Coriolis force model predicts r^{-4} metabolic cost surge for radial inward walk on rotating platform

The arXiv preprint by Mario Pinheiro at arXiv:2606.27400 replaces the textbook point-mass treatment with an active controller that continuously nulls Coriolis acceleration while moving radially. Metabolic power is modeled as P proportional to F_C^n, yielding cost divergences of r^{-2n} near the axis; the standard n=2 case produces a steep r^{-4} climb. A minimal PD-controller reformulation recovers identical scaling, and a one-line entropy-production argument links the effort to non-equilibrium thermodynamics.

Standard undergraduate conservation-of-angular-momentum analysis correctly predicts kinetic-energy increase yet omits the dominant sideways stabilization cost that any real walker experiences. The paper supplies an order-of-magnitude playground protocol using a phone accelerometer and heart-rate strap to test the predicted divergence, explicitly labeling the estimate as such. This framing turns a mechanics exercise into a lesson on assumption sensitivity and model validity.

Related work on vestibular and proprioceptive control during locomotion (e.g., studies of Coriolis perturbations in rotating rooms) shows that humans generate anticipatory torques whose amplitude grows with rotation rate, consistent with the n=2 cost curve. The preprint therefore bridges classical mechanics and applied biophysics without invoking new data.

Future measurements on actual merry-go-rounds will be required to discriminate between linear and quadratic cost exponents and to determine whether subjects adopt curved trajectories that trade angular-momentum change against reduced lateral force.