Physics Book - User contributions [en]

File:Pic3.png

2016-11-25T20:34:28Z

Tconnors3:

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2016-11-25T20:18:01Z

Tconnors3:

Main Page

2016-11-25T18:53:42Z

Tconnors3: /* Electric field */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
edit: Maria Furukawa
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
Claimed by pg66
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">
==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
Aniruddha Nadkarni

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy - Claimed by Janki Patel]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

*[[RLC Circuits]]
*[[LR Circuits]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2016-11-25T18:45:25Z

Tconnors3: /* Electric field */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
edit: Maria Furukawa
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
Claimed by pg66
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">
==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
Aniruddha Nadkarni

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy - Claimed by Janki Patel]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

*[[RLC Circuits]]
*[[LR Circuits]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2016-11-25T18:44:43Z

Tconnors3: /* Electric field */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
edit: Maria Furukawa
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
Claimed by pg66
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">
==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
Terrence Connors
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
Aniruddha Nadkarni

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy - Claimed by Janki Patel]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

*[[RLC Circuits]]
*[[LR Circuits]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Iterative Prediction

2015-12-05T19:10:04Z

Tconnors3: /* History */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum (shown here as <math>\vec{p}_{future}</math>) of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).
[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==

Iterative Prediction serves as a basis for modeling complex motion throughout time. While some of the basic examples do not appear to be too trivial, iterative prediction can be used to solve more difficult problems. Having now almost completed a semester of mechanics, one topic that I became interested in almost right away was this idea of being able to solve problems in which we aren't necessarily concerned with the physics of the system at the current moment in time. Iterative Prediction of motion is just one of the many different techniques we have used to study the "physics of the future."

Iterative Prediction can have many applications to the field of Chemical Engineering, namely in the principles governing momentum transfer in chemical processes. A simple example is in studying fluid flow in a process. By making use of iterative prediction and the momentum principle, a chemical engineer can model the change in momentum of the fluid flow by analyzing the net force on the fluid (likely due to pressure) and the initial momentum of the fluid flow. In industry, this can be important so as to predict accumulation in a process and thus allow for modeling of an efficient process to maximize output.

==History==

The physics behind iterative prediction is nothing more than simple application of the momentum principle and projectile motion, which has existed in classical mechanics for quite some time. However, the practical application of iterative prediction for analyzing systems has evolved due to advances in computational methods and technology. With the computational power of a computer to iteratively calculate changes in momentum through time, one can analyze a system's motion extremely quickly without tedious and difficult mathematical calculations.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-27T20:24:29Z

Tconnors3: /* Connectedness */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum (shown here as <math>\vec{p}_{future}</math>) of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).
[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==

Iterative Prediction serves as a basis for modeling complex motion throughout time. While some of the basic examples do not appear to be too trivial, iterative prediction can be used to solve more difficult problems. Having now almost completed a semester of mechanics, one topic that I became interested in almost right away was this idea of being able to solve problems in which we aren't necessarily concerned with the physics of the system at the current moment in time. Iterative Prediction of motion is just one of the many different techniques we have used to study the "physics of the future."

Iterative Prediction can have many applications to the field of Chemical Engineering, namely in the principles governing momentum transfer in chemical processes. A simple example is in studying fluid flow in a process. By making use of iterative prediction and the momentum principle, a chemical engineer can model the change in momentum of the fluid flow by analyzing the net force on the fluid (likely due to pressure) and the initial momentum of the fluid flow. In industry, this can be important so as to predict accumulation in a process and thus allow for modeling of an efficient process to maximize output.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-27T20:10:46Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum (shown here as <math>\vec{p}_{future}</math>) of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).
[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T18:40:31Z

Tconnors3: /* A Visual Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum (shown here as <math>\vec{p}_{future}</math>) of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).
[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T18:39:57Z

Tconnors3: /* A Visual Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum (shown here as <math>/vec{p}_{future}</math>) of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).
[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T18:38:52Z

Tconnors3: /* A Visual Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change (<math>\vec{F}_{net}{Δt}</math>).

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T18:37:49Z

Tconnors3: /* A Visual Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum (denoted <math>\vec{p}_{now}</math>) and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T02:01:38Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1)}\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2)}\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T02:01:12Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}|center|\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T02:00:54Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)}|right|\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T02:00:14Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3)|right|}\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T01:58:39Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div><div style="text-align: right;"><math>{(3)}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T01:57:21Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>{(3)|right|}

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-26T01:56:15Z

Tconnors3: /* A Mathematical Model */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the ''momentum update form'' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1) }\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2) }\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3) }\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-25T23:51:45Z

Tconnors3: /* See also */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the '''momentum update form''' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1) }\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2) }\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3) }\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

There are many public resources that delve further into iterative prediction examples of more complex motion.

