# Encyclopedia

.
The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path.
^ At the bottom its potential energy has been converted into kinetic energy so that it now has its maximum kinetic energy.
• Potential and Kinetic Energy 10 January 2010 8:32 UTC www.usoe.k12.ut.us [Source type: FILTERED WITH BAYES]
• Potential and Kinetic Energy 10 January 2010 8:32 UTC www.usoe.k12.ut.us [Source type: General]

^ This car has a lot of kinetic energy.

^ At this point, her speed and kinetic energy have reached a maximum.
• Energy Transformation for Downhill Skiing 10 January 2010 8:32 UTC www.physicsclassroom.com [Source type: FILTERED WITH BAYES]

.When they start rising, the kinetic energy begins to be converted to gravitational potential energy.^ When the water begins to fall, its potential energy is changed into kinetic energy.
• Potential and Kinetic Energy 10 January 2010 8:32 UTC www.usoe.k12.ut.us [Source type: FILTERED WITH BAYES]

^ This changes the potential energy into kinetic energy.
• The Atoms Family - The Mummy's Tomb - Raceways 10 January 2010 8:32 UTC www.miamisci.org [Source type: News]

^ Gravitational potential energy is an example of ordered energy.

The sum of kinetic and potential energy in the system remains constant, assuming negligible losses to friction.
.The kinetic energy of an object is the extra energy which it possesses due to its motion.^ Pronunciation Key The energy possessed by a system or object as a result of its motion.
• Kinetic energy Definition | Definition of Kinetic energy at Dictionary.com 10 January 2010 8:32 UTC dictionary.reference.com [Source type: Reference]

^ Kinetic energy is the energy an object has due to its motion.

^ Kinetic energy, or energy from motion, turns into an explosion of the object's material.
• Kinetic Energy Impactor - SolarSailWiki 10 January 2010 8:32 UTC wiki.solarsails.info [Source type: FILTERED WITH BAYES]

.It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.^ K.E. gained by the body = work done during acceleration .
• The Open Door Web Site : IB Physics : Kinetic and Potential Energy 10 January 2010 8:32 UTC www.saburchill.com [Source type: Academic]

^ The amount of kinetic energy of a body of mass m travelling with velocity v is given by: .
• SEI - Learn It: Kinetic Energy 10 January 2010 8:32 UTC www.sei.ie [Source type: Academic]

^ It is formally defined as the work needed to accelerate a body from rest to its current velocity .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.^ Can a body change in kinetic energy without changing in momentum?

^ This changes the potential energy into kinetic energy.
• The Atoms Family - The Mummy's Tomb - Raceways 10 January 2010 8:32 UTC www.miamisci.org [Source type: News]

^ Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
• Kinetic energy? - Yahoo! Answers 10 January 2010 8:32 UTC answers.yahoo.com [Source type: General]
• Kinetic Water Ram - Kinetic Energy 10 January 2010 8:32 UTC www.waterram.com [Source type: FILTERED WITH BAYES]
• Kinetic IT solutions for your business technolgy problems | Jennings Technologies | managed services, digital marketing, web design, website design, custom application development NJ PA DE NY 10 January 2010 8:32 UTC www.jngstech.com [Source type: General]

.Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.^ F does work on the body and changes its velocity from u to v .
• Energy 10 January 2010 8:32 UTC www.splung.com [Source type: Academic]

^ Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]
• Kinetic energy? - Yahoo! Answers 10 January 2010 8:32 UTC answers.yahoo.com [Source type: General]
• Kinetic Water Ram - Kinetic Energy 10 January 2010 8:32 UTC www.waterram.com [Source type: FILTERED WITH BAYES]
• Kinetic IT solutions for your business technolgy problems | Jennings Technologies | managed services, digital marketing, web design, website design, custom application development NJ PA DE NY 10 January 2010 8:32 UTC www.jngstech.com [Source type: General]

^ Kinetic energy is defined as the work necessary to accelerate an object from a state of rest to its current speed.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

.The kinetic energy of a single object is completely frame-dependent (relative).^ Kinetic energy is the energy an object has due to its motion.

^ E = energy of an object in the lab frame .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

^ Kinetic energy is the energy that an object has by virtue of its motion.
• BCIT Math Square :: Entertainment : Rollercoaster Kinetic Energy 10 January 2010 8:32 UTC commons.bcit.ca [Source type: Academic]

.For example, a bullet racing by a non-moving observer has kinetic energy in the reference frame of this observer, but the same bullet has zero kinetic energy in the reference frame which moves with the bullet.^ K is kinetic energy of a mass m moving at speed v .
• Relativistic Escape Velocity using Relativistic Forms of Potential andKinetic Energy 10 January 2010 8:32 UTC mrelativity.net [Source type: Academic]

^ The energy of a moving object is called kinetic energy.
• ActewAGL education site : Energy 10 January 2010 8:32 UTC www.actewagl.com.au [Source type: FILTERED WITH BAYES]

^ Kinetic Energy is often referred to as "energy in motion".
• Kinetic Energy in Fizziks Tilt Game 10 January 2010 8:32 UTC www.theproblemsite.com [Source type: FILTERED WITH BAYES]

.By contrast, the total kinetic energy of systems of objects usually will not be completely removable by simple choice of reference frame, unless all of the objects have the same velocity.^ Kinetic energy is the energy an object has due to its motion.

^ E = energy of an object in the lab frame .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

^ Kinetic energy is the energy that an object has by virtue of its motion.
• BCIT Math Square :: Entertainment : Rollercoaster Kinetic Energy 10 January 2010 8:32 UTC commons.bcit.ca [Source type: Academic]

.In any other case, a residual minimum kinetic energy must remain in the system, as seen by all observers.^ Potential and Kinetic Energy All energy is either potential or kinetic .
• Energy In-Depth--Potential and Kinetic Energy 10 January 2010 8:32 UTC www3.iptv.org [Source type: FILTERED WITH BAYES]

^ Other kinds of potential and kinetic energy .
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

^ B plus kinetic energy at B, must be u at C plus kinetic energy at C, must be u at D plus kinetic energy at D. .
• MIT OpenCourseWare | Physics | 8.01 Physics I: Classical Mechanics, Fall 1999 | Video Lectures | detail 10 January 2010 8:32 UTC ocw.mit.edu [Source type: Original source]

.This kinetic energy (if present) contributes to the system's invariant mass, which is seen as the same value in all reference frames, and by all observers.^ Kinetic Energy is often referred to as "energy in motion".
• Kinetic Energy in Fizziks Tilt Game 10 January 2010 8:32 UTC www.theproblemsite.com [Source type: FILTERED WITH BAYES]

^ Potential and Kinetic Energy All energy is either potential or kinetic .
• Energy In-Depth--Potential and Kinetic Energy 10 January 2010 8:32 UTC www3.iptv.org [Source type: FILTERED WITH BAYES]

^ Enter any two of the values of mass, velocity and kinetic energy.
• Kinetic Energy Calculator 10 January 2010 8:32 UTC www.csgnetwork.com [Source type: Reference]

## History and Etymology

.The adjective "kinetic" has its roots in the Greek word κίνηση (kinesis) meaning "motion" – the same root as in the word cinema (referring to motion pictures).^ Kinetic is just the Greek word for motion , it’s the root word for cinema, meaning movies .

