Physics Experiments with Arduino and Smartphones

Preface
Acknowledgements
Contents
1 Physics and  Nature
	Giovanni Organtini
		1.1 Physics and Other Sciences
		1.2 Measurements and the Laws of Physics
		1.3 The Process of Measurement
		Summary
		References
		References
2 Establishing a  System of Units
	Prof.Giovanni Organtini
		2.1 Measuring Light Intensity
		2.2 Definition of Units
		2.3 Systems of Units
		Summary
		References
		References
3 Collecting Data
	Giovanni Organtini
		3.1 Instruments
		3.2 Smartphones
		3.3 Arduino
		3.4 Open Source Makes It Better
		3.5 Measuring Light Intensity with a Smartphone
		3.6 Measuring Light Intensity with Arduino
		3.7 Understanding Arduino Programming
		3.8 Python Data Collection
		Summary
4 Uncertainties
	Giovanni Organtini
		4.1 Data Analysis
		4.2 Data Analysis with Python
		Summary
5 Establishing Physical Laws
	Giovanni Organtini
		5.1 Light Transmission
		5.2 Taking the Average with Arduino
		5.3 A First Look at Data
		5.4 Plotting Graphs and Interpolating Data
		5.5 An Approximated Model
		5.6 Non-polynomial Models
		5.7 The Exponential Model
		Summary
6 Free-Fall and  Accelerations
	Giovanni Organtini
		6.1 Setting Up the Experiment
		6.2 Measuring Times
		6.3 Photogates
		6.4 Measuring Time with Arduino
		6.5 An Acoustic Stopwatch
		6.6 Uncertainty Propagation
		6.7 Measuring Accelerations
		6.8 MEMS Accelerometers
		6.9 Annotating Graphs
		6.10 Instrument Characteristics
		Summary
7 Understanding Data Distributions
	Giovanni Organtini
		7.1 On the Values Returned by Instruments
		7.2 Probability
		7.3 Bayes Theorem and Physics
		7.4 Statistical Distribution of Data
		7.5 Uniform Distribution
		7.6 Expected Value, Variance and Moments
		7.7 Combining Errors, Revisited
		7.8 The Binomial Distribution
		7.9 The Shape of the Bimonial Distribution
		7.10 Random Walk
		7.11 The Poisson Distribution
		7.12 The Shape of the Poisson Distribution
		Summary
		References
		References
8 Counting Experiments
	Giovanni Organtini
		8.1 Experiments with Binomial and Poisson Statistics
		8.2 Operations on Lists
		8.3 Chauvenet's Criterion
		8.4 Simulating Advanced Experiments
		8.5 Using Arduino Pins
		8.6 The Phyphox Editor
		8.7 Readily Available Particle Detectors
		8.8 Image Manipulation with Python
		Summary
		Reference
		Reference
9 The Normal  Distribution
	Giovanni Organtini
		9.1 A Distribution Depending on the Distance
		9.2 The Central Limit Theorem
		9.3 Experimental Proof of the Central Limit Theorem
		9.4 The Markov and Chebyschev Inequalities
		9.5 Testing Chebyschev's Inequality
		9.6 The Law of Large Numbers
		9.7 The Uncertainty About the Average
		Summary
10 Kinematics
	Giovanni Organtini
		10.1 Designing the Experiment
		10.2 Measuring Time and Distances with Arduino
		10.3 Ultrasonic Sensors
		10.4 Arduino Data Acquisition
		10.5 Collecting Data
		10.6 Data Analysis
		10.7 Evaluating the Goodness of a Fit
		10.8 Data Processing
		10.9 The χ2-Distribution
		10.10 The Least Squares Method
		10.11 Discarding Bad Data
		10.12 Measuring Gravity Acceleration
		Summary
11 Oscillations
	Giovanni Organtini
		11.1 An Experiment to Study Elasticity
		11.2 A Study of Spring Dynamics with Smartphones
		11.3 Obtaining Parameters from Data
		11.4 Extracting and Manipulating Data
		11.5 Optimisation Methods
		11.6 A Harmonic Oscillator with Arduino
		11.7 Newton's Laws
		11.8 A Widely Applicable Model
		Summary
		Reference
		Reference
12 Maximum Likelihood
	Prof.Giovanni Organtini
		12.1 Application of the Bayes Theorem to Measurements
		12.2 An Experimental Proof
		12.3 Parameter Estimation
		Summary
13 Physics in  Non-inertial Systems
	Giovanni Organtini
		13.1 Dynamics in Non-inertial Systems
		13.2 Free-Fall
		13.3 Custom Experiments with Phyphox
		13.4 Centripetal and Centrifugal Accelerations
		13.5 Coriolis Acceleration
		13.6 Euler Acceleration
		Summary
14 Dynamics of  Rigid Bodies
	Giovanni Organtini
		14.1 A Cylinder Rolling Along an Incline
		14.2 Using a Smartphone's Gyroscope Remotely
		14.3 Arduino Gyroscopes and I2C Communications
		14.4 The Arduino Wire Library
		14.5 Using an SD Card
		14.6 Using SD Cards to Store Data
		14.7 The Native SPI Protocol
		Summary
		References
		References
15 Wave Mechanics
	Giovanni Organtini
		15.1 Making Waves
		15.2 Command Line Options
		15.3 Properties of a Wave
		15.4 The Student's t-Distribution
		15.5 Interference
		15.6 Finding the Distribution of a Random Variable
		15.7 Beats
		15.8 Collecting Audio Data with Arduino
		15.9 Dimensional Analysis
		15.10 Temperature Measurements with Arduino
		15.11 The 1-Wire Protocol
		15.12 Establishing a Correlation
		Summary
		References
		References
Index
	Index