unix - ubuntu 9.04 /var/www permissions

ubuntu 9.04, user luca wants to access the /var/www directory.

the directory is owned by user root, group root

I changed the group ownership to www-data (sudo chgrp -R www-data /var/www/) and added write privileges to that group (sudo chmod -R g+w /var/www), and added luca to that group (sudo adduser luca www-data).

Now, why can't luca still write to /var/www? It should be able to, right?

in /etc/group we have: "www-data:x:33:luca"

permissions for /var/www are: "drwxrwxr-x 2 root www-data 4096 Feb 26 15:35 www"