^ The etymology of 'kinetic energy' is the Greek word for motion kinesis and the Greek word for active work energeia .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ The word kinetic relates to, or is characterized by motion.
• Seiko Kinetic Dive Watches 10 January 2010 8:32 UTC www.mydivewatch.com [Source type: FILTERED WITH BAYES]

.The principle in classical mechanics that E ∝ mv² was first theorized by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the "living force", vis viva.^ Note that kinetic energy is defined as ENERGY, not as FORCE. ) .
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

^ Energy in classical mechanics .
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

^ First the kinetic energy of the bullet: .
• Bullets have more kinetic energy than I thought - from Mythbusters video | Dot Physics 10 January 2010 8:32 UTC blog.dotphys.net [Source type: General]

Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship. .By dropping weights from different heights into a block of clay, 's Gravesande determined that their penetration depth was proportional to the square of their impact speed.^ This appartus will drop a mass from different heights.
• Potential Energy 10 January 2010 8:32 UTC jersey.uoregon.edu [Source type: FILTERED WITH BAYES]

^ To convert between different units, enter a value into either text box and select units using the drop-down boxes.
• Units converter for kinetic energy of turbulence 10 January 2010 8:32 UTC www.calculator.org [Source type: Reference]

^ Since the Earth is approximately round, g has very nearly the same value anywhere on the surface of the Earth (but if you were to tunnel far into the Earth, you would experience a different weight).
• Labs from Chicago, Fall 1993 - Gravitational Potential Energy. 10 January 2010 8:32 UTC astro.uchicago.edu [Source type: FILTERED WITH BAYES]

Émilie du Châtelet recognized the implications of the experiment and published an explanation.[1]
.The terms "kinetic energy" and "work" with their present scientific meanings date back to the mid 19th century.^ Chapter 15 Work and Kinetic Energy Chapter 15 Work and Kinetic Energy .
• Chapter 15 Work and Kinetic Energy 10 January 2010 8:32 UTC users.rowan.edu [Source type: Academic]

^ Work - kinetic energy theorem .
• Work - kinetic energy theorem 10 January 2010 8:32 UTC cnx.org [Source type: FILTERED WITH BAYES]

^ Back Next Kinetic energy .
• BBC - GCSE Bitesize - Kinetic energy and momentum 10 January 2010 8:32 UTC www.bbc.co.uk [Source type: News]

.Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis who in 1829 published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy.^ The kinetic energy of calculation 3 is from the firecracker.
• Energy: Demonstration 1 10 January 2010 8:32 UTC matse1.mse.uiuc.edu [Source type: FILTERED WITH BAYES]

^ What is the equation for calculating an object's kinetic energy?
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ Who needs Kinetic™ Energy ?
• Remedies Kinetic™ Energy - free from artificial stimulants and caffeine 10 January 2010 8:32 UTC www.remediesproducts.com.au [Source type: General]

.William Thomson, later Lord Kelvin, is given the credit for coining the term "kinetic energy" c.^ The kinetic energy of a point mass (m) is given by Kinetic energy.
• Kinetic Energy - Kinetic Energy Electric Provider - Kinetic Wind Energy - Agonist Learning Center 10 January 2010 8:32 UTC www.agonist.org [Source type: FILTERED WITH BAYES]

^ The first to recognize this clearly was William Thomson (Lord Kelvin).
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

^ Lord Kelvin (1824-1907) added the adjective "kinetic" to separate it from "potential energy", which was named by William Rankine (1820-1872) in 1853.
• Kinetic Energy - The Physics Hypertextbook 10 January 2010 8:32 UTC physics.info [Source type: Academic]

1849 - 1851.[2][3]

## Introduction

.There are various forms of energy: chemical energy, heat, electromagnetic radiation, potential energy (gravitational, electric, elastic, etc.^ Gravitational potential energy is a little weird.
• Physics Help - Work and Energy 10 January 2010 8:32 UTC www.fortunecity.com [Source type: Original source]

^ Gravitational potential energy is an example of ordered energy.

^ Heat is a form of energy.
• The Energy Story - Chapter 1: What Is Energy? 10 January 2010 8:32 UTC www.energyquest.ca.gov [Source type: FILTERED WITH BAYES]

), .^ We now discuss how electromagnetic radiation (light) and nuclear energy (the so-called "rest-mass" energy of matter) came to be known.  .
• How was Energy Discovered 10 January 2010 8:32 UTC www.nmsea.org [Source type: FILTERED WITH BAYES]

.These can be categorized in two main classes: potential energy and kinetic energy.^ This changes the potential energy into kinetic energy.
• The Atoms Family - The Mummy's Tomb - Raceways 10 January 2010 8:32 UTC www.miamisci.org [Source type: News]

^ Its kinetic energy decreases and its potential energy increases.
• Glencoe Online Science Quiz Chapter 10 January 2010 8:32 UTC www.glencoe.com [Source type: Academic]

^ Potential and Kinetic Energy All energy is either potential or kinetic .
• Energy In-Depth--Potential and Kinetic Energy 10 January 2010 8:32 UTC www3.iptv.org [Source type: FILTERED WITH BAYES]

.Kinetic energy can be best understood by examples that demonstrate how it is transformed to and from other forms of energy.^ Perhaps one of the best ways to understand kinetic energy is to look at examples to demonstrate how such energy can be changed into and from other various forms of energy.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

^ (They are an example of kinetic energy.
• Science NetLinks: Transforming Energy 10 January 2010 8:32 UTC www.sciencenetlinks.com [Source type: FILTERED WITH BAYES]

^ The frog leaping is an example of kinetic energy.
• Energy 10 January 2010 8:32 UTC www.nyu.edu [Source type: FILTERED WITH BAYES]

.For example, a cyclist will use chemical energy that was provided by food to accelerate a bicycle to a chosen speed.^ The chemical energy in food is used by our bodies to move.
• What is Energy? Two Main Forms of Energy 10 January 2010 8:32 UTC www.uwsp.edu [Source type: Reference]

^ For example a cyclist will use chemical energy that was provided by food to accelerate a bicycle to a chosen speed.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ One of the most ubiquitous examples of this in everyday life is that of a cyclist using the chemical energy provided by food in order to pedal and thus accelerate a bicycle in order to allow it to reach particular speed.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

.This speed can be maintained without further work, except to overcome air-resistance and friction.^ This speed can be maintained without further work, except to overcome air-resistance and friction.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Once the cyclist reaches a certain speed this speed can be easily maintained without much further effort, although more may be required in order to counter air-resistance and normal friction upon the road.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

^ By Newton's first law, without friction a car would not need any mechanical energy once it had reached constant speed.
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

.The energy has been converted into kinetic energy – the energy of motion – but the process is not completely efficient and heat is also produced within the cyclist.^ Kinetic Energy The energy due to motion.

^ A machine that converts electricity into mechanical energy or motion.
• What is the definition of kinetic energy? 10 January 2010 8:32 UTC www.toolingu.com [Source type: Reference]

^ Does kinetic energy within the neuron convert to electrical energy?
• WikiAnswers - How do you convert kinetic energy into electrical energy 10 January 2010 8:32 UTC wiki.answers.com [Source type: General]

.The kinetic energy in the moving cyclist and the bicycle can be converted to other forms.^ K is kinetic energy of a mass m moving at speed v .
• Relativistic Escape Velocity using Relativistic Forms of Potential andKinetic Energy 10 January 2010 8:32 UTC mrelativity.net [Source type: Academic]

^ Move with kinetic energy .
• Kinetic Energy Concerns Movement of Matter - Succeed in Understanding Physics: School for Champions 10 January 2010 8:32 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

^ Most forms of energy where material is moving are kinetic energy.
• Kinetic Energy Concerns Movement of Matter - Succeed in Understanding Physics: School for Champions 10 January 2010 8:32 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

.For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top.^ For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ If the cyclist comes to a hill that is fairly steep and comes to a stop at the top of the hill all of the kinetic energy is mostly converted into potential energy thanks to gravity – most of which can be tapped and released by cycling free-wheel down the reverse side.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

^ Allow the ball to hit the block wall until it has used up all of its energy (until the ball comes to a complete stop) .
• Kinetic Energy and Work 10 January 2010 8:32 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

.The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill.^ Gravitational potential energy is a little weird.
• Physics Help - Work and Energy 10 January 2010 8:32 UTC www.fortunecity.com [Source type: Original source]

^ Gravitational potential energy is an example of ordered energy.

