Personally, my favourite theorem in classical mechanics is the so called 'tennis racket theorem', sometimes known as the 'intermediate axis theorem'.
It explains why objects with roughly three different moments of intertia have unstable rotation about their intermediate moment.
It can be easily demonstrated with a tennis racket, or even most smartphones (be careful not to break it though).
https://en.wikipedia.org/wiki/Tennis_racket_theorem
https://www.youtube.com/watch?v=4dqCQqI-Gis
Personally, my favourite theorem in classical mechanics is the so called 'tennis racket theorem', sometimes known as the 'intermediate axis theorem'.
It explains why objects with roughly three different moments of intertia have unstable rotation about their intermediate moment.
It can be easily demonstrated with a tennis racket, or even most smartphones (be careful not to break it though).
https://en.wikipedia.org/wiki/Tennis_racket_theorem