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2015-12-05T22:41:10Z

Lwalker37: /* Angular Momentum */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources 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!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#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 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]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Escape Velocity]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Free Body Diagram]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
*[[Time Dilation]]
*[[Pauli exclusion principle]]
</div>
</div>

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

===Modeling with VPython===
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython 3D Objects]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Einstein's Theory of General Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
*[[Newton's Laws]]
*[[Higgs field]]
*[[Supersymmetry]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Alexei Alexeyevich Abrikosov]]
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Siméon Denis Poisson]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrord Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[William Lawrence Bragg]]
*[[Robert Goddard]]
*[[Léon Foucault]]
*[[Henri Poincaré]]
*[[Steven Weinberg]]
*[[Arthur Compton]]
*[[Pythagoras of Samos]]
*[[Subrahmanyan Chandrasekhar]]
*[[Wilhelm Eduard Weber]]
*[[Edmond Becquerel]]
*[[Joseph Rotblat]]
*[[Carl David Anderson]]
*[[Hermann von Helmholtz]]
*[[Nicolas Leonard Sadi Carnot]]
*[[Wallace Carothers]]
*[[David J. Wineland]]
*[[Rudolf Clausius]]
*[[Edward L. Norton]]
*[[Shuji Nakamura]]
*[[Pierre Laplace Pt. 2]]
*[[William B. Shockley]]
*[[Osborne Reynolds]]
*[[Alexander Graham Bell]]
*[[Hans Bethe]]
*[[Erwin Schrodinger]]
*[[Wolfgang Pauli]]
*[[Paul Dirac]]

</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
*[[Plasma]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in Solids]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Change in Momentum in Time for Curving Motion]]
* [[Momentum with respect to external Forces]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a cylinder]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Torque vs Work]]
* [[Angular Impulse]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]
*[[Torque 2]]

</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[Work]]
**[[Work Done By A Nonconstant Force]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
*[[Energy in a Circuit]]
*[[The Photovoltaic Effect]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
[[File:opener.png]]

*[[Collisions]]
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.
[[File:pe.png]]

*[[Elastic Collisions]]
A collision is deemed "elastic" when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.
[[File:Elco.png]]

*[[Inelastic Collisions]]
A collision is said to be "inelastic" when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:
*Objects stick together after the collision
*An object is in an excited state after the collision
*An object becomes deformed after the collision
*The objects become hotter after the collision
*There exists more vibration or rotation after the collision
[[File:inve.gif]]

*[[Maximally Inelastic Collision]]
Maximally inelastic collisions, also known as "sticking collisions", are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can't change and must be conserved.
[[File:inel.gif]]

*[[Head-on Collision of Equal Masses]]
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.
[[File:momentum-real-life-applications-2895.jpg]] [[File:8ball.gif]]

*[[Head-on Collision of Unequal Masses]]
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let's take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let's imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.
[[File:mi3e.jpg]]

*[[Frame of Reference]]
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed "noninertial" meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as "anchored" to the train.
[[File:train.png]]

*[[Scattering: Collisions in 2D and 3D]]
Experiments that involve scattering are often used to study the structure and behavior of atoms, nuclei, as well as of other small particles. In an experiment like such, a beam of particles collides with other particles. If it is an atomic or nuclear collision, we are unable to observe the curving trajectories inside the tiny region of interaction. Instead, we can only truly observe the trajectories before and after the collision. This is only possible because the particles are at a farther distance apart and have a very weak mutual interaction; this essentially means that the particles are moving almost in a straight line. A good example which demonstrates scattering is the collision between an alpha particle (the nucleus of a helium atom) and the nucleus of a gold atom. One will understand this phenomenon more in depth after first understanding the Rutherford Experiment which will get touched on later.

