Hide ribbon from annonymous users - SP 2010

Use this link info to hide ribbon effectively from annonymous users. It also resolves the scrollbar issue,
http://www.portalsolutions.net/Blog/Lists/Posts/Post.aspx?ID=91

If you want authenticated users to see the ribbon then you have multiple options,
1. Move the "welcome user" to another location on the page.
2. Provide a new link that points to /_layouts/authenticate.aspx which will open up IE login window.