slight breeze blowing you in the direction of rotation of the station.  This in turn would cause you to slowly drift radially outward, until you hit the floor and rolled along until you were at rest with respect to the floor.

Even if the station is not running up from zero rotation rate, you can experience some strange effects.

If the station is big enough, you can travel with low energy.  Simply run against the rotation of the station.  When you are running at the rotation speed, lift your feet, and drift in place until your destination comes along.  Put down you feet, start running, and slow to a walk.

Be careful, though.  If you face in the wrong direction and run at that same speed, your apparent weight will quadruple as you crash to the floor...