I've been asked to replace a professor for a couple of classes in an undergraduate quantum mechanic course. I have to present some topics on angular momentum, including the addition of angular momentum. I have no problem with the general theory and can present it just fine. But I would like to give an example where the addition of angular momentum is needed. And I would like a small but physical example where the addition of angular momentum is relevant. The most standard example, the hyperfine splitting in hydrogen, is too long for me to present in a couple of short lectures.