In my computer networking class I have the option of doing a project where I set up a dns server for our classroom network. The problem is that this network is totally separate from the school network and we aren't allowed to connect it to the internet. I want all the machines to ping each other by name instead of ip using dns instead of host files on all 20 computers. I read on a site somewhere that you cannot do this because the dns queries will always go to the root servers. Is this correct? Is there some way I can do this using dns? The machine in question is using Ubuntu 9.04.

You can do this, you only need access the root servers for systems that can't be found by the local DNS server.
Actually, DNS is hierarchical and your ISP's DNS cache would likely resolve a lot of names; otherwise the root servers would be flooded.
Anyway, there's a good guide here: http://www.linuxtopia.org/online_boo...5_ch-bind.html.
DNS is distro neutral at the cmd line.