Author Proof Units & Symbols

Total Page：16

File Type：pdf, Size：1020Kb

Unit Symbol Unit Symbol Unit Symbol Ampere A Henry H Ohm Ω Ampere per Meter A/m Henry per Meter H/m Pascal Pa Ampere per Square Meter A/m2 Hertz Hz Pascal Second Pa·s Ångström Å Hour h Peta P Are (Area) a Joule J Pico p Astronomical Unit ua Joule per Cubic Meter J/m3 Rad rad Atto a Joule per Kelvin J/K Radian rad Bar bar Joule per Kilogram J/kg Radian per Second rad/s Barn b Joule per Kilogram Kelvin J/(kg·K) Radian per Second Squared rad/s2 Becquerel Bq Joule per Mole J/mol Reciprocal Meter m-1 Bel B Joule per Mole Kelvin J/(mol·K) Rem rem Candela cd Katal kat Roentgen R Candela per Square Meter cd/m2 Katal per Cubic Meter kat/m3 Second s Centi c Kelvin K Second (Angle) ″ Coulomb C Kilo k Siemens S Coulomb per Cubic Meter C/m3 Kilogram per Cubic Meter kg/m3 Sievert Sv Coulomb per Kilogram C/kg Kilogram kg Square Meter m2 Coulomb per Square Meter C/m2 Liter L Steradian sr Cubic Meter m3 Lumen lm Tera T Cubic Meter per Kilogram m3/kg Lux lx Tesla T Curie Ci Mega M Unified Atomic Mass Unit u Day d Meter m Volt V Deci d Meter per Second m/s Volt per Meter V/m Degree (Angle) ° Meter per Second Squared m/s2 Watt W Degree Celsius °C Metric Ton t Watt per Meter Kelvin W/(m·K) Deka da Micro µ Watt per Square Meter W/m2 Electronvolt eV Milli m Watt per Square Meter Steradian W/(m2·sr) Exa E Minute (Angle) ′ Watt per Steradian W/sr Farad F Minute (Time) min Weber Wb Farad per Meter F/m Mole mol Yocto y Femto f Mole per Cubic Meter mol/m3 Yotta Y Giga G Nano n Zepto z Gray Gy Neper Np Zetta Z Gray per Second Gy/s Newton N Hecto h Hectare ha Newton Meter N·m Newton per Meter N/m.