^ Now the initial potential energy is converted into both translational and rotational kinetic energy.
• Rotational Kinetic Energy of a Soup Can 10 January 2010 8:32 UTC homepage.mac.com [Source type: FILTERED WITH BAYES]

.(Since the bicycle lost some of its energy to friction, it will never regain all of its speed without further pedaling.^ (There are some frictional losses so that the bicycle will never quite regain all the original speed.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Calculate the energy lost to friction.
• Physics Homework Help: Work, Kinetic Energy 10 January 2010 8:32 UTC www.physics247.com [Source type: Academic]

^ As the bicycle will lose part of its original energy because of friction it will require further pedaling in order to regain all of its original speed.
• What is kinetic energy | BiofuelsWatch.com 10 January 2010 8:32 UTC www.biofuelswatch.com [Source type: FILTERED WITH BAYES]

.Note that the energy is not destroyed; it has only been converted to another form by friction.^ It is only converted from one form to another.

^ Machines are used to convert energy from one form to another.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Energy can be transferred from one form to another.
• ENERGY 10 January 2010 8:32 UTC ed.fnal.gov [Source type: FILTERED WITH BAYES]

) .Alternatively the cyclist could connect a dynamo to one of the wheels and also generate some electrical energy on the descent.^ Alternatively the cyclist could connect a dynamo to one of the wheels and also generate some electrical energy on the descent.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ If the mechanical energy generated by the movement of these spinning wheels could be harnessed, we could potentially reduce the size of our current carbon footprint and supplement an inadequate and unreliable electrical grid for numerous individuals.

^ The following equation can be used to calculate the deceleration forces generated when an object slows from one speed to another in some given distance.
• VCU Transportation Safety Training Center – Kinetic Energy 10 January 2010 8:32 UTC www.vcu.edu [Source type: FILTERED WITH BAYES]

.The bicycle would be traveling more slowly at the bottom of the hill because some of the energy has been diverted into making electrical power.^ Powered by electrical energy.
• KINETIC ENERGY SUPPORTED ELECTRICALLY POWERED TRANSPORTATION STRUCTURES 10 January 2010 8:32 UTC www.home.earthlink.net [Source type: FILTERED WITH BAYES]

^ Some of the chemical energy went into making the light in the spark.
• Energy: Demonstration 1 10 January 2010 8:32 UTC matse1.mse.uiuc.edu [Source type: FILTERED WITH BAYES]

^ (The electricity was converted into kinetic energy.
• Science NetLinks: Transforming Energy 10 January 2010 8:32 UTC www.sciencenetlinks.com [Source type: FILTERED WITH BAYES]

.Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as thermal energy.^ The initial kinetic energy would be, .
• Physics Help - Work and Energy 10 January 2010 8:32 UTC www.fortunecity.com [Source type: Original source]

^ It means that thermal energy is a measure of kinetic energy.

^ Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated as heat energy.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.Like any physical quantity which is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference.^ E = energy of an object in the lab frame .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

^ K = kinetic energy of an object .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

^ The kinetic energy of an object depends on the object's speed and mass.
• Introduction to Kinetic Energy 10 January 2010 8:32 UTC www.cdli.ca [Source type: FILTERED WITH BAYES]

.Thus, the kinetic energy of an object is not invariant.^ K = kinetic energy of an object .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

^ Kinetic energy is the energy an object possesses when it’s moving.
• VCU Transportation Safety Training Center – Kinetic Energy 10 January 2010 8:32 UTC www.vcu.edu [Source type: FILTERED WITH BAYES]

^ Kinetic energy is the energy of a moving object.
• What does kinetic energy,light energy, potential energy, chemical energy, gravitational potential energy mean? - Yahoo!7 Answers 10 January 2010 8:32 UTC au.answers.yahoo.com [Source type: General]

### Examples

.Spacecraft use chemical energy to take off and gain considerable kinetic energy to reach orbital velocity.^ The cart gains kinetic energy.

^ Then, this density and sonic velocity are used in Equation 2 to find the kinetic energy.
• FLUID KINETIC ENERGY AS A SELECTION CRITERIA FOR CONTROL VALVES 10 January 2010 8:32 UTC www.iceweb.com.au [Source type: Academic]

^ What is happens to kinetic energy when the velocity is doubled?
• Types of Energy - Succeed in Understanding Physics: School for Champions 10 January 2010 8:32 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

.This kinetic energy gained during launch will remain constant while in orbit because there is almost no friction.^ This kinetic energy gained during launch will remain constant while in orbit because there is almost no friction.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ The cart gains kinetic energy.

^ Kinetic energy is the energy an object has because of its motion.
• Physics Help - Work and Energy 10 January 2010 8:32 UTC www.fortunecity.com [Source type: Original source]

.However it becomes apparent at re-entry when the kinetic energy is converted to heat.^ Heat energy is kinetic energy, right?
• Chemical Potential to Kinetic Energy 10 January 2010 8:32 UTC www.newton.dep.anl.gov [Source type: FILTERED WITH BAYES]

^ Entries tagged with 'kinetic energy' .

^ Re: Converting kinetic energy to degrees Celsius .
• Converting kinetic energy to degrees Celsius - OnlineConversion Forums 10 January 2010 8:32 UTC forum.onlineconversion.com [Source type: General]

.Kinetic energy can be passed from one object to another.^ Another definition of Kinetic Energy is m /2 * v elocity^2.

^ One kind is called kinetic energy.

^ K = kinetic energy of an object .
• ModPhy/Unit1/SpecialRelativity/RelativeView/ 10 January 2010 8:32 UTC physics.tamuk.edu [Source type: Academic]

.In the game of billiards, the player gives kinetic energy to the cue ball by striking it with the cue stick.^ In a "break" at the start of a game of billiards, the initial kinetic energy of the cue ball is distributed among all the balls on the table.

^ If the ball was dropped, gravity would accelerate it to give it kinetic energy.

^ In the game of billiards, the player gives kinetic energy to the cue ball by striking it with the cue stick.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.If the cue ball collides with another ball, it will slow down dramatically and the ball it collided with will accelerate to a speed as the kinetic energy is passed on to it.^ Another definition of Kinetic Energy is m /2 * v elocity^2.

^ K is kinetic energy of a mass m moving at speed v .
• Relativistic Escape Velocity using Relativistic Forms of Potential andKinetic Energy 10 January 2010 8:32 UTC mrelativity.net [Source type: Academic]

^ If the ball was dropped, gravity would accelerate it to give it kinetic energy.

.Collisions in billiards are effectively elastic collisions, where (by definition) kinetic energy is preserved.^ Another definition of Kinetic Energy is m /2 * v elocity^2.