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-25T23:50:24Z

Tconnors3: /* External links */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the '''momentum update form''' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1) }\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2) }\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3) }\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

[http://en.wikipedia.org/wiki/Portal:Physics Physics Portal]

[http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics Concept Map]

[http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MIT Open Courseware Introductory Mechanics]

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-25T23:46:22Z

Tconnors3: /* References */

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the '''momentum update form''' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1) }\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2) }\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3) }\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Wednesday, Week 2 Lecture Slides. Fenton, Flavio H

Georgia Institute of Technology. Physics Department. PHYS 2211. Fall 2015. Monday, Week 3 Lecture Slides. Fenton, Flavio H

Iterative Prediction

2015-11-25T23:43:20Z

Tconnors3:

Claimed by tconnors3

==An Overview==

The Momentum Principle is one of the fundamental principles in the study of mechanics and dynamics. By applying it to real world problems, the motion of systems can be modeled at specific points in time. Additionally, analyzing the implications of the momentum principle, physicists can not only pinpoint behavior of systems, but can also predict the motion of systems at specified times in the future.

===A Mathematical Model===

By starting from the general equation for the Momentum Principle, a formula can derived to predict the momentum of a given system at a specified point in the future. This is often referred to as the '''momentum update form''' of the Momentum Principle:

<div style="text-align: center;"><math>{{(1) }\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math></div>

<div style="text-align: center;"><math>{{(2) }\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math></div>

<div style="text-align: center;"><math>{{(3) }\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math></div>

Equation <math>{(3)}</math> gives the momentum update form of the momentum principle. As it shows, the momentum of a system can be predicted if the time period of the interaction and the external net force on the system are known. Momentum can be iteratively predicted like such for uniform or non-uniform time periods. Additionally, with update of momentum, velocity and position can be updated similarly to better reflect the motion over time of the system:

<div style="text-align: center;">'''Velocity Update Formula''':

<math>{\vec{v}_{f} = \vec{v}_{i} + \frac{{F}_{net}}{m}}{Δt}</math>

'''Position Update Formula''':

<math>{\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}}</math></div>

===A Visual Model===

As the momentum update formula suggests, the final momentum of a system after a given change in time should be the vector sum of the initial momentum and the net force on the system multiplied by the scalar time change.

[[Image:MOTION.png|center|650x300px|]]

As the diagram suggests, each individual step can be analyzed through application of the momentum update form of the Momentum Principle. Once the final momentum is calculated, by utilizing the position and velocity update formulae, the final velocity and position of the system can be determined at the end of the time interval of interest.

==Example Calculations==

There are a variety of different problems that can be solved by utilizing the momentum update form of the Momentum Principle. They can vary in difficulty and require any number of iterations. It is often prudent to calculate these iterations in a program loop to save time and avoid miscalculations.

===Example #1 - Momentum Update===

'''A boy standing on level ground throws a 2 kg ball into the air at an initial velocity of <math>{<8,6,0> m/s}</math>. If the only force acting on the ball is gravity, what is the final momentum of the ball after 0.2 seconds?'''

This problem can be solved simply by solving for final momentum in the momentum update equation:

<div style="text-align: center;"><math>{\vec{p}_{f} = {m}\vec{v} + \vec{F}_{grav}{Δt}}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,12,0> + <0,-3.92,0>}</math></div>

<div style="text-align: center;"><math>{\vec{p}_{f} = <16,8.08,0>}</math></div>

===Example #2 - Trajectory Maxima===

'''A 1 kg ball is kicked from location <math>{<9,0,0> m}</math> giving it an initial velocity of <math>{<-10,13,0> m/s}</math>. What is the maximum height that the ball will reach along its trajectory?'''

This problem is a bit more complicated than the previous one. Before calculating the maximum height of the ball, we must know the time it takes for the ball to reach its maximum height by analyzing the motion of the ball in the +y direction through the momentum update equation:

<div style="text-align: center;"><math>{t}_{f} = {v}_{i,y}{m}/{F}_{net,y}</math></div>

<div style="text-align: center;"><math>{t}_{f} = \frac{(13)(1)}{(1)(9.8)} = 1.326 s</math></div>

Now that we know how long it takes for the ball to reach its maximum height, we can solve for the final height of the ball by utilizing the position update equation:

<div style="text-align: center;"><math>{r}_{f,y} = {r}_{i,y} + {v}_{avg,y}{Δt}</math></div>

<div style="text-align: center;"><math>{r}_{f,y} = 0 + \frac{13+0}{2}(1.326) = 8.64 m</math></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

Iterative Prediction

2015-11-25T23:41:49Z

Tconnors3: /* A Mathematical Model */

Iterative Prediction

2015-11-25T23:41:05Z

Tconnors3: /* A Mathematical Model */

Iterative Prediction

2015-11-25T23:39:45Z

Tconnors3: /* Example #2 - Trajectory Maxima */

Iterative Prediction

2015-11-25T23:39:23Z

Tconnors3: /* Example #2 - Trajectory Maxima */

Iterative Prediction

2015-11-25T23:37:12Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T23:36:56Z

Tconnors3: /* Example #1 */

Iterative Prediction

2015-11-25T23:35:04Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T23:32:11Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T23:31:40Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T23:30:24Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:59:18Z

Tconnors3: /* Example Calculations */

Iterative Prediction

2015-11-25T22:59:00Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:58:49Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:58:08Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:56:59Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:56:39Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:56:26Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:56:14Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:56:00Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:55:23Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:55:04Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:54:32Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:52:47Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:52:27Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:51:44Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:50:53Z

Tconnors3: /* Example #2 */

Iterative Prediction

2015-11-25T22:42:12Z

Tconnors3: /* Middling */