*[[Rutherford Experiment and Atomic Collisions]]
In England in 1911, a famous experiment was performed by a group of scientists led by Mr. Ernest Rutherford. This experiment, later known as "The Rutherford Experiment", was a tremendous breakthrough for its time because it led to the discovery of the nucleus inside the atom. Rutherford's experiment involved the scattering of a high-speed alpha particle (now known as a helium nuclei - 2 protons and 2 neutrons) as it was shot at a thin gold foil (consisting of a nuclei with 79 protons and 118 neutrons). In the experiment, Rutherford and his team discovered that the velocity of the alpha particles was not high enough to allow the particles to make actual contact with the gold nucleus. Although they never actually made contact, it is still deemed a collision because there exists a sizable force between the alpha particle and the gold nucleus over a very short period of time. In conclusion, we say the alpha particle is "scattered" by its interaction with the nucleus of a gold atom and experiments like such are called "scattering" experiments.
[[File:ruthef.jpg]]

*[[Coefficient of Restitution]]
The coefficient of restitution is a measure of the elasticity in a collision. It is the ratio of the differences in velocities before and after the collision. The coefficient is evaluated by taking the difference in the velocities of the colliding objects after the collision and dividing by the difference in the velocities of the colliding objects before the collision.

All of the following information was collected from the Matter and Interactions 4th Edition physics textbook. The book is cited as follows...

Chabay, Ruth W., and Bruce A. Sherwood. "Chapter 10: Collisions." Matter & Interactions. Fourth Edition ed. Wiley, 2015. 383-409. Print.

</div>
</div>

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Charge Density]]
*[[Superposition Principle]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Potential Difference at One Location]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
**[[charged conductor and charged insulator]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Torque]]
**[[Magnetic Force]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Electric Motors]]
**[[Solenoid Applications]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Work and Power In A Circuit]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
*[[Insulators]]
*[[Voltage]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[Magnetic Fields]]
**[[Proof of Gauss's Law]]
*[[Ampere's 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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers (Physics)]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Lenz's Rule]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
*[[Rayleigh Effect]]
*[[Image Formation]]
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Speed of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
*[[Sound Rarefaction]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Bragg's Law]]
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[The Wave Equation]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
*[[interference]]
*[[Polarization of Waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Generator]]
*[[Measuring Water Level]]
*[[Cyclotron]]
*[[Railgun]]
*[[Magnetic Resonance Imaging]]
*[[Electric Eels]]
*[[Windshield Wipers]]
*[[Galvanic Cells]]
*[[Magnetoreception]]

</div>
</div>

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

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
*[[Lasers]]

</div>
</div>

== 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

Torque 2

2015-12-05T22:40:43Z

Lwalker37: Created page with "== Torque == Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F..."

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]

Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
Torque can also be defined as τ = dL/dt , or the derivative of angular momentum, L.
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

[[File:Rhr_torque.JPG]]

If your thumb points up, the force is coming out of the page and is in the positive z-directon. If your thumb points down, the force is going into the page and is in the negative z-direction.
===A Computational Model===

[[File:Torque.gif]]

The above picture is a great example of what torque would look like in the real world. To make a similar simulation in vpython, all you would need to do is update position and angular momentum. The code would look something like this:

While t<some number:

L=L+tnet*deltat

v=L/mass

r=r+v*deltat

t=t+deltat

Where L is your angular momentum initialized earlier, tnet is total torque, deltat is your time step, and r is your original location.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

In a hurry to catch a cab, you rush through a frictionless swinging door and onto the sidewalk. The force you extered on the door was 50N, applied perpendicular to the plane of the door. The door is 1.0m wide. Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge as the pivot point)?

[[File:torqueE1.gif]]

(50N)(1.0m)sin(90) = 50 Nm
===Middling===

A uniform solid disk with radius 9 cm has mass 0.5 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 25 radians/s in the −z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 14 cm.

[[File:disk torque.jpg]]

What are the magnitude and direction of the torque on the disk, about the center of mass of the disk?

(12N)(0.09m)= 1.08 Nm

Direction: -z direction because of the right hand rule

===Difficult===

We want to place another mass on the see-saw to keep the see-saw from tipping. The only other one we have is a 5.0kg mass. Where would we place this to balance the original 3kg mass that was placed 2.00m to the right of the pivot point?

[[File:prob2.jpg]]

(3kg)(9.8 m/s^2)(2.00m) = (5kg)(9.8 m/s^2)(x)

58.8 = 49x

x=1.2

==Connectedness==
How is this topic connected to something that you are interested in?
I have a heavy interest in cars. More specifically, I love race cars, and I love watching Formula1, BTCC, WRC, and other car racing series. Torque, in cars, gives you an idea of how fast the car can accelerate. But more importantly, torque can make cars do this:

[[File:burnout_loop.gif]]

and this:

[[File:corvetteburnout.gif]]

How is it connected to your major?

