A Rotation-Compensated Smartphone Accelerometer Application for Undergraduate Mechanics Experiments

TL;DR

This work developed a web-based accelerometer application that can provide acceleration in a stationary global coordinate system and shows that rotation-compensated acceleration enables accurate reconstruction of velocity, displacement, and trajectories even when the smartphone changes its orientation.

Abstract

Smartphones equipped with sensors such as accelerometers, gyroscopes, and magnetometers offer valuable opportunities for physics education, allowing students to measure motion using their own devices. However, commonly used applications provide acceleration only in the device-fixed coordinate system, which makes it difficult to analyze two- or three-dimensional motion when the device rotates. To address this limitation, we developed a web-based accelerometer application that can provide acceleration in a stationary global coordinate system. This is achieved by simultaneously recording acceleration in the device-fixed coordinate system and Euler angles, and converting them to rotation-compensated acceleration in real time. We also built a companion web application for numerical integration, noise reduction, and visualization of the measured data. Both applications are installation-free and can be accessed directly through a smartphone browser. We demonstrate the capabilities of the newly developed system through several representative types of motion, including sliding motion, projectile motion, and circular motion, by showing that rotation-compensated acceleration enables accurate reconstruction of velocity, displacement, and trajectories even when the smartphone changes its orientation. The applications were implemented in undergraduate mechanics classes, where students used them in group-based experiments. Classroom observations suggested that the use of these tools facilitated a deeper understanding of the relationships among acceleration, velocity, and position. These results suggest that rotation-compensated smartphone measurements provide a practical and effective tool for physics education.

Figures (13)

• Figure 1: Order of rotation of $z$-$x$-$y$ Euler angles. (i), (ii) and (iii) are the schematic representations of rotation of a mobile device around $z$, $x$ and $y$ axes, respectively. The light purple plate represents the device such as a smartphone.
• Figure 2: Conversion of acceleration from a device-fixed coordinate system to a stationary one.
• Figure 3: (a) Screen of acceleration measurement app. (b) Two-dimensional code of the measurement app. (c) Bottom area of this application.
• Figure 4: Screen of acceleration data analysis app. The inset at the right bottom is the two-dimensional code of the manual page for the analysis app.
• Figure 5: Acceleration, velocity, and position for sliding motion on a horizontal surface under kinetic friction: (a) Measured acceleration in the stationary coordinate system. (b) Velocity obtained by numerical integration. (c) Position obtained by further integration.