International System of Units - Wikipedia
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Summer 2018 Astron 9 Week 2 FINAL
ORDER OF MAGNITUDE PHYSICS RICHARD ANANTUA, JEFFREY FUNG AND JING LUAN WEEK 2: FUNDAMENTAL INTERACTIONS, NUCLEAR AND ATOMIC PHYSICS REVIEW OF BASICS • Units • Systems include SI and cgs • Dimensional analysis must confirm units on both sides of an equation match • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'. UNITS REVIEW – BASE UNITS • Physical quantities may be expressed using several choices of units • Unit systems express physical quantities in terms of base units or combinations thereof Quantity SI (mks) Gaussian (cgs) Imperial Length Meter (m) Centimeter (cm) Foot (ft) Mass Kilogram (kg) Gram (g) Pound (lb) Time Second (s) Second (s) Second (s) Temperature Kelvin (K) Kelvin (K)* Farenheit (ºF) Luminous intensity Candela (cd) Candela (cd)* Amount Mole (mol) Mole (mol)* Current Ampere (A) * Sometimes not considered a base cgs unit REVIEW – DERIVED UNITS • Units may be derived from others Quantity SI cgs Momentum kg m s-1 g cm s-1 Force Newton N=kg m s-2 dyne dyn=g cm s-2 Energy Joule J=kg m2 s-2 erg=g cm2 s-2 Power Watt J=kg m2 s-3 erg/s=g cm2 s-3 Pressure Pascal Pa=kg m-1 s-2 barye Ba=g cm-1 s-2 • Some unit systems differ in which units are considered fundamental Electrostatic Units SI (mks) Gaussian cgs Charge A s (cm3 g s-2)1/2 Current A (cm3 g s-4)1/2 REVIEW – UNITS • The cgs system for electrostatics is based on the assumptions kE=1, kM =2kE/c2 • EXERCISE: Given the Gaussian cgs unit of force is g cm s-2, what is the electrostatic unit of charge? # 2 ! = ⟹ # = ! & 2 )/+ = g cm/ s1+ )/+ [&]2 REVIEW – BUCKINGHAM’S PI THEOREM • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'. -
Db Math Marco Zennaro Ermanno Pietrosemoli Goals
dB Math Marco Zennaro Ermanno Pietrosemoli Goals ‣ Electromagnetic waves carry power measured in milliwatts. ‣ Decibels (dB) use a relative logarithmic relationship to reduce multiplication to simple addition. ‣ You can simplify common radio calculations by using dBm instead of mW, and dB to represent variations of power. ‣ It is simpler to solve radio calculations in your head by using dB. 2 Power ‣ Any electromagnetic wave carries energy - we can feel that when we enjoy (or suffer from) the warmth of the sun. The amount of energy received in a certain amount of time is called power. ‣ The electric field is measured in V/m (volts per meter), the power contained within it is proportional to the square of the electric field: 2 P ~ E ‣ The unit of power is the watt (W). For wireless work, the milliwatt (mW) is usually a more convenient unit. 3 Gain and Loss ‣ If the amplitude of an electromagnetic wave increases, its power increases. This increase in power is called a gain. ‣ If the amplitude decreases, its power decreases. This decrease in power is called a loss. ‣ When designing communication links, you try to maximize the gains while minimizing any losses. 4 Intro to dB ‣ Decibels are a relative measurement unit unlike the absolute measurement of milliwatts. ‣ The decibel (dB) is 10 times the decimal logarithm of the ratio between two values of a variable. The calculation of decibels uses a logarithm to allow very large or very small relations to be represented with a conveniently small number. ‣ On the logarithmic scale, the reference cannot be zero because the log of zero does not exist! 5 Why do we use dB? ‣ Power does not fade in a linear manner, but inversely as the square of the distance. -
Quantity Symbol Value One Astronomical Unit 1 AU 1.50 × 10
Quantity Symbol Value One Astronomical Unit 1 AU 1:50 × 1011 m Speed of Light c 3:0 × 108 m=s One parsec 1 pc 3.26 Light Years One year 1 y ' π × 107 s One Light Year 1 ly 9:5 × 1015 m 6 Radius of Earth RE 6:4 × 10 m Radius of Sun R 6:95 × 108 m Gravitational Constant G 6:67 × 10−11m3=(kg s3) Part I. 1. Describe qualitatively the funny way that the planets move in the sky relative to the stars. Give a qualitative explanation as to why they move this way. 2. Draw a set of pictures approximately to scale showing the sun, the earth, the moon, α-centauri, and the milky way and the spacing between these objects. Give an ap- proximate size for all the objects you draw (for example example next to the moon put Rmoon ∼ 1700 km) and the distances between the objects that you draw. Indicate many times is one picture magnified relative to another. Important: More important than the size of these objects is the relative distance between these objects. Thus for instance you may wish to show the sun and the earth on the same graph, with the circles for the sun and the earth having the correct ratios relative to to the spacing between the sun and the earth. 3. A common unit of distance in Astronomy is a parsec. 1 pc ' 3:1 × 1016m ' 3:3 ly (a) Explain how such a curious unit of measure came to be defined. Why is it called parsec? (b) What is the distance to the nearest stars and how was this distance measured? 4. -