Torque is heavily related to mechanical engineering. Whether it be driving a conveyor belt in a factor, a driveshaft in a car, turning a wrench, or otherwise, torque is involved in almost all mechanical systems. Mechanical engineers use torque to transform energy into a useful form. For example, they use torque in electric motors to turn electric energy into rotational energy that can be used in all sorts of appliances. Mechanical engineers also take the chemical energy from gasoline combustion and turn it into torque to power planes, trains, and automobiles. Torque is applicable in all types of engineering.

Is there an interesting industrial application?

The amount of industrial applications of torque is nearly infinite, but one machine I find interesting is the lathe. The lathe uses torque and rotation to shape various materials [https://www.youtube.com/watch?v=9qt5ui3P9QA]

==History==

The idea of torque originated with Archimedes studies on levers. Archimedes may not have invented the lever, but he was one of the first scientists to investigate how they work in 241 BC.

== See also ==

[https://en.wikipedia.org/wiki/Torque]
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]
[https://en.wikipedia.org/wiki/Torque
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]]
[http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html]

==References==

This section contains the the references you used while writing this page
[[https://en.wikipedia.org/wiki/Torque]]
[http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html]
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]
[[Category:Angular Momentum]]

Main Page

2015-12-05T22:39:26Z

Lwalker37: /* Angular Momentum */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources 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!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#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 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]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Escape Velocity]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Free Body Diagram]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
*[[Time Dilation]]
*[[Pauli exclusion principle]]
</div>
</div>

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

===Modeling with VPython===
<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython 3D Objects]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Einstein's Theory of General Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
*[[Newton's Laws]]
*[[Higgs field]]
*[[Supersymmetry]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Alexei Alexeyevich Abrikosov]]
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Siméon Denis Poisson]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrord Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[William Lawrence Bragg]]
*[[Robert Goddard]]
*[[Léon Foucault]]
*[[Henri Poincaré]]
*[[Steven Weinberg]]
*[[Arthur Compton]]
*[[Pythagoras of Samos]]
*[[Subrahmanyan Chandrasekhar]]
*[[Wilhelm Eduard Weber]]
*[[Edmond Becquerel]]
*[[Joseph Rotblat]]
*[[Carl David Anderson]]
*[[Hermann von Helmholtz]]
*[[Nicolas Leonard Sadi Carnot]]
*[[Wallace Carothers]]
*[[David J. Wineland]]
*[[Rudolf Clausius]]
*[[Edward L. Norton]]
*[[Shuji Nakamura]]
*[[Pierre Laplace Pt. 2]]
*[[William B. Shockley]]
*[[Osborne Reynolds]]
*[[Alexander Graham Bell]]
*[[Hans Bethe]]
*[[Erwin Schrodinger]]
*[[Wolfgang Pauli]]
*[[Paul Dirac]]

</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
*[[Plasma]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in Solids]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Change in Momentum in Time for Curving Motion]]
* [[Momentum with respect to external Forces]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a cylinder]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Torque vs Work]]
* [[Angular Impulse]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]
*[[Torque]]

</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[Work]]
**[[Work Done By A Nonconstant Force]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
*[[Energy in a Circuit]]
*[[The Photovoltaic Effect]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
[[File:opener.png]]

*[[Collisions]]
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.
[[File:pe.png]]

*[[Elastic Collisions]]
A collision is deemed "elastic" when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.
[[File:Elco.png]]

*[[Inelastic Collisions]]
A collision is said to be "inelastic" when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:
*Objects stick together after the collision
*An object is in an excited state after the collision
*An object becomes deformed after the collision
*The objects become hotter after the collision
*There exists more vibration or rotation after the collision
[[File:inve.gif]]

*[[Maximally Inelastic Collision]]
Maximally inelastic collisions, also known as "sticking collisions", are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can't change and must be conserved.
[[File:inel.gif]]

*[[Head-on Collision of Equal Masses]]
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.
[[File:momentum-real-life-applications-2895.jpg]] [[File:8ball.gif]]

*[[Head-on Collision of Unequal Masses]]
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let's take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let's imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.
[[File:mi3e.jpg]]

*[[Frame of Reference]]
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed "noninertial" meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as "anchored" to the train.
[[File:train.png]]

*[[Scattering: Collisions in 2D and 3D]]
Experiments that involve scattering are often used to study the structure and behavior of atoms, nuclei, as well as of other small particles. In an experiment like such, a beam of particles collides with other particles. If it is an atomic or nuclear collision, we are unable to observe the curving trajectories inside the tiny region of interaction. Instead, we can only truly observe the trajectories before and after the collision. This is only possible because the particles are at a farther distance apart and have a very weak mutual interaction; this essentially means that the particles are moving almost in a straight line. A good example which demonstrates scattering is the collision between an alpha particle (the nucleus of a helium atom) and the nucleus of a gold atom. One will understand this phenomenon more in depth after first understanding the Rutherford Experiment which will get touched on later.

