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PolskiCarnival Ferris Wheel (2D): Centripetal Force & Apparent Weight
A real pendulum-with-accelerating-pivot model swings each gondola around a rotating wheel, while a live readout tracks angular velocity, rim speed and how a rider's apparent weight rises and falls with every rotation.
The 3D version of this ride is a decorative orbit-camera scene — you can fly around a glowing night-time wheel, but nothing on screen actually responds to a control. This 2D companion builds the physics the title promises: the wheel turns at a rotation rate you set, and each gondola is modeled as a genuine pendulum whose pivot accelerates because it is riding on a rotating rim. That coupling — a pendulum bob reacting to its own moving anchor point — is exactly what keeps a real Ferris-wheel cabin hanging level instead of getting dragged around with the arm, and the same coupling is what makes it sway when the ride starts, stops, or runs too fast. A live panel tracks the wheel's angular velocity and period, the rim's linear speed, the centripetal acceleration at that radius, and — for one tracked gondola — its height above the lowest point, its swing angle, and the rider's apparent weight and g-force as it cycles between heaviest at the bottom and lightest at the top.
Each gondola integrates L·α″ = −g·sin(α) − a_pivot_x·cos(α) + a_pivot_y·sin(α) − c·α′, the equation of motion for a pendulum whose pivot itself accelerates — here the pivot's acceleration is the wheel's own centripetal acceleration, a_pivot = −ω²·(pivot − center). Apparent weight at the tracked gondola follows N = m·(g + ω²R·cos θ), θ measured from the bottom of the wheel, which is the standard result for why a Ferris-wheel rider feels heaviest at the bottom and lightest at the top.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install
Apparent weight depends on the direction of the centripetal acceleration relative to gravity, not on whether the speed itself changes. At the bottom of the wheel the centripetal acceleration points straight up (toward the center), adding to what the seat must supply, so the rider feels heavier. At the top it points straight down, subtracting from the seat force, so the rider feels lighter — even though ω never changes.
Real Ferris-wheel cabins are hinged, not bolted rigidly to the wheel — gravity keeps them oriented downward, like a pendulum, rather than spinning with the arm. This sim integrates that pendulum explicitly, including the extra push from the pivot's own centripetal acceleration, so raising the RPM or lowering the damping visibly makes the cabins swing wider.
It stands in for the combined effect of the gondola's hinge friction and air resistance. At zero damping a gondola disturbed from vertical would swing indefinitely; realistic Ferris wheels use enough mechanical damping that the swing settles out within a few rotations, which is what higher slider values reproduce.