^ Collisions in billiards are elastic collisions, where kinetic energy is preserved.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Comments What is the definition of kinetic energy?
• What is the definition of kinetic energy? 10 January 2010 8:32 UTC www.toolingu.com [Source type: Reference]
• What is the definition of kinetic energy? 10 January 2010 8:32 UTC www.toolingu.com [Source type: Reference]

.In inelastic collisions, kinetic energy is dissipated as: heat, sound, binding energy (breaking bound structures), or other kinds of energy.^ One kind is called kinetic energy.

^ Heat energy is kinetic energy, right?
• Chemical Potential to Kinetic Energy 10 January 2010 8:32 UTC www.newton.dep.anl.gov [Source type: FILTERED WITH BAYES]

^ Other kinds of potential and kinetic energy .
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

.Flywheels are being developed as a method of energy storage (see Flywheel energy storage).^ Flywheels are being developed as a method of energy storage (see article flywheel energy storage).
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Generally spoken, like any other energy storage device, the stored energy in flywheels has a destructive potential when released uncontrolled.
• FAQ: Kinetic Energy Storage 10 January 2010 8:32 UTC www.aspes.ch [Source type: Original source]

^ A pair of very massive flywheels rotating at 6 Hz are used to convert rotational kinetic energy into magnetic energy and vice versa for energy storage.
• Lecture 19: Rotating Rigid Bodies - Moment of Inertia - Parallel Axis and Perpendicular Axis Theorem - Rotational Kinetic Energy - Fly Wheels - Neutron Stars - Pulsars 10 January 2010 8:32 UTC videolectures.net [Source type: General]

.This illustrates that kinetic energy can also be rotational.^ This illustrates that kinetic energy can also be rotational.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ This "lost" energy is actually the rotational kinetic energy of the can.
• Rotational Kinetic Energy of a Soup Can 10 January 2010 8:32 UTC homepage.mac.com [Source type: FILTERED WITH BAYES]

^ A description of kinetic energy for rotating objects.
• Search Results | Explore | physics.org 10 January 2010 8:32 UTC www.physics.org [Source type: General]

### Calculations

.There are several different equations that may be used to calculate the kinetic energy of an object.^ I want to calculate Kinetic Energy(KE) .
• Kinetic Energy Calculator, Calculate Mass, Velocity. 10 January 2010 8:32 UTC www.easycalculation.com [Source type: Academic]

^ What is the equation for kinetic energy ?

^ There are tons of different kinds of energy.
• Physics Help - Work and Energy 10 January 2010 8:32 UTC www.fortunecity.com [Source type: Original source]

.In many cases they give almost the same answer to well within measurable accuracy.^ The problem is that these two scales give convenient numbers for "comfortable" temperatures, but they do not very well correspond with the energy being measured.
• Heat and Energy 10 January 2010 8:32 UTC www.dbooth.net [Source type: FILTERED WITH BAYES]

^ In that case, they are not only powering the store, they're saving your brake pads by a completely negligible amount as well :) .
• Sainsbury's Rolls Out Kinetic Energy Generator | GreenBiz.com 10 January 2010 8:32 UTC www.greenbiz.com [Source type: FILTERED WITH BAYES]

^ How does EPE differ from GPE? Give examples of other systems in which each type of energy exists and describe how they change as the motion within the system progresses.
• Teachers' Domain: Investigating Kinetic and Potential Energy 10 January 2010 8:32 UTC www.teachersdomain.org [Source type: FILTERED WITH BAYES]

.Where they differ, the choice of which to use is determined by the velocity of the body or its size.^ When humans or other animals eat food, they use its stored energy to keep warm, maintain and repair their bodies, and move about.
• ENERGY — Infoplease.com 10 January 2010 8:32 UTC www.infoplease.com [Source type: FILTERED WITH BAYES]

^ So-called "high velocity" rounds are not necessarily more damaging because they are jacketed and the bullet is smaller in size.

^ Remembering that the average velocity for each interval is a real velocity for the average time in this interval graph these velocities versus time using a standard size graph paper.
• AN INTRODUCTION TO NEWTONIAN MECHANICS (p.8) 10 January 2010 8:32 UTC www2.dsu.nodak.edu [Source type: FILTERED WITH BAYES]

.Therefore, if the object is moving at a velocity much smaller than the speed of light, the Newtonian (classical) mechanics will be sufficiently accurate; but if the speed is comparable to the speed of light, relativity starts to make significant differences to the result and should be used.^ Note that the velocity of the object must be much less than the speed of light.
• Types of Energy - Succeed in Understanding Physics: School for Champions 10 January 2010 8:32 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

^ A moving object has energy resulting from its velocity.

^ At large velocities the differences are significant.
• kinetic energy@Everything2.com 10 January 2010 8:32 UTC www.everything2.com [Source type: FILTERED WITH BAYES]

.If the size of the object is sub-atomic, the quantum mechanical equation is most appropriate.^ We have seen in equation 2, that due to quantum mechanics, the atom must be compatible with the de Broglie equation.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ When dealing with classical mechanics, its best to think of the results as approximations (good at large scales), but at the quantum level, the equations fall apart.
• Can Kinetic energy ever be negative? - Yahoo! Answers India 10 January 2010 8:32 UTC in.answers.yahoo.com [Source type: General]

^ Using equation 7 in classical physics, (but without quantum mechanics) the radius of curvature r of the electron orbit is inversely proportional ( ) to the square of the velocity.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

## Newtonian kinetic energy

### Kinetic energy of rigid bodies

In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body, is given by the equation
$E_k = frac{1}{2} mv^2$
where .$m\;$ is the mass and $v\;$ is the speed (or the velocity) of the body.^ Book article from: A Dictionary of Astronomy kinetic energy The energy possessed by a body by virtue...much less than the speed of light, kinetic energy is equal to ½ mv 2 , where m...is its velocity.
• kinetic energy – FREE kinetic energy information | Encyclopedia.com: Find kinetic energy research 10 January 2010 8:32 UTC www.encyclopedia.com [Source type: Academic]

^ Consider a body of mass m subjected to a force F = ma , moving from rest to a velocity v.

^ Given a force F exerted on a body of mass m over a distance d s , the work done is given by W= ∫ F ·d s Noting Newtons second law ( F =m d v /dt) and the definition of velocity ( v =d s /dt) the equation may be rewritten.
• kinetic energy@Everything2.com 10 January 2010 8:32 UTC www.everything2.com [Source type: FILTERED WITH BAYES]

.In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ The units for measuring energy are joules (J) .
• ENERGY 10 January 2010 8:32 UTC ed.fnal.gov [Source type: FILTERED WITH BAYES]

^ Where in the swing does the pendulum have the most kinetic energy (speed)?

For example, one would calculate the kinetic energy of an 80 kg mass traveling at 18 meters per second (40 mph) as
$E_k = frac{1}{2} \cdot 80 \cdot 18^2 = 12 960 \ \mathrm{joules}.$
.Note that the kinetic energy increases with the square of the speed.^ Note that kinetic energy is defined as ENERGY, not as FORCE. ) .
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

^ The average kinetic energy, and so the average speed, of molecules in a gas increases with temperature.
• AUFBAU1 [SELECTED PRINCIPLES: KINETIC THEORY] 10 January 2010 8:32 UTC www.wissensdrang.com [Source type: Academic]

^ The increase in penetration will not be proportional to the increase in kinetic energy .
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

.This means, for example, that an object traveling twice as fast will have four times as much kinetic energy.^ What is its kinetic energy at this time?

