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WUN2K for LECTURE 19 These Are Notes Summarizing the Main Concepts You Need to Understand and Be Able to Apply
Duke University Department of Physics Physics 361 Spring Term 2020 WUN2K FOR LECTURE 19 These are notes summarizing the main concepts you need to understand and be able to apply. • Newton's Laws are valid only in inertial reference frames. However, it is often possible to treat motion in noninertial reference frames, i.e., accelerating ones. • For a frame with rectilinear acceleration A~ with respect to an inertial one, we can write the equation of motion as m~r¨ = F~ − mA~, where F~ is the force in the inertial frame, and −mA~ is the inertial force. The inertial force is a “fictitious” force: it's a quantity that one adds to the equation of motion to make it look as if Newton's second law is valid in a noninertial reference frame. • For a rotating frame: Euler's theorem says that the most general mo- tion of any body with respect to an origin is rotation about some axis through the origin. We define an axis directionu ^, a rate of rotation dθ about that axis ! = dt , and an instantaneous angular velocity ~! = !u^, with direction given by the right hand rule (fingers curl in the direction of rotation, thumb in the direction of ~!.) We'll generally use ~! to refer to the angular velocity of a body, and Ω~ to refer to the angular velocity of a noninertial, rotating reference frame. • We have for the velocity of a point at ~r on the rotating body, ~v = ~! ×~r. ~ dQ~ dQ~ ~ • Generally, for vectors Q, one can write dt = dt + ~! × Q, for S0 S0 S an inertial reference frame and S a rotating reference frame. -
Rotating Reference Frame Control of Switched Reluctance
ROTATING REFERENCE FRAME CONTROL OF SWITCHED RELUCTANCE MACHINES A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Tausif Husain August, 2013 ROTATING REFERENCE FRAME CONTROL OF SWITCHED RELUCTANCE MACHINES Tausif Husain Thesis Approved: Accepted: _____________________________ _____________________________ Advisor Department Chair Dr. Yilmaz Sozer Dr. J. Alexis De Abreu Garcia _____________________________ _____________________________ Committee Member Dean of the College Dr. Malik E. Elbuluk Dr. George K. Haritos _____________________________ _____________________________ Committee Member Dean of the Graduate School Dr. Tom T. Hartley Dr. George R. Newkome _____________________________ Date ii ABSTRACT A method to control switched reluctance motors (SRM) in the dq rotating frame is proposed in this thesis. The torque per phase is represented as the product of a sinusoidal inductance related term and a sinusoidal current term in the SRM controller. The SRM controller works with variables similar to those of a synchronous machine (SM) controller in dq reference frame, which allows the torque to be shared smoothly among different phases. The proposed controller provides efficient operation over the entire speed range and eliminates the need for computationally intensive sequencing algorithms. The controller achieves low torque ripple at low speeds and can apply phase advancing using a mechanism similar to the flux weakening of SM to operate at high speeds. A method of adaptive flux weakening for ensured operation over a wide speed range is also proposed. This method is developed for use with dq control of SRM but can also work in other controllers where phase advancing is required. -
Principle of Relativity and Inertial Dragging
ThePrincipleofRelativityandInertialDragging By ØyvindG.Grøn OsloUniversityCollege,Departmentofengineering,St.OlavsPl.4,0130Oslo, Norway Email: [email protected] Mach’s principle and the principle of relativity have been discussed by H. I. HartmanandC.Nissim-Sabatinthisjournal.Severalphenomenaweresaidtoviolate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenonofinertialdraggingbeeninvoked,andnocalculationhavebeenoffered byeithersidetosubstantiatetheirclaims.HereIdiscussthepossiblevalidityofthe principleofrelativityforrotatingmotionwithinthecontextofthegeneraltheoryof relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculationstodemonstratehowthesepointscomeoutasconsequencesofthegeneral theoryofrelativity. 1 1.Introduction H. I. Hartman and C. Nissim-Sabat 1 have argued that “one cannot ascribe all pertinentobservationssolelytorelativemotionbetweenasystemandtheuniverse”. They consider an UR-scenario in which a bucket with water is atrest in a rotating universe,andaBR-scenariowherethebucketrotatesinanon-rotatinguniverseand givefiveexamplestoshowthatthesesituationsarenotphysicallyequivalent,i.e.that theprincipleofrelativityisnotvalidforrotationalmotion. When Einstein 2 presented the general theory of relativity he emphasized the importanceofthegeneralprincipleofrelativity.Inasectiontitled“TheNeedforan -
Leonhard Euler - Wikipedia, the Free Encyclopedia Page 1 of 14
Leonhard Euler - Wikipedia, the free encyclopedia Page 1 of 14 Leonhard Euler From Wikipedia, the free encyclopedia Leonhard Euler ( German pronunciation: [l]; English Leonhard Euler approximation, "Oiler" [1] 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[2] He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. [3] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is our teacher in all things," which has also been translated as "Read Portrait by Emanuel Handmann 1756(?) Euler, read Euler, he is the master of us all." [4] Born 15 April 1707 Euler was featured on the sixth series of the Swiss 10- Basel, Switzerland franc banknote and on numerous Swiss, German, and Died Russian postage stamps. The asteroid 2002 Euler was 18 September 1783 (aged 76) named in his honor. He is also commemorated by the [OS: 7 September 1783] Lutheran Church on their Calendar of Saints on 24 St. Petersburg, Russia May – he was a devout Christian (and believer in Residence Prussia, Russia biblical inerrancy) who wrote apologetics and argued Switzerland [5] forcefully against the prominent atheists of his time. -
Static Limit and Penrose Effect in Rotating Reference Frames
1 Static limit and Penrose effect in rotating reference frames A. A. Grib∗ and Yu. V. Pavlov† We show that effects similar to those for a rotating black hole arise for an observer using a uniformly rotating reference frame in a flat space-time: a surface appears such that no body can be stationary beyond this surface, while the particle energy can be either zero or negative. Beyond this surface, which is similar to the static limit for a rotating black hole, an effect similar to the Penrose effect is possible. We consider the example where one of the fragments of a particle that has decayed into two particles beyond the static limit flies into the rotating reference frame inside the static limit and has an energy greater than the original particle energy. We obtain constraints on the relative velocity of the decay products during the Penrose process in the rotating reference frame. We consider the problem of defining energy in a noninertial reference frame. For a uniformly rotating reference frame, we consider the states of particles with minimum energy and show the relation of this quantity to the radiation frequency shift of the rotating body due to the transverse Doppler effect. Keywords: rotating reference frame, negative-energy particle, Penrose effect 1. Introduction The study of relativistic effects related to rotation began immediately after the theory of relativity appeared [1], and such effects are still actively discussed in the literature [2]. The importance of studying such effects is obvious in relation to the Earth’s rotation. In [3], we compared the properties of particles in rotating reference frames in a flat space with the properties of particles in the metric of a rotating black hole. -
Jeremiah Horrocks's Lancashire
Transits of Venus: New Views of the Solar System and Galaxy Proceedings IAU Colloquium No. 196, 2004 c 2004 International Astronomical Union D.W. Kurtz, ed. doi:10.1017/S1743921305001237 Jeremiah Horrocks’s Lancashire John K. Walton Department of History, University of Central Lancashire, Preston PR1 2HE, UK (email: [email protected]) Abstract. This paper sets Jeremiah Horrocks and Much Hoole in the context of Lancashire society on the eve of the English Civil War. It focuses on the complexities of what it was to be a “Puritan” in an environment where religious labels and conflicts mattered a great deal; it examines the economic circumstances of county and locality at the time, pointing out the extent to which (despite widespread and deep poverty) the county’s merchants were looking outwards to London, northern Europe and beyond; and it emphasizes that even in the apparently remote and rustic location of Much Hoole it was possible for Horrocks to sustain a scientific correspondence and to keep in touch with, and make his contribution to, developments on a much wider stage. This contribution is intended to complement Allan Chapman’s plenary lecture by devel- oping the local and Lancashire dimension to Jeremiah Horrocks’s astronomical activities at Much Hoole, less than three years before the outbreak of the great Civil War in 1642, which culminated in the execution of Charles I in 1649 and ushered in Britain’s only pe- riod of republican government, which lasted until the Restoration in 1660 (see Chapman 1994, to which this paper runs -
STFC Phd Studentship Allocation for 2021
STFC PHD STUDENTSHIP ALLOCATIONS FOR 2021 University Department 2021 Aberystwyth University Institute of Mathematics and Physical Sciences 1 Armagh Observatory Astronomy 1 University of Bath Department of Physics 1 Birkbeck, University of London Department of Earth and Planetary Science 0 University of Birmingham School of Physics and Astronomy 5 University of Brighton School of Computing, Engineering and 0 Mathematics University of Bristol School of Earth Sciences 1 University of Bristol School of Physics 3 Brunel University College of Engineering, Design and Physical 0 Science University of Cambridge Department of Applied Maths and Theoretical 5 Physics University of Cambridge Institute of Astronomy 6 University of Cambridge Department of Physics 4 Cardiff University School of Physics and Astronomy 4 University of Central Lancashire Jeremiah Horrocks Institute 2 City, University of London Department of Mathematics 1 University of Derby School of Computing and Engineering 0 University of Dundee Department of Mathematics 2 University of Durham Department of Mathematical Sciences 2 University of Durham Department of Physics 10 University of Edinburgh School of Mathematics 1 University of Edinburgh School of Physics and Astronomy 11 University of Exeter Mathematics 1 University of Exeter School of Physics and Astronomy 2 University of Glasgow School of Geographical and Earth Sciences 0 University of Glasgow School of Physics and Astronomy 7 Heriot Watt University School of Engineering and Physical Sciences 0 Heriot Watt University School -
Chapter 6 the Equations of Fluid Motion
Chapter 6 The equations of fluid motion In order to proceed further with our discussion of the circulation of the at- mosphere, and later the ocean, we must develop some of the underlying theory governing the motion of a fluid on the spinning Earth. A differen- tially heated, stratified fluid on a rotating planet cannot move in arbitrary paths. Indeed, there are strong constraints on its motion imparted by the angular momentum of the spinning Earth. These constraints are profoundly important in shaping the pattern of atmosphere and ocean circulation and their ability to transport properties around the globe. The laws governing the evolution of both fluids are the same and so our theoretical discussion willnotbespecifictoeitheratmosphereorocean,butcanandwillbeapplied to both. Because the properties of rotating fluids are often counter-intuitive and sometimes difficult to grasp, alongside our theoretical development we will describe and carry out laboratory experiments with a tank of water on a rotating table (Fig.6.1). Many of the laboratory experiments we make use of are simplified versions of ‘classics’ that have become cornerstones of geo- physical fluid dynamics. They are listed in Appendix 13.4. Furthermore we have chosen relatively simple experiments that, in the main, do nor require sophisticated apparatus. We encourage you to ‘have a go’ or view the atten- dant movie loops that record the experiments carried out in preparation of our text. We now begin a more formal development of the equations that govern the evolution of a fluid. A brief summary of the associated mathematical concepts, definitions and notation we employ can be found in an Appendix 13.2. -
Appendix A: Educational Resources in Astronomy
Appendix A: Educational Resources in Astronomy A.I Planetariums, Museums, and Exhibits A.I.I Planetariums and Museums in the United Kingdom England - AAC Planetarium, Amateur Astronomy Centre, Bacup Road, Clough Bank, Tod morden, Lancs. OLl4 7HW. Tel: 0706816964. - British Museum, Great Russell Street, London WC1B 3DG; Tel: 071-323 8395 ext. 395. Astronomical clocks. - British Museum (Natural History), Cromwell Road, South Kensington, London SW7 5BD; Tel: 071-938 9123. Extensive meteorite collection. - Caird Planetarium, Old Royal Observatory, Greenwich, London SE 10. - William Day Planetarium, Plymouth Polytechnic, School of Maritime Studies, Ply- mouth PL4 8AA. Tel: 0752 264666. - Electrosonic Ltd., 815 Woolwich Road, London SE7 8LT. - Greenwich Planetarium, South Building, Greenwich Park, Greenwich, London SE 10. Tel: 081-858 1167. - William Herschel House and Museum, 19 New King Street, Bath, BA1 2Bl. Con tact: Dr. A.V. Sims, 30 Meadow Park, Bathford, Bath; Tel: 0225 859529. Open Mar-Oct daily 2-5 pm, Nov-Feb Sundays only, 2-5 pm. - lodrell Bank Planetarium and Visitor Center, Lower Withington, Nr. Macclesfield, Cheshire SK11 9DL; Tel: 0477 71339. - Kings Observatory, Kew, Old Deer Park, Richmond, Surrey TW9 2AZ. - University of Leicester, The Planetarium, Department of Astronomy, University Road, Leicester LEI 7RH; Tel: 0533 522522. - Liverpool Museum Planetarium, William Brown Street, Liverpool, Merseyside L3 8EN. Tel: 051-2070001 ext. 225. - London Planetarium, Marylebone Road, London NW1 5LR; Tel: 071-486 1121 (9:30--5:30), 071-486 1121 (recording). - City of London Polytechnic, The Planetarium, 100 Minories, Tower Hill, London EC3N BY. 071-283 1030. - London Schools Planetarium, John Archer School Building, Wandsworth Rd., Sutherland Grove, London SW18; Tel: 081-788 4253. -
Classical Mechanics
Stony Brook University Academic Commons Essential Graduate Physics Department of Physics and Astronomy 2013 Part CM: Classical Mechanics Konstantin Likharev SUNY Stony Brook, [email protected] Follow this and additional works at: https://commons.library.stonybrook.edu/egp Part of the Physics Commons Recommended Citation Likharev, Konstantin, "Part CM: Classical Mechanics" (2013). Essential Graduate Physics. 2. https://commons.library.stonybrook.edu/egp/2 This Book is brought to you for free and open access by the Department of Physics and Astronomy at Academic Commons. It has been accepted for inclusion in Essential Graduate Physics by an authorized administrator of Academic Commons. For more information, please contact [email protected], [email protected]. Konstantin K. Likharev Essential Graduate Physics Lecture Notes and Problems Beta version Open online access at http://commons.library.stonybrook.edu/egp/ and https://sites.google.com/site/likharevegp/ Part CM: Classical Mechanics Last corrections: September 10, 2021 A version of this material was published in 2017 under the title Classical Mechanics: Lecture notes IOPP, Essential Advanced Physics – Volume 1, ISBN 978-0-7503-1398-8, with model solutions of the exercise problems published in 2018 under the title Classical Mechanics: Problems with solutions IOPP, Essential Advanced Physics – Volume 2, ISBN 978-0-7503-1401-5 However, by now this online version of the lecture notes and the problem solutions available from the author, have been better corrected Note also: Konstantin K. Likharev (ed.) Essential Quotes for Scientists and Engineers Springer, 2021, ISBN 978-3-030-63331-8 (see https://essentialquotes.wordpress.com/) © K. -
Kiss of the Goddess | the Economist
5/9/2016 Kiss of the goddess | The Economist Transits of Venus Kiss of the goddess Venus will soon cross the face of the sun, and astronomers around the world will have a party May 27th 2004 | From the print edition FOR about six hours on Tuesday June 8th, the sun will be fainter than usual. There is no need to panic. It will fade by a mere 0.1%. Only a diligent observer with the correct viewing equipment will notice something odd: there will be a small, dark dot on the disc of the sun, like a solitary pea on a yellow dinner plate. The pea is Venus, passing directly between Earth and the sun for the first time since 1882. Insignificant though it may seem, this rare celestial event, a “transit of Venus”, was once thought a key to understanding the universe. Two and a half centuries ago, countries dispatched astronomers on risky and expensive expeditions to observe transits from far-flung points across the globe. By doing this, they hoped to make a precise measurement of the distance to the sun and thus acquire an accurate yardstick by which the distance to everything else in the solar system could be measured. Though this quest fell short of its goal, it did produce a much better estimate of that distance. It also produced some interesting spin-offs, such as the invention of the movie camera and the discovery of Australia's Great Barrier Reef. In any case, astronomers—both professional and amateur—are eagerly awaiting the forthcoming transit so that they can commune with the shades of their predecessors. -
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Learning Outcomes in Focus Contextual strand: PW3 Students should be able to investigate patterns and relationships between physical observables. INVESTIGATE: Observe, study or make detailed and systematic examination, in order to establish facts and reach new conclusions Nature of science: NoS1 Students should be able to appreciate how scientists work and how scientific ideas are modified over time. APPRECIATE: Have a practical understanding of Learning Intentions As this activity relates to many learning outcomes, including those above, be sure to decide on the specific Learning intentions you have for your class if they are to engage with this activity. Introduction and Teacher Background Students will use a light sensor at the beginning of this activity. A light sensor is an electronic device used to detect light. They usually consist of a photoelectric cell which converts light energy into electrical energy. (You might see links to PW5 and PW6). While the unit LUX is in fact itself a derived unit (Lumen m-2), it is a measure of the light intensity as perceived by the human eye and so students will explore light intensity in lux as a physical observable and investigate its relationship to distance from a source and varied obstacles. In the second half of this activity students will try to apply what they have learned to analyse data from the NASA Kepler mission. While in the initial part of the activity variation in light intensity was achieved by allowing a pendulum to swing over and back in front of a light source, a similar pattern, including regular drops in light intensity, would also be achieved as a planet rotated around a star.