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From Ordinate 2D ✓

Script Moment of inertia from rolling times Script · Ordinate 2D ✓ A disc, a thick ring, a thin hoop and a sliding block race down equal slopes; k = g sin θ t²/2L − 1 gives each one's I/mr². Script A gas in a box: pressure from collisions Script · Ordinate 2D ✓ Forty atoms bounce in a closed box; the wall's pressure against N⟨KE⟩/A. The Yo-Yo Scene · Ordinate 2D ✓ A disc falls as its string unwinds: a = g/(1 + I/mR²) = ⅔ g, and the string holds a third of its weight, until the string runs out. A box beside it falls at g. Slipping, then Rolling Scene · Ordinate 2D ✓ A disc and a hoop are thrown along the floor without spinning: both slide at first, friction slows the centre and spins the body up until v = ωR, then both roll steadily at v₀/(1 + k): ⅔ v₀ for the disc, a little over half for the hoop. Tossed Hammer: Centre of Mass Scene · Ordinate 2D ✓ A handle welded to a heavy head is tossed with a spin: it tumbles, but its centre of mass follows the parabola of a thrown point mass. Flywheel with Bearing Friction Scene · Ordinate 2D ✓ A hexagonal flywheel spun at 12 rad/s against a dry-friction bearing: a constant torque slows it linearly, ω = ω₀ − τt/I. Rolling Race: Slider, Discs and a Hoop Scene · Ordinate 2D ✓ Four ramps: with no friction nothing spins and the slider wins at g sin θ; a disc turns I = ½mr² and runs at g sin θ / 1.5, small or big, light or heavy; a hoop (a ring, I = ½m(R² + r²), nearly mr²) comes last at g sin θ / 1.9. Vertical Circle Scene · Ordinate 2D ✓ A ball swung in a vertical circle: the rod pulls hardest at the bottom (mg + mv²/r) and least at the top, while the energy stays constant.

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