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I'm diagreeing with the idea, not to answer a question according to the known facts. Of course, when learning about classical mechanics in the very first semesters you cannot explain relativity and quantum mechanics in all detail, but you can tell the students already then, in a qualitative way, as I tried in my answers above, that you need more advanced physics to answer the question. After all, we teach classical mechanics not so much for its own sake but as the preparation for the more advanced and up-to-date topics of modern physics.
For me the main justification to teach the fascinating subject of rigid bodies and spinning tops is to introduce the rotation group as a Lie group and use Lie-algebra arguments to derive the equations of motion using Hamilton's principle (at my university it's usualy taught in the 2nd semester in the 2nd theory-course lecture, where analiytical mechanics is treated). It's a great opportunity to introduce these quite advanced topics at the example of a non-trivial but fascinating phenomenon.
For me the main justification to teach the fascinating subject of rigid bodies and spinning tops is to introduce the rotation group as a Lie group and use Lie-algebra arguments to derive the equations of motion using Hamilton's principle (at my university it's usualy taught in the 2nd semester in the 2nd theory-course lecture, where analiytical mechanics is treated). It's a great opportunity to introduce these quite advanced topics at the example of a non-trivial but fascinating phenomenon.