*[[Rutherford Experiment and Atomic Collisions]]
In England in 1911, a famous experiment was performed by a group of scientists led by Mr. Ernest Rutherford. This experiment, later known as "The Rutherford Experiment", was a tremendous breakthrough for its time because it led to the discovery of the nucleus inside the atom. Rutherford's experiment involved the scattering of a high-speed alpha particle (now known as a helium nuclei - 2 protons and 2 neutrons) as it was shot at a thin gold foil (consisting of a nuclei with 79 protons and 118 neutrons). In the experiment, Rutherford and his team discovered that the velocity of the alpha particles was not high enough to allow the particles to make actual contact with the gold nucleus. Although they never actually made contact, it is still deemed a collision because there exists a sizable force between the alpha particle and the gold nucleus over a very short period of time. In conclusion, we say the alpha particle is "scattered" by its interaction with the nucleus of a gold atom and experiments like such are called "scattering" experiments.
[[File:ruthef.jpg]]

*[[Coefficient of Restitution]]
The coefficient of restitution is a measure of the elasticity in a collision. It is the ratio of the differences in velocities before and after the collision. The coefficient is evaluated by taking the difference in the velocities of the colliding objects after the collision and dividing by the difference in the velocities of the colliding objects before the collision.

All of the following information was collected from the Matter and Interactions 4th Edition physics textbook. The book is cited as follows...

Chabay, Ruth W., and Bruce A. Sherwood. "Chapter 10: Collisions." Matter & Interactions. Fourth Edition ed. Wiley, 2015. 383-409. Print.

</div>
</div>

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Charge Density]]
*[[Superposition Principle]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Potential Difference at One Location]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
**[[charged conductor and charged insulator]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Torque]]
**[[Magnetic Force]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Electric Motors]]
**[[Solenoid Applications]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Work and Power In A Circuit]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
*[[Insulators]]
*[[Voltage]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[Magnetic Fields]]
**[[Proof of Gauss's Law]]
*[[Ampere's 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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers (Physics)]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Lenz's Rule]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
*[[Rayleigh Effect]]
*[[Image Formation]]
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Speed of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
*[[Sound Rarefaction]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Bragg's Law]]
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[The Wave Equation]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
*[[interference]]
*[[Polarization of Waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Generator]]
*[[Measuring Water Level]]
*[[Cyclotron]]
*[[Railgun]]
*[[Magnetic Resonance Imaging]]
*[[Electric Eels]]
*[[Windshield Wipers]]
*[[Galvanic Cells]]
*[[Magnetoreception]]

</div>
</div>

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

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
*[[Lasers]]

</div>
</div>

== 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

Talk:Main Page

2015-12-03T23:59:49Z

Lwalker37:

Talk:Main Page

2015-12-03T23:59:05Z

Lwalker37:

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]

Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
Torque can also be defined as τ = dL/dt , or the derivative of angular momentum, L.
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

[[File:Rhr_torque.JPG]]

If your thumb points up, the force is coming out of the page and is in the positive z-directon. If your thumb points down, the force is going into the page and is in the negative z-direction.
===A Computational Model===

[[File:Torque.gif]]

The above picture is a great example of what torque would look like in the real world. To make a similar simulation in vpython, all you would need to do is update position and angular momentum. The code would look something like this:

While t<some number:

L=L+tnet*deltat

v=L/mass

r=r+v*deltat

t=t+deltat

Where L is your angular momentum initialized earlier, tnet is total torque, deltat is your time step, and r is your original location.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

In a hurry to catch a cab, you rush through a frictionless swinging door and onto the sidewalk. The force you extered on the door was 50N, applied perpendicular to the plane of the door. The door is 1.0m wide. Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge as the pivot point)?

