Does the tokina AT-X 16-28mm work on a DX format Nikon?

I own a Nikon D7100. The Tokina lens is intended for FX Nikon cameras. I was wondering it if would still be able to work with a DX format Nikon without the vignetting. Also. What would the focal length be when mounted to a DX camera?

You only get vignetting when you use a DX lens on a FX camera

Just do the 1.5X conversion for your focal length.

http://photographylife.com/using-nikon-dx-lenses-on-fx-cameras

It'll work fine. It's only when you go from DX to FX bodies you might get vignetting (although using Nikon DX lenses on a FX body doesn't result in vignetting because the camera recognises a DX lens is attached and readjusts the sensor).

The focal length doesn't magically change whatever camera body It's mounted on - it's a physical property of the lens.

The field of view will be different - it will be equivalent to a 24-42mm lens on a full frame camera.