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Desk Physics

Six experiments with things on an office desk, drawn in 3D, each worked from the physics and held to it by tests, with sliders for the sizes you measure. The leaning tower is the harmonic stack: each item L/2k past the one below, the overhang L/2 times the harmonic number, every level balancing exactly at the limit, and for 76 mm pads four the fewest that put the top one clear of the desk at the limit, five with each step backed off a millimetre. The rolling race times each shape by g sin(angle) / (1 + k), and the tests check those times against rolling worked out from the forces for light and heavy, small and big. The paper pull is friction while the sheet slides and after, checked against friction stepped through time, with the speed below which the mug rides along. The keys swing with the exact pendulum period, and two on one string hand the whole swing over at the time it is set from. The book is the tennis racket flip with a book's three moments of inertia. The spinning coin rolls round on its rim at the rate the desk's push allows, the square root of 4g over (radius times the sine of the tilt), checked by the angular momentum's rate of change against that push, with no slip. Ours: every default size and speed, both friction figures until you measure them, the jerk to full speed in the pull, the string's link between the keys, the 2% off-axis start of every toss, a thin coin, and how fast it lies down.