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A Learner's Guide to SI Units and Their Conversion
A Learner's Guide to SI Units and their Conversion October 2004 Workbook for students Learner's Guide to SI Units and their Conversion their and Units SI to Guide Learner's Edexcel A London Qualifications is one of the leading examining and awarding bodies in the UK and throughout the world. It incorporates all the qualifications previously awarded under the Edexcel and BTEC brand. We provide a wide range of qualifications including general (academic), vocational, occupational and specific programmes for employers. Through a network of UK and overseas offices, our centres receive the support they need to help them deliver their education and training programmes to learners. For further information please call Customer Services on 0870 240 9800, or visit our website at www.edexcel.org.uk Authorised by Jim Dobson Prepared by Sarah Harrison All the material in this publication is copyright © London Qualifications Limited 2004 CONTENTS Introduction 1 What are units? 2 Operations with units 5 Submultiple and multiple units 9 Conversion of units 11 Conversion examples and exercises 13 Length 13 Area 14 Volume 15 Mass 16 Time 17 Temperature 18 Density 19 Force 20 Stress and pressure 21 Answers to exercises 23 Introduction One of the important areas where Science and Technology students need support is in the conversion of units. This booklet is designed to be useful for students in all Science, Technology and Engineering subjects. This booklet has been produced to: S introduce students to SI base and derived units and S help students with the conversion of multiple and sub-multiple units to SI base and derived units. -
On the Covariant Representation of Integral Equations of the Electromagnetic Field
On the covariant representation of integral equations of the electromagnetic field Sergey G. Fedosin PO box 614088, Sviazeva str. 22-79, Perm, Perm Krai, Russia E-mail: [email protected] Gauss integral theorems for electric and magnetic fields, Faraday’s law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are presented in a covariant form. Covariant formulas for magnetic and electric fluxes, for electromotive force and circulation of the vector potential are provided. In particular, the electromotive force is expressed by a line integral over a closed curve, while in the integral, in addition to the vortex electric field strength, a determinant of the metric tensor also appears. Similarly, the magnetic flux is expressed by a surface integral from the product of magnetic field induction by the determinant of the metric tensor. A new physical quantity is introduced – the integral scalar potential, the rate of change of which over time determines the flux of vector potential through a closed surface. It is shown that the commonly used four-dimensional Kelvin-Stokes theorem does not allow one to deduce fully the integral laws of the electromagnetic field and in the covariant notation requires the addition of determinant of the metric tensor, besides the validity of the Kelvin-Stokes theorem is limited to the cases when determinant of metric tensor and the contour area are independent from time. This disadvantage is not present in the approach that uses the divergence theorem and equation for the dual electromagnetic field tensor. -
Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
Weberˇs Planetary Model of the Atom
Weber’s Planetary Model of the Atom Bearbeitet von Andre Koch Torres Assis, Gudrun Wolfschmidt, Karl Heinrich Wiederkehr 1. Auflage 2011. Taschenbuch. 184 S. Paperback ISBN 978 3 8424 0241 6 Format (B x L): 17 x 22 cm Weitere Fachgebiete > Physik, Astronomie > Physik Allgemein schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Weber’s Planetary Model of the Atom Figure 0.1: Wilhelm Eduard Weber (1804–1891) Foto: Gudrun Wolfschmidt in der Sternwarte in Göttingen 2 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Band 19 Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt Weber’s Planetary Model of the Atom Ed. by Gudrun Wolfschmidt Hamburg: tredition science 2011 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Hg. von Gudrun Wolfschmidt, Geschichte der Naturwissenschaften, Mathematik und Technik, Universität Hamburg – ISSN 1610-6164 Diese Reihe „Nuncius Hamburgensis“ wird gefördert von der Hans Schimank-Gedächtnisstiftung. Dieser Titel wurde inspiriert von „Sidereus Nuncius“ und von „Wandsbeker Bote“. Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt: Weber’s Planetary Model of the Atom. Ed. by Gudrun Wolfschmidt. Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, Band 19. Hamburg: tredition science 2011. Abbildung auf dem Cover vorne und Titelblatt: Wilhelm Weber (Kohlrausch, F. (Oswalds Klassiker Nr. 142) 1904, Frontispiz) Frontispiz: Wilhelm Weber (1804–1891) (Feyerabend 1933, nach S. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
2019 Redefinition of SI Base Units
2019 redefinition of SI base units A redefinition of SI base units is scheduled to come into force on 20 May 2019.[1][2] The kilogram, ampere, kelvin, and mole will then be defined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k), and the Avogadro constant (NA), respectively. The metre and candela are already defined by physical constants, subject to correction to their present definitions. The new definitions aim to improve the SI without changing the size of any units, thus ensuring continuity with existing measurements.[3][4] In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes,[5][6] which the International Committee for Weights and Measures (CIPM) had proposed earlier that year.[7]:23 The previous major change of the metric system was in 1960 when the International System of Units (SI) was formally published. The SI is a coherent system structured around seven base units whose definitions are unconstrained by that of any other unit and another twenty-two named units derived from these base units. The metre was redefined in terms of the wavelength of a spectral line of a The SI system after the 2019 redefinition: krypton-86 radiation,[Note 1] making it derivable from universal natural Dependence of base unit definitions onphysical constants with fixed numerical values and on other phenomena, but the kilogram remained defined in terms of a physical prototype, base units. leaving it the only artefact upon which the SI unit definitions depend. The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena,[8] but practical limitations necessitated the use of artefacts (the prototype metre and prototype kilogram) when the metric system was first introduced in France in 1799. -
Worksheet 2 the Metric System and SI Units
Unit Conversions Worksheet 2 The Metric System and SI Units 1 © MathTutorDVD.com Here is a helpful list of all the prefixes and their exponents and abbreviations: 109 giga G one billion 106 mega M one million 103 kilo k one thousand 102 hecto h one hundred 101 deca da ten 10-1 deci d one tenth 10-2 centi c one hundredth 10-3 milli m one thousandth 10-6 micro µ one millionth 10-9 nano n one billionth 10-12 pico p one trillionth 2 © MathTutorDVD.com 1. Give the abbreviation for each of the SI base units below. a. kilogram b. Kelvin c. meter d. second 2. State what quantities the following SI units are used to measure. a. kg b. m c. s d. K 3. Give the power of 10 that each of the following prefixes represents. a. kilo b. micro c. centi d. deca e. mega 3 © MathTutorDVD.com 4. Write the following numbers in their base units. a. 5 kilometers b. 12 centimeters c. 2 micrograms d. 4.1 megagrams 5. Write the abbreviations for the following measurements. a. 67 micrograms b. 831 kilometers c. 1.2 meters d. 791 megagrams 4 © MathTutorDVD.com 6. Express the following numbers with an appropriate SI prefix (e.g., 5,000 g = 5 kg). a. 7800 m b. 5.0 x 10-6 g c. 7.8 x 106 m d. 1.6 x 10-3 g 7. Convert the following to scientific notation using the base SI unit. a. 4.51 microseconds b. 6700 grams c. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Units and Magnitudes (Lecture Notes)
physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass. -
Vocabulary of Magnetism
