Circular motion, rotation, gravitation
12 ready-made scenes and Python scripts. Each opens in the studio; press Play to run it, then change anything: masses, lengths, the forces, what the graphs show.
- Disk on a Cart Research
A disk rolling without slipping on a spring-tied cart. Dimensions x and R. - Whirling Mass Research
A ball on a rod in zero gravity at 3 m/s: the rod's pull is the centripetal force mv²/r and the acceleration is v²/r. - Vertical Circle Research
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. - Rolling Race: Slider, Discs and a Hoop Research
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. - Flywheel with Bearing Friction Research
A hexagonal flywheel spun at 12 rad/s against a dry-friction bearing: a constant torque slows it linearly, ω = ω₀ − τt/I. - Tossed Hammer: Centre of Mass Research
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. - Orbits: a Planet and a Comet Research
A fixed sun, a planet on a circular orbit and a comet that starts too slowly and falls in on an ellipse: r v and ½v² − GM/r stay constant for each. - Slipping, then Rolling Research
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. - The Yo-Yo Research
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. - Orbits and Kepler's third law Python Research
Gravitation between bodies (s.G, body.gravitates): circular planets give T²/r³ constant, a slow comet gives an ellipse and conserves r·v. - A gas in a box: pressure from collisions Python Research
Forty atoms bounce in a closed box; the wall's pressure against N⟨KE⟩/A. - Moment of inertia from rolling times Python Research
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.