[[File:torqueE1.gif]]

(50N)(1.0m)sin(90) = 50 Nm
===Middling===

A uniform solid disk with radius 9 cm has mass 0.5 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 25 radians/s in the −z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 14 cm.

[[File:disk torque.jpg]]

What are the magnitude and direction of the torque on the disk, about the center of mass of the disk?

(12N)(0.09m)= 1.08 Nm

Direction: -z direction because of the right hand rule

===Difficult===

We want to place another mass on the see-saw to keep the see-saw from tipping. The only other one we have is a 5.0kg mass. Where would we place this to balance the original 3kg mass that was placed 2.00m to the right of the pivot point?

[[File:prob2.jpg]]

(3kg)(9.8 m/s^2)(2.00m) = (5kg)(9.8 m/s^2)(x)

58.8 = 49x

x=1.2

==Connectedness==
How is this topic connected to something that you are interested in?
I have a heavy interest in cars. More specifically, I love race cars, and I love watching Formula1, BTCC, WRC, and other car racing series. Torque, in cars, gives you an idea of how fast the car can accelerate. But more importantly, torque can make cars do this:

[[File:burnout_loop.gif]]

and this:

[[File:corvetteburnout.gif]]

How is it connected to your major?

Torque is heavily related to mechanical engineering. Whether it be driving a conveyor belt in a factor, a driveshaft in a car, turning a wrench, or otherwise, torque is involved in almost all mechanical systems. Mechanical engineers use torque to transform energy into a useful form. For example, they use torque in electric motors to turn electric energy into rotational energy that can be used in all sorts of appliances. Mechanical engineers also take the chemical energy from gasoline combustion and turn it into torque to power planes, trains, and automobiles. Torque is applicable in all types of engineering.

Is there an interesting industrial application?

The amount of industrial applications of torque is nearly infinite, but one machine I find interesting is the lathe. The lathe uses torque and rotation to shape various materials [https://www.youtube.com/watch?v=9qt5ui3P9QA]

==History==

The idea of torque originated with Archimedes studies on levers. Archimedes may not have invented the lever, but he was one of the first scientists to investigate how they work in 241 BC.

== See also ==

[https://en.wikipedia.org/wiki/Torque]
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]
[https://en.wikipedia.org/wiki/Torque
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]]
[http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html]

==References==

This section contains the the references you used while writing this page
[https://en.wikipedia.org/wiki/Torque]
[http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html]
[https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html]
[[Category:Angular Momentum]]

Talk:Main Page

2015-12-03T23:54:27Z

Lwalker37:

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]

Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
Torque can also be defined as τ = dL/dt , or the derivative of angular momentum, L.
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

[[File:Rhr_torque.JPG]]

If your thumb points up, the force is coming out of the page and is in the positive z-directon. If your thumb points down, the force is going into the page and is in the negative z-direction.
===A Computational Model===

[[File:Torque.gif]]

The above picture is a great example of what torque would look like in the real world. To make a similar simulation in vpython, all you would need to do is update position and angular momentum. The code would look something like this:

While t<some number:

L=L+tnet*deltat

v=L/mass

r=r+v*deltat

t=t+deltat

Where L is your angular momentum initialized earlier, tnet is total torque, deltat is your time step, and r is your original location.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

In a hurry to catch a cab, you rush through a frictionless swinging door and onto the sidewalk. The force you extered on the door was 50N, applied perpendicular to the plane of the door. The door is 1.0m wide. Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge as the pivot point)?

[[File:torqueE1.gif]]

(50N)(1.0m)sin(90) = 50 Nm
===Middling===

A uniform solid disk with radius 9 cm has mass 0.5 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 25 radians/s in the −z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 14 cm.

[[File:disk torque.jpg]]

What are the magnitude and direction of the torque on the disk, about the center of mass of the disk?

(12N)(0.09m)= 1.08 Nm

Direction: -z direction because of the right hand rule

===Difficult===

We want to place another mass on the see-saw to keep the see-saw from tipping. The only other one we have is a 5.0kg mass. Where would we place this to balance the original 3kg mass that was placed 2.00m to the right of the pivot point?

[[File:prob2.jpg]]

(3kg)(9.8 m/s^2)(2.00m) = (5kg)(9.8 m/s^2)(x)

58.8 = 49x

x=1.2

==Connectedness==
How is this topic connected to something that you are interested in?
I have a heavy interest in cars. More specifically, I love race cars, and I love watching Formula1, BTCC, WRC, and other car racing series. Torque, in cars, gives you an idea of how fast the car can accelerate. But more importantly, torque can make cars do this:

[[File:burnout_loop.gif]]

and this:

[[File:corvetteburnout.gif]]

How is it connected to your major?

