Using Theme park rides and smartphones for demonstrating Newtonian mechanics

Researchers demonstrate that consumer smartphones can reconstruct full three-dimensional trajectories of theme-park rides using inertial odometry to teach Newtonian mechanics. Using 100 Hz acceleration and gyroscope data recorded with the phyphox app, orientation was obtained via quaternion integration with drift correction using zero-velocity updates and spherical linear interpolation. Gravity-corrected double integration of the oriented accelerations produced spatial paths, allowing direct calculation of velocities, kinetic and potential energy, and detailed motion features. Measurements were taken on a launched roller coaster and a pendulum ship, with phones carried in pockets to keep them fixed relative to the carriage; video was used to time-correlate ride events.

Reconstructed coaster and pendulum trajectories capture launch acceleration, loop and roll dynamics, periodic pendulum motion, and active energy input, with the roller-coaster path matching satellite imagery to within about 5 m. The approach reveals energy exchange between elevation and speed and provides a tangible platform for testing conservation of mechanical energy in complex rides. Limitations include sensor noise, occasional phone reorientation, and omitted formal uncertainty propagation, but repeated measurements across different phone models produced consistent patterns. The method is presented as an accessible, hands-on tool for first-year mechanics education and open problem-based learning.