Change  class on one specific menu?
You can do this with theme_menu_tree() hook in your theme's template.php file.
Or with a more specific version of theme_mene_tree() hook like MYTHEME_menu_tree__MYMENU().  

function MYTHEME_menu_tree__MYMENU(&amp;$variables) {
    return '&lt;ul class="nav newclass"&gt;' . $variables['tree'] . '&lt;/ul&gt;';
}


See more here https://gist.github.com/gagarine/3201854

UPDATE:

if menu machine name have hyphne like main-menu then change hyphen to underscore, like MYTHEME_menu_tree__main_menu()