Torque is heavily related to mechanical engineering. Whether it be driving a conveyor belt in a factor, a driveshaft in a car, turning a wrench, or otherwise, torque is involved in almost all mechanical systems. Mechanical engineers use torque to transform energy into a useful form. For example, they use torque in electric motors to turn electric energy into rotational energy that can be used in all sorts of appliances. Mechanical engineers also take the chemical energy from gasoline combustion and turn it into torque to power planes, trains, and automobiles. Torque is applicable in all types of engineering.

Is there an interesting industrial application?

The amount of industrial applications of torque is nearly infinite, but one machine I find interesting is the lathe. The lathe uses torque and rotation to shape various materials [https://www.youtube.com/watch?v=9qt5ui3P9QA]

==History==

The idea of torque originated with Archimedes studies on levers. Archimedes may not have invented the lever, but he was one of the first scientists to investigate how they work in 241 BC.

== 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://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Angular Momentum]]

Talk:Main Page

2015-12-03T23:53:53Z

Lwalker37:

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]

Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
Torque can also be defined as τ = dL/dt , or the derivative of angular momentum, L.
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

[[File:Rhr_torque.JPG]]

If your thumb points up, the force is coming out of the page and is in the positive z-directon. If your thumb points down, the force is going into the page and is in the negative z-direction.
===A Computational Model===

[[File:Torque.gif]]

The above picture is a great example of what torque would look like in the real world. To make a similar simulation in vpython, all you would need to do is update position and angular momentum. The code would look something like this:

While t<some number:

L=L+tnet*deltat

v=L/mass

r=r+v*deltat

t=t+deltat

Where L is your angular momentum initialized earlier, tnet is total torque, deltat is your time step, and r is your original location.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

In a hurry to catch a cab, you rush through a frictionless swinging door and onto the sidewalk. The force you extered on the door was 50N, applied perpendicular to the plane of the door. The door is 1.0m wide. Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge as the pivot point)?

[[File:torqueE1.gif]]

(50N)(1.0m)sin(90) = 50 Nm
===Middling===

A uniform solid disk with radius 9 cm has mass 0.5 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 25 radians/s in the −z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 14 cm.

[[File:disk torque.jpg]]

What are the magnitude and direction of the torque on the disk, about the center of mass of the disk?

(12N)(0.09m)= 1.08 Nm

Direction: -z direction because of the right hand rule

===Difficult===

We want to place another mass on the see-saw to keep the see-saw from tipping. The only other one we have is a 5.0kg mass. Where would we place this to balance the original 3kg mass that was placed 2.00m to the right of the pivot point?

[[File:prob2.jpg]]

(3kg)(9.8 m/s^2)(2.00m) = (5kg)(9.8 m/s^2)(x)

58.8 = 49x

x=1.2

==Connectedness==
How is this topic connected to something that you are interested in?
I have a heavy interest in cars. More specifically, I love race cars, and I love watching Formula1, BTCC, WRC, and other car racing series. Torque, in cars, gives you an idea of how fast the car can accelerate. But more importantly, torque can make cars do this:

[[File:burnout_loop.gif]]

and this:

[[File:corvetteburnout.gif]]

How is it connected to your major?

Torque is heavily related to mechanical engineering. Whether it be driving a conveyor belt in a factor, a driveshaft in a car, turning a wrench, or otherwise, torque is involved in almost all mechanical systems. Mechanical engineers use torque to transform energy into a useful form. For example, they use torque in electric motors to turn electric energy into rotational energy that can be used in all sorts of appliances. Mechanical engineers also take the chemical energy from gasoline combustion and turn it into torque to power planes, trains, and automobiles. Torque is applicable in all types of engineering.

Is there an interesting industrial application?

The amount of industrial applications of torque is nearly infinite, but one machine I find interesting is the lathe. The lathe uses torque and rotation to shape various materials [https://www.youtube.com/watch?v=9qt5ui3P9QA]

==History==

The idea of torque originated with Archimedes studies on levers. Archimedes may not have invented the lever, but he was one of the first scientists to investigate how they work in 241 BC.

