  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.
