The strobe is suspended from the box, so it doesn't rotate. The pumpkin sits on the turntable under the strobe (actually the strobe hangs slightly into the pumpkin.) Eight images, slightly different, are carved into the skin of the pumpkin, forming the animation cycle. I chose a nice round pumpkin (a cylindrical one would have been good) so the distortion isn't too great.
Here's an animated gif of the zoetrope in action (animated gif by Jason Hull.)
Here's what it looks like unplugged: