Newtonian mechanics
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enWho's looking at you?
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Rachel Thomas </div>
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<p>Observers are, of course, vital in physics: we test our theories by comparing them to our observations. But in cosmology, as Jim Hartle explains, we could be one of many possible observers in the Universe and knowing which one we are is vital in testing our theories.</p>
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<h3>View from the inside or the outside?</h3>
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"Observers, of course, are important in all of physics," says <a href="http://web.physics.ucsb.edu/~hartle/">Jim Hartle</a>, Professor of Physics at the University of California, Santa Barbara. This is because predicting, making and comparing observations is fundamentally how physics is done. We (or rather, our fellow human physicists) use theories to predict what our observations will be and we test these theories by checking if the observations that are predicted match what we actually observe.
</p></p><p><a href="http://plus.maths.org/content/whos-looking-you" target="_blank">read more</a></p>http://plus.maths.org/content/whos-looking-you#commentsBoltzmann brainFP-carouselNewtonian mechanicsphilosophy of cosmologyquantum mechanicsWed, 21 Jan 2015 11:44:17 +0000Rachel6274 at http://plus.maths.org/contentCereal, sand and snow
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<p>As your cereal tumbled into your bowl this morning, were you daydreaming of sand dunes or snowy mountains? It wouldn't be surprising given the drab grey skies outside. But now you have another excuse: the cereal, sand and snow can all be examples of <em>granular flows</em>.</p>
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As your cereal tumbled into your bowl this morning, were you daydreaming of sand dunes or snowy mountains? It wouldn't be surprising given the drab grey skies outside. But now you have another excuse: the cereal, sand and snow can all be examples of <em>granular flows</em>. These occur when a large number of particles move together, say snow avalanching down a mountain, the shifting of sand dunes in the desert or some industrial process in which materials tumble down chutes.
</p><p><a href="http://plus.maths.org/content/cereal-sand-and-snow" target="_blank">read more</a></p>http://plus.maths.org/content/cereal-sand-and-snow#commentsavalanchefluid dynamicsgranular flowNewtonian mechanicsstatistical physicsWed, 26 Mar 2014 10:38:47 +0000Rachel6040 at http://plus.maths.org/contentMaths in a minute: Newton's laws of motion
http://plus.maths.org/content/maths-minute-newtons-laws-motion
<p>We've been dabbling a lot in the mysterious world of <a href="http://plus.maths.org/content/category/tags/quantum-physics">quantum physics</a> lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics.
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<div class="rightimage" style="width: 400px"><img src="http://plus.maths.org/content/sites/plus.maths.org/files/news/2011/velo/velo_interior.jpg" width="400" height="258" alt="The London velodrome"/><p>The London Velodrome's track is designed for maximum speed using Newton's laws of motion.</p><p><a href="http://plus.maths.org/content/maths-minute-newtons-laws-motion" target="_blank">read more</a></p>http://plus.maths.org/content/maths-minute-newtons-laws-motion#commentsNewtonian mechanicsThu, 07 Mar 2013 12:19:02 +0000mf3445863 at http://plus.maths.org/contentSchrödinger's equation — what is it?
http://plus.maths.org/content/schrodinger-1
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Marianne Freiberger </div>
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<p>In the 1920s the Austrian physicist Erwin Schrödinger came up with what has become the central equation of quantum mechanics. It tells you all there is to know about a quantum physical system and it also predicts famous quantum weirdnesses such as superposition and quantum entanglement. In this, the first article of a three-part series, we introduce Schrödinger's equation and put it in its historical context.</p>
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[maths]Here is a typical textbook question. Your car has run out of petrol. With how much force do you need to push it to accelerate it to a given speed?
The answer comes from Newton's second law of motion:
$$F=ma,$$ where $a$ is acceleration, $F$ is force and $m$ is mass.<p><a href="http://plus.maths.org/content/schrodinger-1" target="_blank">read more</a></p>http://plus.maths.org/content/schrodinger-1#commentsmathematical realityNewtonian mechanicsquantum mechanicsquantum physicsquantum uncertaintySchrödinger equationwave functionwave-particle dualityThu, 02 Aug 2012 08:30:52 +0000mf3445704 at http://plus.maths.org/contentThe maths of gold medals: Four Olympic thoughts
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Rob Eastaway and John Haigh </div>
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<p>It's not the winning, it's the taking part that counts. At least, that's what the Olympic creed would have us believe. But, like it or not, what the media and governments focus on is the tally of gold medals. This article explores some of the maths of gold.</p>
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<div class="rightimage" style="width: 400px"><img src="/sites/plus.maths.org/files/articles/2011/olympic/stadium.jpg" alt="Olympic stadium" width="400" height="186" /><p>A computer generated image of the 2012 Olympic stadium in London. Image: <a href="http://www.london2012.com/">London 2012</a>.</p><p><a href="http://plus.maths.org/content/maths-gold-medals-four-olympic-thoughts" target="_blank">read more</a></p>http://plus.maths.org/content/maths-gold-medals-four-olympic-thoughts#commentsmathematics in sportNewtonian mechanicsolympicsFri, 03 Jun 2011 08:54:45 +0000mf3445485 at http://plus.maths.org/contentMaking gold for 2012
http://plus.maths.org/content/making-gold
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<p>Last week leading researchers in sports technology met at the Royal Academy of Engineering in London to demonstrate just how far their field has come over recent years. The changes they make to athletes' equipment and clothes may only make a tiny difference to their performance, but once they're added up they can mean the difference between gold and silver.</p>
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<div class="packagebacklink">Back to the <a href="http://plus.maths.org/content/ingenious-constructing-our-lives">Constructing our lives package</a></div><br clear="all"><p>Isaac Newton didn't really distinguish between science and his
other great interest, alchemy. So it's only fitting that his laws of
motion are today being used to produce gold. Not from base metals,
but from the effort of Britain's top athletes, backed by teams of
engineers who research, analyse, model and tweak to gain their
athlete the tiny advantage that can make the crucial difference.<p><a href="http://plus.maths.org/content/making-gold" target="_blank">read more</a></p>http://plus.maths.org/content/making-gold#commentsaerodynamicscomputer programmingcomputer simulationengineeringfinite elementsmathematical modellingmathematics in sportNewtonian mechanicsolympicsFri, 01 Apr 2011 09:00:00 +0000mf3445459 at http://plus.maths.org/contentMaths on a plane
http://plus.maths.org/content/maths-plane
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Phil Trinh </div>
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<b>Phil Trinh</b> discovers how maths helps solve the mysteries of flight and love. </div>
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<div class="pub_date">June 2008</div>
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<p><i>This article is the winner of the university student category of the <a href="/issue47/winners.html#schools">Plus new writers award 2008</a>.</i></p><p><a href="http://plus.maths.org/content/maths-plane" target="_blank">read more</a></p>http://plus.maths.org/content/maths-plane#commentsaerodynamicsnavier-stokes equationsNewtonian mechanicsPlus new writers award 2008Sat, 31 May 2008 23:00:00 +0000plusadmin2338 at http://plus.maths.org/contentMaths and climate change: the melting Arctic
http://plus.maths.org/content/maths-and-climate-change-melting-arctic
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Marianne Freiberger </div>
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The Arctic ice cap is melting fast and the consequences are grim. Mathematical modelling is key to predicting how much longer the ice will be around and assessing the impact of an ice free Arctic on the rest of the planet. <i>Plus</i> spoke to <b>Peter Wadhams</b> from the Polar Ocean Physics Group at the University of Cambridge to get a glimpse of the group's work. </div>
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<p>The Arctic ice cap is in trouble. Due to global warming, summer sea ice cover has been disappearing at approximately 70,000 km<sup>2</sup> per year, an area the size of Scotland. Measurements from submarines indicate that the ice has grown thinner by at least 40% over the last two decades. Predictions of if and when the permanent ice will disappear from the Arctic vary widely, but few models
give it longer than 100 years and many predict that a total melt-down of the Arctic will occur within our lifetimes.</p><p><a href="http://plus.maths.org/content/maths-and-climate-change-melting-arctic" target="_blank">read more</a></p>http://plus.maths.org/content/maths-and-climate-change-melting-arctic#comments46accelerationCMSCoriolis forcedifferential equationmathematical modellingmathematics and climate changemathematics and the environmentNewtonian mechanicsstefan problemvectorSat, 01 Mar 2008 00:00:00 +0000plusadmin2326 at http://plus.maths.org/content101 uses of a quadratic equation: Part II
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Chris Budd and Chris Sangwin </div>
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In issue 29 of <i>Plus</i>, we heard how a simple mathematical equation became the subject of a debate in the UK parliament. <b>Chris Budd</b> and <b>Chris Sangwin</b> continue the story of the mighty quadratic equation. </div>
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<div class="pub_date">May 2004</div>
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<p><i>In <a href="/issue29/features/quadratic/index.html">101 uses of a quadratic equation: Part I</a> in issue 29 of Plus we took a look at quadratic equations and saw how they arose naturally in various simple problems. In this second part we continue our journey. We shall soon see how the humble quadratic makes its appearance in many different and important applications.</i></p><p><a href="http://plus.maths.org/content/101-uses-quadratic-equation-part-ii" target="_blank">read more</a></p>http://plus.maths.org/content/101-uses-quadratic-equation-part-ii#comments30accelerationbernoulli equationchaosdifferential equationellipsegravitynavier-stokes equationsNewtonian mechanicsparabolapublic understanding of mathematicsquadratic equationFri, 30 Apr 2004 23:00:00 +0000plusadmin2248 at http://plus.maths.org/contentFinding order in chaos
http://plus.maths.org/content/finding-order-chaos
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Chris Budd </div>
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All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in <b>chaos</b>. </div>
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<div class="pub_date">September 2003</div>
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<h2>Can we predict the future?</h2>
<p>In general it is easy enough to predict what will happen one second into the future, harder but not impossible to predict what will happen an hour into the future, but more or less impossible to predict what will happen a year into the future.<p><a href="http://plus.maths.org/content/finding-order-chaos" target="_blank">read more</a></p>http://plus.maths.org/content/finding-order-chaos#comments26butterfly effectchaosgalileoLaplaceLorenzNewtonian mechanicspendulumperiodplanetary motionpredictionweather forecastingSun, 31 Aug 2003 23:00:00 +0000plusadmin2227 at http://plus.maths.org/contentFaster than a falling bullet...
http://plus.maths.org/content/faster-falling-bullet
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Scientists have for the first time measured the speed of gravity and tested Einstein's assumption - or have they? </div>
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<div class="pub_date">07/03/2003</div>
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<p>The idea that gravity has a speed seems strange - ever since Newton's day it has been assumed that the gravitational force of an object is felt instantaneously.<p><a href="http://plus.maths.org/content/faster-falling-bullet" target="_blank">read more</a></p>http://plus.maths.org/content/faster-falling-bullet#commentscosmologygeneral relativitygravitational lensinggravitational wavegravityNewtonian mechanicsrelativityFri, 07 Mar 2003 00:00:00 +0000plusadmin2728 at http://plus.maths.org/contentHeavenly choreography
http://plus.maths.org/content/heavenly-choreography
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<p>When heavenly bodies such as stars and planets attract each other by means of gravity, what are the possible effects on their motion? In general this is an insoluble problem, even though the equations of gravity were described by Sir Isaac Newton three centuries ago. But one new possibility has recently been discovered by mathematicians Richard Montgomery and Alain Chenciner.</p><p><a href="http://plus.maths.org/content/heavenly-choreography" target="_blank">read more</a></p>http://plus.maths.org/content/heavenly-choreography#commentsLagrangian systemNewtonian mechanicsplanetary orbitthree body problemMon, 30 Apr 2001 23:00:00 +0000plusadmin2788 at http://plus.maths.org/contentAll about asteroids
http://plus.maths.org/content/all-about-asteroids
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<blockquote><i>"A long time ago I heard a story that stars are the remains of a tribe of evil deities banished by the sun goddess."</i>
<p align="right"><i>from "Murasaki", by Lisa Dalby</i></p><p><a href="http://plus.maths.org/content/all-about-asteroids" target="_blank">read more</a></p>http://plus.maths.org/content/all-about-asteroids#commentsasteroidasteroid collisionmeteoriteNewtonian mechanicsspace explorationThu, 01 Mar 2001 00:00:00 +0000plusadmin2791 at http://plus.maths.org/content