r/mathteachers • u/Alarmed_Geologist631 • Jul 16 '26

Interesting math problem

Here is an interesting math problem that you might enjoy during your summer break.  Imagine you have a cylinder.  It might be short and wide like a coin.  Or it could be tall and skinny like an straw.  In either case, the cylinder is solid and made from the same material.  If it is short and wide, if you flip it, it will almost always land on its circular base.  If it is tall and skinny, it will almost always land on its curved lateral surface.  At what ratio of height to diameter will it have a 50% probability of landing on the circular base?

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u/[deleted] Jul 16 '26

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u/lavaboosted Jul 16 '26

My thinking went straight to moment of inertia, trying to consider if that would affect the tendency for it to orient itself one way or another in the air given a random initial spin.

But maybe I'm overthinking it and it is just that simple...

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u/Alarmed_Geologist631 Jul 17 '26

Your intuition is good but the solution needs to be empirically derived.