TECHNotes The Vocabulary of Magnetism Symbols for key magnetic parameters continue to maximum energy point and the value of B•H at represent a challenge: they are changing and vary this point is the maximum energy product. (You by author, country and company. Here are a few may have noticed that typing the parentheses equivalent symbols for selected parameters. for (BH)MAX conveniently avoids autocorrecting Subscripts in symbols are often ignored so as to the two sequential capital letters). Units of simplify writing and typing. The subscripted letters maximum energy product are kilojoules per are sometimes capital letters to be more legible. In cubic meter, kJ/m3 (SI) and megagauss•oersted, ASTM documents, symbols are italicized. According MGOe (cgs). to NIST’s guide for the use of SI, symbols are not italicized. IEC uses italics for the main part of the • µr = µrec = µ(rec) = recoil permeability is symbol, but not for the subscripts. I have not used measured on the normal curve. It has also been italics in the following definitions. For additional called relative recoil permeability. When information the reader is directed to ASTM A340[11] referring to the corresponding slope on the and the NIST Guide to the use of SI[12]. Be sure to intrinsic curve it is called the intrinsic recoil read the latest edition of ASTM A340 as it is permeability. In the cgs-Gaussian system where undergoing continual updating to be made 1 gauss equals 1 oersted, the intrinsic recoil consistent with industry, NIST and IEC usage. equals the normal recoil minus 1. -
Introduction to Electrostatics
Introduction to Electrostatics Charles Augustin de Coulomb (1736 - 1806) December 23, 2000 Contents 1 Coulomb's Law 2 2 Electric Field 4 3 Gauss's Law 7 4 Di®erential Form of Gauss's Law 9 5 An Equation for E; the Scalar Potential 10 r £ 5.1 Conservative Potentials . 11 6 Poisson's and Laplace's Equations 13 7 Energy in the Electric Field; Capacitance; Forces 15 7.1 Conductors . 20 7.2 Forces on Charged Conductors . 22 1 8 Green's Theorem 27 8.1 Green's Theorem . 29 8.2 Applying Green's Theorem 1 . 30 8.3 Applying Green's Theorem 2 . 31 8.3.1 Greens Theorem with Dirichlet B.C. 34 8.3.2 Greens Theorem with Neumann B.C. 36 2 We shall follow the approach of Jackson, which is more or less his- torical. Thus we start with classical electrostatics, pass on to magneto- statics, add time dependence, and wind up with Maxwell's equations. These are then expressed within the framework of special relativity. The remainder of the course is devoted to a broad range of interesting and important applications. This development may be contrasted with the more formal and el- egant approach which starts from the Maxwell equations plus special relativity and then proceeds to work out electrostatics and magneto- statics - as well as everything else - as special cases. This is the method of e.g., Landau and Lifshitz, The Classical Theory of Fields. The ¯rst third of the course, i.e., Physics 707, deals with physics which should be familiar to everyone; what will perhaps not be familiar are the mathematical techniques and functions that will be introduced in order to solve certain kinds of problems. -
Magnetic Immunity of the MRAM Devices
APPLICATION NOTE AN-MEM-003 Magnetic Immunity of the MRAM Devices Table 1: Cross Reference of Applicable Products Product Name Manufacturer Part Number SMD # Device Type Internal PIC# 16Mb MRAM Device UT8MR2M8 5962-12227 01 WP01 64Mb MRAM Device UT8MR8M8 5962-13207 01 MQ09 *PIC = Product Identification Code 1.0 Overview CAES Colorado Springs offers a 16Mb and 64Mb Non-Volatile Magnetoresistive Random Access Memory (MRAM) device. The MRAM devices are designed specifically for operation in both HiRel and Space environments. This application note addresses concerns with the magnetic immunity of these devices. CAES has determined that the MRAM devices have no magnetic risk in the space environment and recommends proper handling to address terrestrial environments. 2.0 Magnetic Fields All magnetic fields are caused by electrical charge in motion. Even the fields from a stationary permanent magnet RELEASED RELEASED are the result of the rotation (quantum spin) of electrons within the material. There are two "components" of a magnetic field which are both commonly called "magnetic field." They are the B field (historically called Magnetic Induction) and the H field (historically called Magnetic Field). They are related by the equation B = H + 4pM where M is a term called "Magnetization" or "Magnetic Polarization" and is a property of the materials through which the 11 fields pass. Technically, M is the magnetic moment of the material per unit volume. To obtain the total B field, if considering the field in a volume of space, the free (unbound field) H plus the bound fields (magnetic dipoles) M / 13 must be known.