My dad is helping me build this since he's got all the tools and engineery know-how, that's him in the picture on the left. (I did some work too, but I can't use power tools and a camera phone at the same time, so you'll have to trust me on this.)
After cutting the plywood to the right size with a hand held circular saw, we had to make a circular cutting jig for the router. Dust everywhere, good thing we did it in the garden.
After making a recess for the disc to sit in we used a jigsaw to follow the inside edge of the previous cut to leave an almost circular hole.
Here it is. It took a bit of trial and error to get the disc to fit in the hole and rotate freely, we sanded the edge of the acrylic untill it fit just right, although it wasn't far off, considering we took turns hacking it out of a 500x500mm sheet of 5mm acrylic with a coping saw.
The disc was a bit stiff turning on the bare plywood, so I glued some strips of an old T-shirt to the lip it runs on.
Here's the disc in the board with the finger holes drilled to help rotate it, there's not a lot more we can do right now because the lights haven't arrived yet and we need them to see how deep the base needs to be.
That's everything to do with this project so far, I left out the parts where stuff went wrong so it looks more professional like, more later!
PRO TIP: Keep your cuttings! If you try this yourself you'll want them to test tools on and make sure the acrylic doesn't just melt with high speed tools. I threw mine away, but luckily everything turned out fine.