USE ROTATION AL SENSORS AND ACCELERATION IN SMARTPHONE FOR PHASE SPACE S

N T odays World The compound system, wheel plus smartphone, defines a physical pendulum which can rotate, giving full turns in one direction, or oscillate about the equilibrium position (performing either small or large oscillations). Paradigm shifts tend to appear in response to critical anomalies or an accumulation of them as well as the proposal of a new theory with the power to encompass both older relevant data and explain r elevant anomalies. New paradigms tend to be most dramatic in sciences that appear to be stable and mature, as in physics at the end of the 19th century. A paradigmatic physical system as the physical pendulum is experimentally studied using the acceleratio n and rotation (gyroscope) sensors available on smartphones and other devices such as iPads and tablets. A smartphone is fixed to the outside of a bicycle wheel whose axis is kept horizontal and fixed. Measurements of the radial and tangential acceleratio n and the angular velocity obtained with smartphone sensors allow a deep insight into the dynamics of the system to be gained. In addition, thanks to the simultaneous use of the acceleration and rotation sensors, trajectories in the phase space are directly obtained. The coherence of the measures obtained with the different sensors and by traditional methods is remarkable. Indeed, due to their low cost and increasing availability, smartphone sensors are valuable tools that can be used in most un dergraduate laboratories.