^ This means that if a car is going twice as fast, it has four times the energy.
• HowStuffWorks "How Force, Power, Torque and Energy Work" 10 January 2010 8:32 UTC auto.howstuffworks.com [Source type: FILTERED WITH BAYES]

^ (They are an example of kinetic energy.
• Science NetLinks: Transforming Energy 10 January 2010 8:32 UTC www.sciencenetlinks.com [Source type: FILTERED WITH BAYES]

.As a result of this, a car traveling twice as fast requires four times as much distance to stop (assuming a constant braking force.^ This means that if a car is going twice as fast, it has four times the energy.
• HowStuffWorks "How Force, Power, Torque and Energy Work" 10 January 2010 8:32 UTC auto.howstuffworks.com [Source type: FILTERED WITH BAYES]

^ The distance traveled is the average speed times D t, .

^ Work is force times distance .
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

See mechanical work).
The kinetic energy of an object is related to its momentum by the equation:
$E_k = \frac{p^2}{2m}$
where:
$p\;$ is momentum
$m\;$ is mass of the body
For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a body with constant mass $m\;$, whose center of mass is moving in a straight line with speed $v\;$, as seen above is equal to
$E_t = frac{1}{2} mv^2$
where:
$m\;$ is the mass of the body
$v\;$ is the speed of the .center of mass of the body.^ Recall that the motion of a rigid body, in translation, is described by assigning motional quantities to the "center of mass(COM)".
• Work - kinetic energy theorem for rotational motion 10 January 2010 8:32 UTC cnx.org [Source type: FILTERED WITH BAYES]

^ It sometimes is convenient to split the total kinetic energy of body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass rotational energy : .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ If we look at the expression of center of mass in x-direction, then we realize that the concept of COM is actually designed to incorporate distribution of mass in the body.
• Work - kinetic energy theorem for rotational motion 10 January 2010 8:32 UTC cnx.org [Source type: FILTERED WITH BAYES]

.The kinetic energy of any entity is unique to the reference frame in which it is measured.^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Kinetic energy is measured in "foot pounds".
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

.An isolated system is one for which energy can neither enter nor leave, and has a total energy which is unchanging over time as measured in any reference frame.^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Conservation of energy It states that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system, ...
• Work, power and energy, Thermal physics 10 January 2010 8:32 UTC www.educypedia.be [Source type: Academic]

^ As seen from a stationary frame of reference which is not that of the center of inertia, the total amount of mass T shown below never changes: T = 3 kg.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

.Thus, the chemical energy converted to kinetic energy by a rocket engine will be divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame.^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ It has converted some potential energy to kinetic energy.
• MIT OpenCourseWare | Physics | 8.01 Physics I: Classical Mechanics, Fall 1999 | Video Lectures | detail 10 January 2010 8:32 UTC ocw.mit.edu [Source type: Original source]

^ An actuator converts potential energy to kinetic energy.
• What is the definition of kinetic energy? 10 January 2010 8:32 UTC www.toolingu.com [Source type: Reference]

This is called the Oberth effect. .But the total energy of the system (including kinetic energy, fuel chemical energy, heat energy, etc) will be conserved over time, regardless of the choice of reference frame.^ What is its kinetic energy at this time?

^ Is kinetic energy conserved?

^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.However, different observers moving with different reference frames will disagree on the value of this conserved energy.^ However, the physical length of the rod is certainly different in the moving frame.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ However a difference in gravitational potential energy .

^ However, it is not so when a moving observer is moving with the mass, because the reference units in the moving frame are different, due to their kinetic energy.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

.In addition, although the energy of such systems is dependent on the choice of reference frame, the minimal total energy which is seen in any frame will be the total energy seen by observers in the center of momentum frame; this minimal energy corresponds to the invariant mass of the aggregate.^ It is lowest with respect to the center of mass , i.e., in a frame of reference in which the center of mass is stationary.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ In another frame of reference the additional kinetic energy is that corresponding to the total mass and the speed of the center of mass.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.The calculated value of this invariant mass compensates for changing energy in different frames, and is thus the same for all frames and observers.^ For example - one would calculate the kinetic energy of an 80 kg mass travelling at 40 mph (17.8816 metres per second) as joules.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ As seen from a stationary frame of reference which is not that of the center of inertia, the total amount of mass T shown below never changes: T = 3 kg.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

#### Derivation

The work done accelerating a particle during the infinitesimal time interval dt is given by the dot product of force and displacement:
$\mathbf{F} \cdot d \mathbf{x} = \mathbf{F} \cdot \mathbf{v} d t = \frac{d \mathbf{p}}{d t} \cdot \mathbf{v} d t = \mathbf{v} \cdot d \mathbf{p} = \mathbf{v} \cdot d (m \mathbf{v}).$
Applying the product rule we see that:
$d(\mathbf{v} \cdot \mathbf{v}) = (d \mathbf{v}) \cdot \mathbf{v} + \mathbf{v} \cdot (d \mathbf{v}) = 2(\mathbf{v} \cdot d\mathbf{v}).$
Therefore (assuming constant mass), the following can be seen:
$\mathbf{v} \cdot d (m \mathbf{v}) = \frac{m}{2} d (\mathbf{v} \cdot \mathbf{v}) = \frac{m}{2} d v^2 = d \left(\frac{m v^2}{2}\right).$
Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call the result kinetic energy:
$E_k = \int \mathbf{F} \cdot d \mathbf{x} = \int \mathbf{v} \cdot d \mathbf{p}= \frac{m v^2}{2}.$
.This equation states that the kinetic energy (Ek) is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal change of the body's momentum (p).^ Can a body change in kinetic energy without changing in momentum?

^ MOMENTUM vs. KINETIC ENERGY: .
• Carbon Arrow Selection Guide. Chapter 5: Arrow Speed and Kinetic Energy 10 January 2010 8:32 UTC www.huntersfriend.com [Source type: General]

^ Specifically, the change in microscopic kinetic energy is .
• Kinetic Energy, Work, Momentum, Force times Time, andForce dot Distance 10 January 2010 8:32 UTC www.av8n.com [Source type: FILTERED WITH BAYES]

.It is assumed that the body starts with no kinetic energy when it is at rest (motionless).^ It is assumed that the body starts at rest (motionless).
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

^ Kinetic Energy: Encyclopedia - Brake A brake is a device for slowing or stopping the motion of a machine, and to keep it from starting to move.

### Rotating bodies

If a rigid body is rotating about any line through the center of mass then it has rotational kinetic energy (Er) which is simply the sum of the kinetic energies of its moving parts, and is thus given by:
$E_r = \int \frac{v^2 dm}{2} = \int \frac{(r \omega)^2 dm}{2} = \frac{\omega^2}{2} \int{r^2}dm = \frac{\omega^2}{2} I = \begin{matrix} \frac{1}{2} \end{matrix} I \omega^2$
where:
• ω is the body's angular velocity
• r is the distance of any mass dm from that line
• I is the body's moment of inertia, equal to $\int{r^2}dm$.
.(In this equation the moment of inertia must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape).^ Precession refers to rotation of the bullet around the center of mass.

^ The rotational inertia I in this equation must also be calculated with respect to the same rotation axis.

^ The rotational inertia around an axis through P, I P , is related to the rotational inertia around an axis through the center of mass, I cm The kinetic energy of the wheel can now be rewritten as where the first term is the kinetic energy associated with the rotation of the wheel about an axis through its center of mass and the second term is associated with the translational motion of the wheel.

### Kinetic energy of systems

.A system of bodies may have internal kinetic energy due to macroscopic movements of the bodies in the system.^ Kinetic energy of an arrow is the energy it has due to its motion.

^ Can a body change in kinetic energy without changing in momentum?

