Cecilia Cabeza

Exploring phase space using smartphone acceleration and rotation sensors simultaneously

A paradigmatic physical system as the physical pendulum is experimentally studied using the acceleration 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. 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). Measurements of the radial and tangential acceleration 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 undergraduate laboratories.

Acceleration measurements using smartphone sensors: Dealing with the equivalence principle

Acceleration sensors built into smartphones, i-pads or tablets can conveniently be used in the physics laboratory. By virtue of the equivalence principle, a sensor fixed in a non-inertial reference frame cannot discern between a gravitational field and an accelerated system. Accordingly, acceleration values read by these sensors must be corrected for the gravitational component. A physical pendulum was studied by way of example, and absolute acceleration and rotation angle values were derived from the measurements made by the accelerometer and gyroscope. Results were corroborated by comparison with those obtained by video analysis. The limitations of different smartphone sensors are discussed.

Influence of coaxial cylinders on the vortex breakdown in a closed flow

The effect of fixed cylindrical rods located at the centerline axis on vortex breakdown (VB) is studied experimentally and numerically. We find that the VB is enhanced for very small values of the rod radius

Learning physics in a water park

d

The Atwood machine revisited using smartphones

, while it is suppressed for values of

Rotational energy in a physical pendulum

d

Electronically-implemented coupled logistic maps

beyond a critical value. In order to characterize this effect, the critical Reynolds number for the appearance of vortex breakdown as a function of the radius of the fixed rods and the different aspect ratios was accurately determined, using digital particle image velocimetry. The numerical and experimental results are compared showing an excellent agreement. In addition, a simple model in order to show that this effect also appears in open pipe flows is presented in the appendix.

EXPERIMENTAL DETERMINATION OF POINT LOCALIZED TIME CORRELATION AND POWER SPECTRUM IN A FARADAY EXPERIMENT

Entertaining and educational experiments that can be conducted in a water park, illustrating physics concepts, principles and fundamental laws, are described. These experiments are suitable for students ranging from senior secondary school to junior university level. Newton?s laws of motion, Bernoulli?s equation, based on the conservation of energy, buoyancy, linear and non-linear wave propagation, turbulence, thermodynamics, optics and cosmology are among the topics that can be discussed. Commonly available devices like smartphones, digital cameras, laptop computers and tablets, can be used conveniently to enable accurate calculation and a greater degree of engagement on the part of students.

The Polarization of Light and Malus’ Law Using Smartphones

The Atwood machine is a simple device used for centuries to demonstrate Newtons second law. It consists of two supports containing different masses joined by a string. Here we propose an experiment in which a smartphone is fixed to one support. With the aid of the built-in accelerometer of the smartphone, the vertical acceleration is registered. By redistributing the masses of the supports, a linear relationship between the mass difference and the vertical acceleration is obtained. In this experiment, the use of a smartphone contributes to enhance a classical demonstration.

Exact Discrete-Time Implementation of the Mackey–Glass Delayed Model

Smartphone usage has expanded dramatically in recent years worldwide. This revolution also has impact in undergraduate laboratories where different experiences are facilitated by the use of the sensors usually included in these devices. Recently, in several articles published in the literature,1,2 the use of smartphones has been proposed for several physics experiments. Although most previous articles focused on mechanical experiments, an aspect that has received less attention is the use of rotation sensors or gyroscopes. Indeed, the use of these sensors paves the way for new experiments enabling the measurement of angular velocities. In a very recent paper the conservation of the angular momentum is considered using rotation sensors.3 In this paper we present an analysis of the rotational energy of a physical pendulum.