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⛸️ Conservation of Angular Momentum

L = I · ω (conserved)
arm radius r0.80 m
moment of inertia I2.28 kg·m²
angular speed ω2.00 rad/s
angular momentum L4.56
rotational KE ½Iω²4.56 J
L stays fixed; pull in → I↓ → ω↑. KE rises (your muscles do the work).

Angular Momentum Simulator: The Spinning Skater Effect

This angular momentum simulator shows the figure-skater effect. With no external torque, angular momentum L = I·ω is conserved, so when the spinning skater pulls their hand masses inward the moment of inertia I drops and the angular speed ω must rise to compensate — they spin faster with no extra push. Drag the arm radius in and out and watch the platform whirl up or slow down while a card holds L essentially constant and shows I, ω, and the rotational kinetic energy ½Iω². A subtle point the lab makes clear: that KE actually increases when you pull in, because your muscles do work hauling the masses inward against their inertia — energy that returns when you let them out. The same conservation law spins a collapsing stellar core into a millisecond pulsar. Predict whether the spin speeds up or slows before you move the arms.

What you can do in this simulation

  • Pull a spinning skater's arms in and out and watch the spin rate change to conserve L = Iω
  • A card shows arm radius, moment of inertia, angular speed, angular momentum, and rotational KE
  • See L stay essentially constant while I and ω trade off inversely
  • Notice rotational KE rises when you pull in — the work your muscles do against inertia
  • Predict mode: call faster / slower / same before moving the arms; arms-in, arms-out, and spin-harder presets

Concepts covered

angular momentum · conservation of angular momentum · moment of inertia · rotational kinetic energy · figure skater effect · pulsar spin-up · rotational dynamics

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