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You will find that conservation of momentum is a principle that works
quite well in the horizontal plane in an accelerated frame. There is no
need to give it up. I'm very curious about how you teach your students
the first law of motion. I start by showing my students that we don't
live in an inertial frame. The first law is not trivial by any means;
it is a great intellectual feat to abstract to an environment one has
never experienced for any appreciable time - and lived to tell of it!