Varying Constants, Gravitation and Cosmology
Varying constants, Gravitation and Cosmology Jean-Philippe Uzan Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa). email: [email protected] http//www2.iap.fr/users/uzan/ September 29, 2010 Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to mat- ter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local posi- tion invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pul- sar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we arXiv:1009.5514v1 [astro-ph.CO] 28 Sep 2010 describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of differ- ent constants. -
Units, Conversations, and Scaling Giving Numbers Meaning and Context Author: Meagan White; Sean S
Units, Conversations, and Scaling Giving numbers meaning and context Author: Meagan White; Sean S. Lindsay Version 1.3 created August 2019 Learning Goals In this lab, students will • Learn about the metric system • Learn about the units used in science and astronomy • Learn about the units used to measure angles • Learn the two sky coordinate systems used by astronomers • Learn how to perform unit conversions • Learn how to use a spreadsheet for repeated calculations • Measure lengths to collect data used in next week’s lab: Scienctific Measurement Materials • Calculator • Microsoft Excel • String as a crude length measurement tool Pre-lab Questions 1. What is the celestial analog of latitude and longitude? 2. What quantity do the following metric prefixes indicate: Giga-, Mega-, kilo-, centi-, milli-, µicro-, and nano? 3. How many degrees is a Right Ascension “hour”; How many degrees are in an arcmin? Arcsec? 4. Use the “train-track” method to convert 20 ft to inches. 1. Background In any science class, including astronomy, there are important skills and concepts that students will need to use and understand before engaging in experiments and other lab exercises. A broad list of fundamental skills developed in today’s exercise includes: • Scientific units used throughout the international science community, as well as units specific to astronomy. • Unit conversion methods to convert between units for calculations, communication, and conceptualization. • Angular measurements and their use in astronomy. How they are measured, and the angular measurements specific to astronomy. This is important for astronomers coordinate systems, i.e., equatorial coordinates on the celestial sphere. • Familiarity with spreadsheet programs, such as Microsoft Excel, Google Sheets, or OpenOffice. -
The Avogadro Constant to Be Equal to Exactly 6.02214X×10 23 When It Is Expressed in the Unit Mol −1
[august, 2011] redefinition of the mole and the new system of units zoltan mester It is as easy to count atomies as to resolve the propositions of a lover.. As You Like It William Shakespeare 1564-1616 Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States and Venezuela 1875 -May 20 1875, BIPM, CGPM and the CIPM was established, and a three- dimensional mechanical unit system was setup with the base units metre, kilogram, and second. -1901 Giorgi showed that it is possible to combine the mechanical units of this metre–kilogram–second system with the practical electric units to form a single coherent four-dimensional system -In 1921 Consultative Committee for Electricity (CCE, now CCEM) -by the 7th CGPM in 1927. The CCE to proposed, in 1939, the adoption of a four-dimensional system based on the metre, kilogram, second, and ampere, the MKSA system, a proposal approved by the ClPM in 1946. -In 1954, the 10th CGPM, the introduction of the ampere, the kelvin and the candela as base units -in 1960, 11th CGPM gave the name International System of Units, with the abbreviation SI. -in 1970, the 14 th CGMP introduced mole as a unit of amount of substance to the SI 1960 Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Much improved atomic weight estimates, oxygen = 100 . Jöns Jacob Berzelius (1779–1848) Further improved atomic weight estimates . -
