The mobile phone as a free-rotation laboratory

TL;DR

This paper demonstrates how modern smartphones with MEMS gyroscopes can be used as accessible tools to experimentally study free rotation dynamics, including steady states and instabilities, for educational purposes.

Contribution

It introduces a novel method for using smartphones as portable, low-cost laboratories to investigate rotational physics phenomena at home or in remote learning environments.

Findings

Demonstrated steady states of rotation about principal axes.

Observed instability in rotation about the intermediate axis.

Showed approximate conservation of angular momentum and energy.

Abstract

Modern mobile phones contain a three-axis microelectromechanical system (MEMS) gyroscope, capable of taking accurate measurements of the angular velocity along the three principal axes of the phone with a sampling rate of 100 Hz or better. If the phone is tossed in the air, then, neglecting air resistance, it is in free rotation (rotation in the absence of a torque) with respect to its centre of mass, and the phone's gyroscope can be used to record the rotational dynamics. This enables experimental investigation of free rotation. In this paper, we use a mobile phone to demonstrate the steady states for rotation of the phone about two of its principal axes, and the instability in rotation about the third corresponding to the intermediate moment of inertia. We also show the approximate conservation of angular momentum and rotational kinetic energy during motion in the air, and compare the data with numerical solution of Euler's equations for free rotation. Our results demonstrate the capability of smartphones for investigating free rotation, and should be of interest to college and university teachers developing "at home" physics labs for remote learning.