Tekneτέχνη

T-19 · Rigid bodies

Things that turn.

A body that turns resists by its moment of inertia, a sum of squared distances, and so Pythagoras is everywhere: in the parallel-axis theorem, in the radius of Mohr's circle, in the speed of a rolling wheel's rim. Bodies race down a slope in exact fractions, and a box spun about its middle axis flips over on a clock set by the pendulum's elliptic integral.

dgreen: the centre of mass and the principal axesviolet: d from P, the hypotenuse of Δx and ΔyPMohr's circle: moments across, product up2α(Iₓ, −Iₓᵧ)(I_y, Iₓᵧ)principal: 10 and 2.5radius: the hypotenuse of(Iₓ − I_y)/2 and IₓᵧTEKNE · T-19 RIGID BODIES · MOMENTSarea 6 · centre (3/2, 1) · unit densityJ_P = J_cm + M d² = 110