Step 4: Cut the pieces!
When you're done, get some finer sand paper and do a final sanding by hand. You can't get a very good finish on the lathe since the glue joints will make the sandpaper bounce, so just take the extra time and do some sanding by hand. The wood piece doesn't need to be very good, if you leave it roughish it makes a good wood texture.
For the tip of the rocket launcher I didn't have a good way to accurately cut foam so I did a rough job with a drill bit then put a PVC pipe in the end. With a little wood glue to fill the big gaps and some layers of Mod Podge on top it blended in nicely.
Once you're done sanding put some layers of Mod Podge on the pieces. We did 3 or 4 coats on each.