== 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://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Disk torque.jpg

2015-12-03T23:41:49Z

Lwalker37:

File:TorqueE1.gif

2015-12-03T23:34:45Z

Lwalker37:

File:Prob2.jpg

2015-12-03T22:58:41Z

Lwalker37:

File:Corvetteburnout.gif

2015-12-03T15:38:11Z

Lwalker37:

File:Burnout loop.gif

2015-12-03T15:33:39Z

Lwalker37:

File:Torque.gif

2015-12-03T14:54:22Z

Lwalker37:

Talk:Main Page

2015-12-03T14:53:33Z

Lwalker37:

File:Rhr torque.JPG

2015-12-03T03:55:52Z

Lwalker37:

Talk:Main Page

2015-12-03T03:28:57Z

Lwalker37: /* Torque */ new section

== Why Energy is conserved ==

The main idea of this page is to elaborate a little more on why energy is conserved and to understand it is a more simplified way. The thought about the fact that energy is neither created nor destroyed can be a mind boggling one simply because energy always seems to be coming from somewhere, so where does it go? The main idea behind why energy is conserved and neither created or destroyed is that it is just transferred to other forms. The first law of Thermodynamics states that the amount of energy in the universe is a constant, fixed amount. Is doesn’t go away and it doesn’t appear randomly.

===A Mathematical Model===

The mathematical equations that are used to model this topic include many different equations, but they all relate back to the energy principle, ΔEsystem = WSurr +Q. W is the work cone by the surroundings and Q is the thermal energy. The change in energy will be always zero because energy is transferring to other forms of energy within the system or surroundings. Other Important equations include:
K = ½mv2, ΔUg = mgΔh, E = K + U, Ei = Ef, Ki + Ui = Kf + Uf, W = F̅Δs cos θ.

===A Computational Model===
This video shows how energy in conserved in a variety of situations.
http://study.com/academy/lesson/first-law-of-thermodynamics-law-of-conservation-of-energy.html

==Examples==

===Simple===

Question: State the law of conservation of energy and explain the law by taking an oscillating simple pendulum as an example.

Answer: The law of conservation of energy says that energy can neither be created nor destroyed but can be transformed from one form to another.
In the case of the simple pendulum when the bob is as far to the left as it can be, it has maximum potential energy as it is raised with respect to the mean position, but its kinetic energy is zero as the bob stops oscillating for a fraction of a second before moving towards the right. When the bob reaches the mean position, it has a zero potential energy but maximum kinetic energy (maximum velocity too). When the bob of the pendulum swings to extreme right, it has the maximum potential energy but zero kinetic energy.
===Middling===
Question: A nail becomes warm when it is hammered into a plank. Explain why.

Answer: A raised hammer has potential energy due to its position above the ground, gravity acts as acceleration. When the hammer comes down and strikes the head of the nail, the potential energy is transformed into kinetic energy. If we continue hitting the nail to secure it, the kinetic energy of the hammer is transferred to the molecules of the material of the nail. The heat content of the body is the total energy that the body possesses (Q in the equation above). As the heat content of the body increases, the nail becomes warm.
===Difficult===
Question:
A stone of mass 10 g placed at the top of a tower 50 m high is allowed to fall freely. Show that law of conservation of energy holds good in the case of the stone.
http://images.tutorvista.com/contentimages/science/CBSEIXSCIENCE/Ch146/images/img179.jpeg
Answer: In this case we have to prove that total energy at A, B and C is the same.
Height = 50 m
Potential energy at A = mgh
= 0.01 x 9.8 x 50
= 0.01 x 98 x 5
= 4.9 J
= 0
Total energy at A = potential energy + kinetic energy= 4.9 + 0
Total energy at A = 4.9 J ...(1)
At B
Height from the ground = 40 m
Potential energy = mgh
= 0.01 x 9.8 x 40
= 0.01 x 98 x 4
Potential energy at B = 3.92 J
To calculate v we make use of III equation of motion,
Here, u = 0, a = 9.8 m/s2 and H = 10 m
= 0.98 J
Total energy at B = potential energy + kinetic energy
= 3.92 + 0.98
Total energy at B = 4.90 J (2)
At C
Height from the ground = 0
Potential energy at C = mgh
To calculate v we use III equation of motion,
Here, u = 0, a = 9.8m/s2 and H = 50 m
= 4.9 J
Total energy at C = potential energy + kinetic energy
= 0 + 4.9
Total energy at C = 4.9 J (3)
The total energy at A, B and C is 4.9 J. This means that law of conservation of energy holds good in the case of a stone falling freely under gravity.