On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics. -
Decibels, Phons, and Sones
Decibels, Phons, and Sones The rate at which sound energy reaches a Table 1: deciBel Ratings of Several Sounds given cross-sectional area is known as the Sound Source Intensity deciBel sound intensity. There is an abnormally Weakest Sound Heard 1 x 10-12 W/m2 0.0 large range of intensities over which Rustling Leaves 1 x 10-11 W/m2 10.0 humans can hear. Given the large range, it Quiet Library 1 x 10-9 W/m2 30.0 is common to express the sound intensity Average Home 1 x 10-7 W/m2 50.0 using a logarithmic scale known as the Normal Conversation 1 x 10-6 W/m2 60.0 decibel scale. By measuring the intensity -4 2 level of a given sound with a meter, the Phone Dial Tone 1 x 10 W/m 80.0 -3 2 deciBel rating can be determined. Truck Traffic 1 x 10 W/m 90.0 Intensity values and decibel ratings for Chainsaw, 1 m away 1 x 10-1 W/m2 110.0 several sound sources listed in Table 1. The decibel scale and the intensity values it is based on is an objective measure of a sound. While intensities and deciBels (dB) are measurable, the loudness of a sound is subjective. Sound loudness varies from person to person. Furthermore, sounds with equal intensities but different frequencies are perceived by the same person to have unequal loudness. For instance, a 60 dB sound with a frequency of 1000 Hz sounds louder than a 60 dB sound with a frequency of 500 Hz. -
Page 1 of 29 Dalton Transactions
Dalton Transactions Accepted Manuscript This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. www.rsc.org/dalton Page 1 of 29 Dalton Transactions Core-level photoemission spectra of Mo 0.3 Cu 0.7 Sr 2ErCu 2Oy, a superconducting perovskite derivative. Unconventional structure/property relations a, b b b a Sourav Marik , Christine Labrugere , O.Toulemonde , Emilio Morán , M. A. Alario- Manuscript Franco a,* aDpto. Química Inorgánica, Facultad de CC.Químicas, Universidad Complutense de Madrid, 28040- Madrid (Spain) bCNRS, Université de Bordeaux, ICMCB, 87 avenue du Dr. A. Schweitzer, Pessac, F-33608, France -
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. -
Topic 0991 Electrochemical Units Electric Current the SI Base
Topic 0991 Electrochemical Units Electric Current The SI base electrical unit is the AMPERE which is that constant electric current which if maintained in two straight parallel conductors of infinite length and of negligible circular cross section and placed a metre apart in a vacuum would produce between these conductors a force equal to 2 x 10-7 newton per metre length. It is interesting to note that definition of the Ampere involves a derived SI unit, the newton. Except in certain specialised applications, electric currents of the order ‘amperes’ are rare. Starter motors in cars require for a short time a current of several amperes. When a current of one ampere passes through a wire about 6.2 x 1018 electrons pass a given point in one second [1,2]. The coulomb (symbol C) is the electric charge which passes through an electrical conductor when an electric current of one A flows for one second. Thus [C] = [A s] (a) Electric Potential In order to pass an electric current thorough an electrical conductor a difference in electric potential must exist across the electrical conductor. If the energy expended by a flow of one ampere for one second equals one Joule the electric potential difference across the electrical conductor is one volt [3]. Electrical Resistance and Conductance If the electric potential difference across an electrical conductor is one volt when the electrical current is one ampere, the electrical resistance is one ohm, symbol Ω [4]. The inverse of electrical resistance , the conductance, is measured using the unit siemens, symbol [S]. -
Mercury Barometers and Manometers
NBS MONOGRAPH 8 Mercuiy Barometers and Manometers U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical problems; in- vention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Research projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's work take the form of either actual equipment and devices or pub- lished papers. These papers appear either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bureau itself publishes three periodicals available from the Government Printing Office: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio communications throughout the world.