Why does walking to the center of a merry-go-round feel so hard? Coriolis stabilization and the metabolic cost of staying on track

Abstract

We revisit Feynman's classic carousel problem (\textit{Feynman Lectures}, Vol.~1, Sec.~19.4), in which a student walks radially inward on a platform driven at constant angular velocity $ω_0$ by an external motor. Working consistently in the frame co-rotating with the platform, we show that the student's kinetic energy in that frame is exactly \emph{constant}: the mechanical work done by the real radial friction force is exactly cancelled by the work done against the centrifugal inertial force. The Coriolis inertial force, and the equal-and-opposite tangential friction force required to cancel it and keep the student on a straight radial path, do \emph{zero} mechanical work, because both are perpendicular to the radial velocity. Yet generating that tangential force costs metabolic energy -- precisely the effect Feynman flagged with ``one has to lean over and push sidewise.'' The mechanical model adopted here (a point mass with kinematically imposed trajectory) is deliberately silent about internal physiology; the metabolic cost discussion of Sec.~\ref{sec:cost} is a separate phenomenological layer, explicitly flagged as such, not derived from the mechanics. We give an order-of-magnitude metabolic estimate, an entropy-production argument connecting the exercise to the second law, a feedback (PD-controller) reformulation of the same physics, and a playground experiment students can run with a phone and a heart-rate strap. Throughout, we are explicit about reference frames and about the limits of each model.