^ In other systems, the 'as found' state may include some potential energy and/or kinetic energy.
• Potential Energy and Fields 10 January 2010 8:32 UTC www.mcasco.com [Source type: FILTERED WITH BAYES]

.For example, in the Solar System the planets and planetoids are orbiting the Sun.^ We have: 8 Equation 8 is also compatible with the behavior of the orbit of planets moving around the Sun described by Newton and Kepler.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ This is somewhat similar to the attracting gravitational force between the orbiting planets around the Sun as presented by Gerhard Herzberg (3) and others.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ As a matter of fact, considering the whole solar system, the sun itself is rotating around a center of inertia.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

.In a tank of gas, the molecules are moving in all directions.^ If the gas molecules were restricted to one dimension, just moving back and forth on a line, then the most likely value of their speed would also be zero.
• Kinetic Theory of Gases: A Brief Review 10 January 2010 8:32 UTC galileo.phys.virginia.edu [Source type: FILTERED WITH BAYES]

^ You can already see that the gravitational potential energy, when I come from infinity with a force in this direction and I move inward, you can already see that gravitational potential energy will always be negative for all points anywhere.
• MIT OpenCourseWare | Physics | 8.01 Physics I: Classical Mechanics, Fall 1999 | Video Lectures | detail 10 January 2010 8:32 UTC ocw.mit.edu [Source type: Original source]

^ However, for gas molecules free to move in two or three dimensions, the most likely value of the speed is not zero.
• Kinetic Theory of Gases: A Brief Review 10 January 2010 8:32 UTC galileo.phys.virginia.edu [Source type: FILTERED WITH BAYES]

.The kinetic energy of a system at any instant in time is the sum of the kinetic energies of the bodies it contains.^ It is the sum of their kinetic energy.
• Kinetic Energy Concerns Movement of Matter - Succeed in Understanding Physics: School for Champions 10 January 2010 8:32 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

^ What is its kinetic energy at this time?

^ We refer to the sum of potential and kinetic energy as the "mechanical energy" of the system.
• Potential Energy and Fields 10 January 2010 8:32 UTC www.mcasco.com [Source type: FILTERED WITH BAYES]

.However, this quantity, as with single objects, depends on the inertial frame of the system observer.^ The revisited Newtonian one is rather relative to the observer's frame of reference, which must however be chosen carefully.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ However, another observer placed in the frame of reference of the other ball would obtain the reversed contradictory version.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ In the presence of multiple bodies, the center of inertia of the whole system is still the best place for establishing the frame of reference from where the observer will have a better view.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

.In systems of masses where two or more masses are traveling with different velocities, the system kinetic energy can be minimized by choice of inertial frame, but cannot be made zero (see discussion of choice of reference frame, below).^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ Therefore the change in kinetic energy plus the change in potential energy of the system is zero.
• Potential Energy and Fields 10 January 2010 8:32 UTC www.mcasco.com [Source type: FILTERED WITH BAYES]

^ Two different formulas for kinetic energy are now available.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

.A complex body that is stationary (i.e., a reference frame has been chosen to correspond to the body's center of momentum) and which is not rotating, nevertheless may have various kinds of internal energy, which may be partly kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin.^ Can a body change in kinetic energy without changing in momentum?

^ Other kinds of potential and kinetic energy .
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

^ Can a body change in momentum without changing in kinetic energy?

.These all contribute to the body's mass, as provided by the special theory of relativity.^ What this suggests is that the formulae for energy and momentum are not special and axiomatic, but rather concepts which emerge from the equation of mass with energy and the principles of relativity.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Einstein showed in his theory of special relativity that the energy of a free particle of (rest) mass m and speed v is equal to .
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

^ The electrical power input to the mass stream pairs initially would be at the planetary surface contact sites, which also provides the re-referencing of the mass stream velocities relative the the ground.
• KINETIC ENERGY SUPPORTED ELECTRICALLY POWERED TRANSPORTATION STRUCTURES 10 January 2010 8:32 UTC www.home.earthlink.net [Source type: FILTERED WITH BAYES]

.For a simple example, the total kinetic energies of the molecules in a tank of gas contribute to the mass of the tank as measured with the tank sitting on a scale.^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ (They are an example of kinetic energy.
• Science NetLinks: Transforming Energy 10 January 2010 8:32 UTC www.sciencenetlinks.com [Source type: FILTERED WITH BAYES]

^ E is the kinetic energy of the molecule.
• Kinetic Theory of Gases: A Brief Review 10 January 2010 8:32 UTC galileo.phys.virginia.edu [Source type: FILTERED WITH BAYES]

.When discussing movements of a macroscopic body (that is, movements of the body's center of mass), the kinetic energy referred to usually that of the macroscopic movement only.^ For example - one would calculate the kinetic energy of an 80 kg mass travelling at 40 mph (17.8816 metres per second) as joules.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ From your velocity measurement and the mass of the marble, calculate the kinetic energy of the marble.
• Roller Coaster Marbles: Converting Potential Energy to Kinetic Energy 10 January 2010 8:32 UTC www.sciencebuddies.org [Source type: FILTERED WITH BAYES]

^ Can a body change in kinetic energy without changing in momentum?

.However all internal energies of all types contribute to body's mass, inertia, and total energy.^ As seen from a stationary frame of reference which is not that of the center of inertia, the total amount of mass T shown below never changes: T = 3 kg.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ Kinetic Energy: Encyclopedia II - Energy - Types of energy All forms of energy: thermal, chemical, electrical, [[radiant energy|radiant], nuclear etc.

^ Kinetic energy is defined as the total energy of a body in motion.
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

### Frame of reference for systems

.The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.^ It is lowest with respect to the center of mass , i.e., in a frame of reference in which the center of mass is stationary.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ In another frame of reference the additional kinetic energy is that corresponding to the total mass and the speed of the center of mass.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

This may be simply shown: let V be the relative speed of the frame k from the center of mass frame i :
$E_k = \int \frac{v^2 dm}{2} = \int \frac{(v_i + V)^2 dm}{2} = \int \frac{(v_i^2 + 2 v_i V + V^2) dm}{2} = \int \frac{v_i^2 dm}{2} + V \int v_i dm + \frac{V^2}{2} \int dm.$
.However, let $\int \frac{v_i^2 dm}{2} = E_i$ the kinetic energy in the center of mass frame, $\int v_i dm$ would be simply the total momentum which is by definition zero in the center of mass frame, and let the total mass: $\int dm = M$.^ MOMENTUM vs. KINETIC ENERGY: .
• Carbon Arrow Selection Guide. Chapter 5: Arrow Speed and Kinetic Energy 10 January 2010 8:32 UTC www.huntersfriend.com [Source type: General]

^ In another frame of reference the additional kinetic energy is that corresponding to the total mass and the speed of the center of mass.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Definition and meaning of kinetic energy : .

Substituting, we get:[4]
$E_k = E_i + \frac{M V^2}{2}.$
.Thus the kinetic energy of a system is lowest with respect to center of momentum reference frames, i.e., frames of reference in which the center of mass is stationary (either the center of mass frame or any other center of momentum frame).^ MOMENTUM vs. KINETIC ENERGY: .
• Carbon Arrow Selection Guide. Chapter 5: Arrow Speed and Kinetic Energy 10 January 2010 8:32 UTC www.huntersfriend.com [Source type: General]

^ Other kinds of potential and kinetic energy .
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

^ The kinetic energy of a system depends on the inertial frame of reference .
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

.In any other frame of reference there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass.^ It is lowest with respect to the center of mass , i.e., in a frame of reference in which the center of mass is stationary.
• PowerPedia:Kinetic Energy - PESWiki 10 January 2010 8:32 UTC peswiki.com [Source type: Reference]

^ Lorentz discovered that moving matter contains additional mass as kinetic energy, which is given by: .
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ Other kinds of potential and kinetic energy .
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

.The kinetic energy of the system in the center of momentum frame contributes to the invariant mass of the system, and this total mass is a quantity which is both invariant (all observers see it to be the same) and is conserved (in an isolated system, it cannot change value, no matter what happens inside the system).^ Can a body change in kinetic energy without changing in momentum?

