The same puck, seen from the room (left) and from the spinning disc (right). Straight in one view, curved in the other.
Each preset changes one idea. In the disc view the arrows show what an observer on the disc calls forces.
The puck starts left of the centre; 0° aims through the centre (angle measured on the disc). Changing anything relaunches.
Turntable: closed form = straight line in the room, rotated back onto the disc. Dish: w = ux + i uy obeys dw/dt = -2iΩw. Neither uses the integrator.
Launches from the centre at your speed and measures the angle the path has curved when it reaches r = 0.8 m, for seven spin rates, then fits a line. Prediction: θ = Ω r / u (the disc turns by Ω times the crossing time r/u).
In a frame rotating at angular velocity Ω a free body obeys a = −2 Ω × v − Ω × (Ω × r). The first term is the Coriolis acceleration (perpendicular to the velocity, does no work); the second is the centrifugal acceleration Ω² r, pointing outward. Neither is a real force: they are what straight, constant-velocity motion looks like to an observer who spins.
Turntable. A frictionless puck leaves with room-frame velocity u + Ω × r₀ and moves in a straight line, so its disc position is the room-frame line rotated by −Ωt. The page compares this closed form with the RK4 integration. The Jacobi energy ½|v|² − ½Ω²r² is conserved.
Dish. On a paraboloid z = Ω² r²/(2g) the slope cancels the centrifugal term exactly (the idea of a liquid-mirror telescope), leaving only Coriolis: dw/dt = −2iΩw. Speed stays constant and the velocity vector turns at rate 2Ω, so the velocity-plane plot is a circle and the puck circles with radius u/(2Ω) and period π/Ω — a model of inertial oscillations in the ocean and atmosphere. The dish is drawn flat here.
What this 2D view adds: both frames side by side, acceleration arrows at the puck, and the velocity plane (vx, vy). The 3D version has the real-Earth latitude calculator.
Simplifications: no friction, point puck, rigid disc at constant Ω. The puck stops at the rim (r = 1 m). This does not decide which way a bathtub drains: at that scale f is far too small compared with other effects.