I've read that in most languages, front vowels are unrounded and back vowels are rounded. This helps make them more distinct from each other so as to be easier to hear in speech. However, different languages make their phonemes distinct in different ways, and apparently some languages contrast unrounded and rounded versions of the same vowels.
My question, then, is whether there are any languages which 'glide' between these vowels. Imagine making a consonant sound, say [p], and then moving first to unrounded [a] and then rounded [a]. Does this sort of thing happen in a consistent way in any known natural language?