^ Is kinetic energy conserved?

^ MOMENTUM vs. KINETIC ENERGY: .
• Carbon Arrow Selection Guide. Chapter 5: Arrow Speed and Kinetic Energy 10 January 2010 8:32 UTC www.huntersfriend.com [Source type: General]

### Rotation in systems

It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass (rotational energy):
$E_k = E_t + E_r \,$
where:
Ek is the total kinetic energy
Et is the translational kinetic energy
Er is the rotational energy or angular kinetic energy in the rest frame
.Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation.^ Thus, if the billiard ball was accelerated again using the same amount of energy, it would accelerate from 0.866 to 0.9428 c.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ This represents a more severe set of conditions for the retrofit trim in controlling any destructive affects due to the higher potential energy that would be converted to kinetic energy across the trim.
• FLUID KINETIC ENERGY AS A SELECTION CRITERIA FOR CONTROL VALVES 10 January 2010 8:32 UTC www.iceweb.com.au [Source type: Academic]

^ The purpose of the division by 2 was that half of kinetic energy had to be used in order to stop the incoming billiard ball.
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## Relativistic kinetic energy of rigid bodies

.In special relativity, we must change the expression for linear momentum.^ We must note the correspondence of this expression with its linear counterpart, where : .
• Work - kinetic energy theorem for rotational motion 10 January 2010 8:32 UTC cnx.org [Source type: FILTERED WITH BAYES]

^ This is the rate of change of momentum, and so must be equal to the balancing force, which is therefore F = mv 2 / L .
• Kinetic Theory of Gases: A Brief Review 10 January 2010 8:32 UTC galileo.phys.virginia.edu [Source type: FILTERED WITH BAYES]

.Using m for rest mass, v resp.^ The mass gain is added to the mass at rest and it can easily be obtained using Lorentz's gamma factor: gamma = 1/g.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

v for the object's velocity resp. speed, and c for the speed of light in vacuum, integrating by parts gives
$E_k = \int \mathbf{v} \cdot d \mathbf{p}= \int \mathbf{v} \cdot d (m \gamma \mathbf{v}) = m \gamma \mathbf{v} \cdot \mathbf{v} - \int m \gamma \mathbf{v} \cdot d \mathbf{v} = m \gamma v^2 - \frac{m}{2} \int \gamma d (v^2)$
Remembering that $\gamma = (1 - v^2/c^2)^{-1/2}\!$, we get:
\begin{align} E_k &= m \gamma v^2 - \frac{- m c^2}{2} \int \gamma d (1 - v^2/c^2) \ &= m \gamma v^2 + m c^2 (1 - v^2/c^2)^{1/2} - E_0 \end{align}
where E0 serves as an integration constant. Thus:
\begin{align} E_k &= m \gamma (v^2 + c^2 (1 - v^2/c^2)) - E_0 \ &= m \gamma (v^2 + c^2 - v^2) - E_0 \ &= m \gamma c^2 - E_0 \end{align}
The constant of integration E0 is found by observing that, when $\mathbf{v }= 0 , \ \gamma = 1\!$ and $E_k = 0 \!$, giving
$E_0 = m c^2 \,$
and giving the usual formula:
$E_k = m \gamma c^2 - m c^2 = \frac{m c^2}{\sqrt{1 - v^2/c^2}} - m c^2$
.If a body's speed is a significant fraction of the speed of light, it is necessary to use relativistic mechanics (the theory of relativity as expounded by Albert Einstein) to calculate its kinetic energy.^ Kinetic energy increases with the square of the speed .

^ But it can also be solved using conservation of mechanical energy.

^ For non-relativistic mechanics, the total kinetic energy of a body can be considered as the sum of the body's translational kinetic energy and its r ...

For a relativistic object the momentum p is equal to:
$p = \frac{m v}{\sqrt{1 - (v/c)^2}}$.
Thus the work expended accelerating an object from rest to a relativistic speed is:
$E_k = \frac{m c^2}{\sqrt{1 - (v/c)^2}} - m c^2$.
.The equation shows that the energy of an object approaches infinity as the velocity v approaches the speed of light c, thus it is impossible to accelerate an object across this boundary.^ At A, the object has no velocity, no speed.
• MIT OpenCourseWare | Physics | 8.01 Physics I: Classical Mechanics, Fall 1999 | Video Lectures | detail 10 January 2010 8:32 UTC ocw.mit.edu [Source type: Original source]

^ Energy is linked to the speed of light squared.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ Use a radiometer to show that light has energy.  .
• What is Energy? Activities and Experiments 10 January 2010 8:32 UTC www.uwsp.edu [Source type: FILTERED WITH BAYES]

The mathematical by-product of this calculation is the mass-energy equivalence formula—the body at rest must have energy content equal to:
$E_\mbox{rest} = E_0 = m c^2 \!$
.At a low speed (v<<c), the relativistic kinetic energy may be approximated well by the classical kinetic energy.^ Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

^ Kinetic energy determines how hard the baseball strikes ; it has no direct bearing on how well it penetrates.
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

^ That is why energy or kinetic energy, whose amount is given by the m c squared formula, is linked to the speed of light "c".
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

This is done by binomial approximation. Indeed, taking Taylor expansion for the reciprocal square root and keeping first two terms we get:
$E_k \approx m c^2 \left(1 + \frac{1}{2} v^2/c^2\right) - m c^2 = \frac{1}{2} m v^2$,
.So, the total energy E can be partitioned into the energy of the rest mass plus the traditional Newtonian kinetic energy at low speeds.^ B plus kinetic energy at B, must be u at C plus kinetic energy at C, must be u at D plus kinetic energy at D. .
• MIT OpenCourseWare | Physics | 8.01 Physics I: Classical Mechanics, Fall 1999 | Video Lectures | detail 10 January 2010 8:32 UTC ocw.mit.edu [Source type: Original source]

^ The revisited Newtonian formula for kinetic energy.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

^ Total kinetic energy depends upon two variables: the mass of the object and the speed of the object.
• Carbon Arrow Selection Guide. Chapter 5: Arrow Speed and Kinetic Energy 10 January 2010 8:32 UTC www.huntersfriend.com [Source type: General]

.When objects move at a speed much slower than light (e.g.^ How much kinetic energy does a moving object have if its mass is 100 kg and it is moving at a speed of 5 meters per second?

^ It is easier to design features that aid deceleration of a larger, slower moving bullet in tissues than a small, high velocity bullet.