==Connectedness==
#I am interested in this topic because Physics has never really clicked in my mind and researching more on why when you do work on a system the energy is conserved is very interesting to me. I learned a lot why doing this and now understand why this is true instead of just memorizing that it is true.
# This is connected to my major because I am a Biology/Pre-Health major and I am interested in making medical products that increase the efficiently of hospitals. This concept can be important because I will want to design products that use as a little energy as possible while still getting the job done effectively.
#The industrial application that can be used concerning this topic is that certain materials can be used when building structures to minimize thermal energy lost, thus making the system more effective.

==History==

There are many people who contributed to the Conservation of Energy laws. In 1639 Galileo, who was from Italy, introduced the pendulum where potential and kinetic energy are always present in different amounts throughout the motion. French physicists Gottfried Wilhelm Leibniz formulated how Kinetic energy is connected to velocity and mass between 1676-1689. How kinetic energy and Work are related was described by Gaspard-Gustave Coriolis and Jean-Victor Poncelet from 1819-1839 in France. All of these men, along with many others played a very important role in formulating what we know about energy today and they did is because they were constantly trying to make improvements to society and science.

== See also ==
More practice problems: http://www.tutorvista.com/content/science/science-i/work-energy/question-answers-2.php#question-21
===Further reading===
One book I found interesting on this topic is called ''Energy, Society, and Environment: Technology for a Sustainable Future'' ''Italic text''by David Elliott. This book talks about connecting the conservation of energy principles that have bee around for a long time to modern technology
===External links===

This link provides very good information about the conservation of energy http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html

==References==
http://study.com/academy/lesson/first-law-of-thermodynamics-law-of-conservation-of-energy.html http://www.tutorvista.com/content/science/science-i/work-energy/question-answers-2.php#question-21
https://en.wikipedia.org/wiki/Conservation_of_energy#History

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.
[[Media:http://www.physicsbook.gatech.edu/images/2/23/Wrench_gif.gif]]

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==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://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]
Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==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://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

== Torque ==

== Torque ==

Torque is a Latin word that roughly means "twist," and is usually symbolized by the lower case Greek letter tau. Torque is the measurement of how much a force, F, acting on an object will cause that object to rotate. This force is usually applied to an arm of some sort that is attached to a fulcrum or pivot point. For example, using a wrench to loosen or tighten a nut requires the use of torque - where the wrench would be the arm you apply the force to and the nut would be the pivot point that the force rotates around.

[[File:wrench_gif.gif]]

==The Main Idea==

In "Matter & Interactions, Fourth Edition," torque is defined as τ = r<sub>A</sub> x F .
Applying a torque to an object changes the angular momentum of that object. Torque, in angular momentum calculations, is analogus to F<sub>net</sub> in regular momentum calculations. Just like how a collection of forces acting on a system is called F<sub>net</sub>, a collection of torques acting on a system is τ<sub>net</sub>.

===A Mathematical Model===

[[File:torque_diagram.gif]]
Torque is defined as the cross product of the distance vector, the distance from pivot point to the location of the applied force, with an applied force. The magnitude of torque can be defined as such:
*τ<sub>A</sub> = r<sub>A</sub>Fsinθ
To determine the direction of torque, one can either compute the cross product or apply the "right-hand rule." To use the "right-hand rule," point your fingers in the direction of r<sub>A</sub> and curl your fingers in the direction of F.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==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://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Talk:Main Page

2015-12-03T03:27:07Z

Lwalker37: /* Torque */ new section

File:Torque diagram.gif

2015-12-03T03:26:46Z

Lwalker37: concept of torque shown in a diagram.

concept of torque shown in a diagram.

Talk:Main Page

2015-12-03T02:47:54Z

Lwalker37: /* Torque */ new section

File:Wrench gif.gif

2015-12-03T02:45:27Z

Lwalker37: wrench using torque to tighten a bolt

wrench using torque to tighten a bolt

Main Page

2015-12-03T02:17:13Z

Lwalker37: /* Angular Momentum */

Main Page

2015-12-03T02:16:38Z

Lwalker37: /* Angular Momentum */