Given how often 2π shows up in formulae: capacitive and inductive reactance, Heisenberg's Uncertainty Principle (and any other equation that uses the Reduced Planck Constant) for starters, but anyone who knows their math and physics will be able to rattle off a few more.
But I wondered if the circle would kill the idea. Surprisingly it didn't! Area of a circle as 1/2τr^2 makes a lot of sense, especially in light of the Quantity - Symbol - Expression table. In fact, that table was missing an important entry! "Kinetic Energy", there should have read "Kinetic Energy - Linear Motion", to be followed by a line for "Kinetic Energy - Angular Motion". The formula? 1/2Iω^2 -- where "I" is the "moment of inertia" (angular mass) of a spinning object and "ω" is "angular velocity".
This idea, this fight looks a bit like tilting at windmills but interesting. I wonder if it's something that will ever get any traction?
I'd like the world to be a place where enough of the life-and-death issues are settled that most people who might possibly be interested in the question would have the leisure to consider it...