^ If a truck and a car are driving parallel to one another down the freeway, at the same speed, the truck has more kinetic energy than the car because it has much more mass.
• The science of energy: A simple introduction from Explain that Stuff! 10 January 2010 8:32 UTC www.explainthatstuff.com [Source type: FILTERED WITH BAYES]

in everyday phenomena on Earth), the first two terms of the series predominate. The next term in the approximation is small for low speeds, and can be found by extending the expansion into a Taylor series by one more term:
$E \approx m c^2 \left(1 + \frac{1}{2} v^2/c^2 + \frac{3}{8} v^4/c^4\right) = m c^2 + \frac{1}{2} m v^2 + \frac{3}{8} m v^4/c^2$.
.For example, for a speed of 10 km/s the correction to the Newtonian kinetic energy is 0.0417 J/kg (on a Newtonian kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 417 J/kg (on a Newtonian kinetic energy of 5 GJ/kg), etc.^ (They are an example of kinetic energy.
• Science NetLinks: Transforming Energy 10 January 2010 8:32 UTC www.sciencenetlinks.com [Source type: FILTERED WITH BAYES]

^ Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

^ Kinetic Energy: Encyclopedia II - Energy - Types of energy All forms of energy: thermal, chemical, electrical, [[radiant energy|radiant], nuclear etc.

For higher speeds, the formula for the relativistic kinetic energy[5] is derived by simply subtracting the rest mass energy from the total energy:
$E_k = m \gamma c^2 - m c^2 = m c^2\left(\frac{1}{\sqrt{1 - (v/c)^2}} - 1\right)$.
The relation between kinetic energy and momentum is more complicated in this case, and is given by the equation:
$E_k = \sqrt{p^2 c^2 + m^2 c^4} - m c^2$.
This can also be expanded as a Taylor series, the first term of which is the simple expression from Newtonian mechanics.
.What this suggests is that the formulas for energy and momentum are not special and axiomatic, but rather concepts which emerge from the equation of mass with energy and the principles of relativity.^ Substituting equation 25 in 24 gives: 26 which gives 27 Equation 27 gives the relative size of the reference units of the Planck energy constant between the rest and the moving frame.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ Einstein showed in his theory of special relativity that the energy of a free particle of (rest) mass m and speed v is equal to .
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

^ The arrows momentum will be a function of the bows output kinetic energy and the arrows mass, but it is not the product of them.
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

## Quantum mechanical kinetic energy of rigid bodies

In the realm of quantum mechanics, the expectation value of the electron kinetic energy, $\langle\hat{T}\rangle$, for a system of electrons described by the wavefunction $\vert\psi\rangle$ is a sum of 1-electron operator expectation values:
$\langle\hat{T}\rangle = -\frac{\hbar^2}{2 m_e}\bigg\langle\psi \bigg\vert \sum_{i=1}^N abla^2_i \bigg\vert \psi \bigg\rangle$
where .me is the mass of the electron and $abla^2_i$ is the Laplacian operator acting upon the coordinates of the ith electron and the summation runs over all electrons.^ In that case, we have seen previously (2) that the mass of all particles like atoms, protons and electrons increases according to: 5 Where: 6 In equation 6, v is the absolute velocity of particles (electron, proton or atom), using stationary units.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ The mass of all electrons being the same, it becomes clear that its force should apply equally on both electrons, especially if the center of inertia and the observer are postulated to be stationary.
• Kinetic energy. 10 January 2010 8:32 UTC www.glafreniere.com [Source type: FILTERED WITH BAYES]

Notice that this is the quantized version of the non-relativistic expression for kinetic energy in terms of momentum:
$E_k = \frac{p^2}{2m}.$
.The density functional formalism of quantum mechanics requires knowledge of the electron density only, i.e., it formally does not require knowledge of the wavefunction.^ Using equation 7 in classical physics, (but without quantum mechanics) the radius of curvature r of the electron orbit is inversely proportional ( ) to the square of the velocity.
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ This quantum condition requires that the circumference of the electron orbit is equal to an integer n, times the de Broglie electron wavelength l B .
• Natural Length Contraction Mechanism Due to Kinetic Energy 10 January 2010 8:32 UTC www.intalek.com [Source type: Academic]

^ The energy of many (but not all) quantum mechanical systems is quantized , meaning that the energy of the system can take on only discrete values.
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

Given an electron density $\rho(\mathbf{r})$, the exact N-electron kinetic energy functional is unknown; however, for the specific case of a 1-electron system, the kinetic energy can be written as
$T[\rho] = \frac{1}{8} \int \frac{ abla \rho(\mathbf{r}) \cdot abla \rho(\mathbf{r}) }{ \rho(\mathbf{r}) } d^3r$
where .T[ρ] is known as the von Weizsäcker kinetic energy functional.^ The arrows momentum will be a function of the bows output kinetic energy and the arrows mass, but it is not the product of them.
• Momentum, Kinetic Energy, and Arrow Penetration 10 January 2010 8:32 UTC www.tradgang.com [Source type: FILTERED WITH BAYES]

^ Their primary function is to provide the storage and exchange of the kinetic energy which supports the compression load of the structures weight, and distributes energy to move payload along the structures.
• KINETIC ENERGY SUPPORTED ELECTRICALLY POWERED TRANSPORTATION STRUCTURES 10 January 2010 8:32 UTC www.home.earthlink.net [Source type: FILTERED WITH BAYES]

^ Lastly, turning to FIG. 3, illustrated is a plot of the final kinetic energy of the ions as a function of their position at the time of application of the extraction pulse--i.e., 200 ns after the laser pulse.
• Kinetic energy focusing for pulsed ion desorption mass spectrometry - Patent 6130426 10 January 2010 8:32 UTC www.freepatentsonline.com [Source type: Academic]

## Notes

1. ^ Judith P. Zinsser Emilie Du Chatelet: Daring Genius of the Enlightenment Penguin, 2007.
2. ^ Crosbie Smith, M. Norton Wise. Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge University Press, 866 pp.
3. ^ John Theodore Merz. A History of European Thought in the Nineteenth Century. Blackwood, 1912, p. 139.
4. ^ Physics notes - Kinetic energy in the CM frame. Duke.edu. Accessed 2007-11-24.
5. ^ In Einstein's original Über die spezielle und die allgemeine Relativitätstheorie (Zu Seite 41) and in most translations (e.g. Relativity - The Special and General Theory) kinetic energy is defined as $m c^2 / \sqrt{1 - v^2/c^2}$.

## References

• Oxford Dictionary 1998
• School of Mathematics and Statistics, University of St Andrews (2000). "Biography of Gaspard-Gustave de Coriolis (1792-1843)". Retrieved 2006-03-03.
• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed. ed.). Brooks/Cole. ISBN 0-534-40842-7.
• Tipler, Paul (2004). .Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.^ Introduction to classical mechanics and electricity: (2004) Physics for Scientists and Engineers, with Modern Physics , 6th Edition.
• Energy (science) - encyclopedia article - Citizendium 10 January 2010 8:32 UTC en.citizendium.org [Source type: Academic]

ed.). W. H. Freeman. ISBN 0-7167-0809-4.

• Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed. ed.). W. H. Freeman. ISBN 0-7167-4345-0.

# Simple English

Kinetic energy is the energy which refers to moving objects. So you can think of Kinetic energy as the energy of movement, because it refers to any object that is moving at that present time. This energy can be changed into other sorts of energy such as heat (if something hits with something soft and does not bounce), potential energy (if it is moving upwards and gets higher), or even light (if it is moving very, very fast or if it hits something which sparks like flint or iron/Aluminium). However, heat, light, sound, mechanical energy, electrical, and other types of energy are also types of kinetic energy.

Kinetic Energy is equal to the mass of something times its velocity (or speed) times its velocity again, all times ½:

$kinetic\ energy = \frac\left\{1\right\}\left\{2\right\}mass \times velocity \times velocity$

Meteors, bullets from a gun, and a kicked football have kinetic energy.

# Citable sentences

Up to date as of December 24, 2010

Here are sentences from other pages on Kinetic energy, which are similar to those in the above article.