Copy Link

Recommended publications

An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant
An atomic physics perspective on the new kilogram defined by Planck’s constant (Wolfgang Ketterle and Alan O. Jamison, MIT) (Manuscript submitted to Physics Today) On May 20, the kilogram will no longer be defined by the artefact in Paris, but through the definition1 of Planck’s constant h=6.626 070 15*10-34 kg m2/s. This is the result of advances in metrology: The best two measurements of h, the Watt balance and the silicon spheres, have now reached an accuracy similar to the mass drift of the ur-kilogram in Paris over 130 years. At this point, the General Conference on Weights and Measures decided to use the precisely measured numerical value of h as the definition of h, which then defines the unit of the kilogram. But how can we now explain in simple terms what exactly one kilogram is? How do fixed numerical values of h, the speed of light c and the Cs hyperfine frequency νCs define the kilogram? In this article we give a simple conceptual picture of the new kilogram and relate it to the practical realizations of the kilogram. A similar change occurred in 1983 for the definition of the meter when the speed of light was defined to be 299 792 458 m/s. Since the second was the time required for 9 192 631 770 oscillations of hyperfine radiation from a cesium atom, defining the speed of light defined the meter as the distance travelled by light in 1/9192631770 of a second, or equivalently, as 9192631770/299792458 times the wavelength of the cesium hyperfine radiation.
[Show full text]
Lord Kelvin and the Age of the Earth.Pdf
ME201/MTH281/ME400/CHE400 Lord Kelvin and the Age of the Earth Lord Kelvin (1824 - 1907) 1. About Lord Kelvin Lord Kelvin was born William Thomson in Belfast Ireland in 1824. He attended Glasgow University from the age of 10, and later took his BA at Cambridge. He was appointed Professor of Natural Philosophy at Glasgow in 1846, a position he retained the rest of his life. He worked on a broad range of topics in physics, including thermody- namics, electricity and magnetism, hydrodynamics, atomic physics, and earth science. He also had a strong interest in practical problems, and in 1866 he was knighted for his work on the transtlantic cable. In 1892 he became Baron Kelvin, and this name survives as the name of the absolute temperature scale which he proposed in 1848. During his long career, Kelvin published more than 600 papers. He was elected to the Royal Society in 1851, and served as president of that organization from 1890 to 1895. The information in this section and the picture above were taken from a very useful web site called the MacTu- tor History of Mathematics Archive, sponsored by St. Andrews University. The web address is http://www-history.mcs.st-and.ac.uk/~history/ 2 kelvin.nb 2. The Age of the Earth The earth shows it age in many ways. Some techniques for estimating this age require us to observe the present state of a time-dependent process, and from that observation infer the time at which the process started. If we believe that the process started when the earth was formed, we get an estimate of the earth's age.
[Show full text]
Linear and Angular Velocity Examples
Linear and Angular Velocity Examples Example 1 Determine the angular displacement in radians of 6.5 revolutions. Round to the nearest tenth. Each revolution equals 2 radians. For 6.5 revolutions, the number of radians is 6.5 2 or 13 . 13 radians equals about 40.8 radians. Example 2 Determine the angular velocity if 4.8 revolutions are completed in 4 seconds. Round to the nearest tenth. The angular displacement is 4.8 2 or 9.6 radians. = t 9.6 = = 9.6 , t = 4 4 7.539822369 Use a calculator. The angular velocity is about 7.5 radians per second. Example 3 AMUSEMENT PARK Jack climbs on a horse that is 12 feet from the center of a merry-go-round. 1 The merry-go-round makes 3 rotations per minute. Determine Jack’s angular velocity in radians 4 per second. Round to the nearest hundredth. 1 The merry-go-round makes 3 or 3.25 revolutions per minute. Convert revolutions per minute to radians 4 per second. 3.25 revolutions 1 minute 2 radians 0.3403392041 radian per second 1 minute 60 seconds 1 revolution Jack has an angular velocity of about 0.34 radian per second. Example 4 Determine the linear velocity of a point rotating at an angular velocity of 12 radians per second at a distance of 8 centimeters from the center of the rotating object. Round to the nearest tenth. v = r v = (8)(12 ) r = 8, = 12 v 301.5928947 Use a calculator. The linear velocity is about 301.6 centimeters per second.
[Show full text]
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.
[Show full text]
Measuring in Metric Units BEFORE Now WHY? You Used Metric Units
Measuring in Metric Units BEFORE Now WHY? You used metric units. You’ll measure and estimate So you can estimate the mass using metric units. of a bike, as in Ex. 20. Themetric system is a decimal system of measurement. The metric Word Watch system has units for length, mass, and capacity. metric system, p. 80 Length Themeter (m) is the basic unit of length in the metric system. length: meter, millimeter, centimeter, kilometer, Three other metric units of length are themillimeter (mm) , p. 80 centimeter (cm) , andkilometer (km) . mass: gram, milligram, kilogram, p. 81 You can use the following benchmarks to estimate length. capacity: liter, milliliter, kiloliter, p. 82 1 millimeter 1 centimeter 1 meter thickness of width of a large height of the a dime paper clip back of a chair 1 kilometer combined length of 9 football fields EXAMPLE 1 Using Metric Units of Length Estimate the length of the bandage by imagining paper clips laid next to it. Then measure the bandage with a metric ruler to check your estimate. 1 Estimate using paper clips. About 5 large paper clips fit next to the bandage, so it is about 5 centimeters long. ch O at ut! W 2 Measure using a ruler. A typical metric ruler allows you to measure Each centimeter is divided only to the nearest tenth of into tenths, so the bandage cm 12345 a centimeter. is 4.8 centimeters long. 80 Chapter 2 Decimal Operations Mass Mass is the amount of matter that an object has. The gram (g) is the basic metric unit of mass.
[Show full text]
The Equation of Radiative Transfer How Does the Intensity of Radiation Change in the Presence of Emission and / Or Absorption?
The equation of radiative transfer How does the intensity of radiation change in the presence of emission and / or absorption? Definition of solid angle and steradian Sphere radius r - area of a patch dS on the surface is: dS = rdq ¥ rsinqdf ≡ r2dW q dS dW is the solid angle subtended by the area dS at the center of the † sphere. Unit of solid angle is the steradian. 4p steradians cover whole sphere. ASTR 3730: Fall 2003 Definition of the specific intensity Construct an area dA normal to a light ray, and consider all the rays that pass through dA whose directions lie within a small solid angle dW. Solid angle dW dA The amount of energy passing through dA and into dW in time dt in frequency range dn is: dE = In dAdtdndW Specific intensity of the radiation. † ASTR 3730: Fall 2003 Compare with definition of the flux: specific intensity is very similar except it depends upon direction and frequency as well as location. Units of specific intensity are: erg s-1 cm-2 Hz-1 steradian-1 Same as Fn Another, more intuitive name for the specific intensity is brightness. ASTR 3730: Fall 2003 Simple relation between the flux and the specific intensity: Consider a small area dA, with light rays passing through it at all angles to the normal to the surface n: n o In If q = 90 , then light rays in that direction contribute zero net flux through area dA. q For rays at angle q, foreshortening reduces the effective area by a factor of cos(q).
[Show full text]
UNITS This Appendix Explains Some of the Abbreviations1•2 Used For
APPENDIX: UNITS This appendix explains some of the abbreviations1•2 used for units in this book and gives conversion factors to SI units and atomic units: length 1 a0 = 1 bohr = 0.5291771 X 10-10 m 1 A= 1 Angstrom= lo-10 m = 1.889727 ao mass 1 me = 1 atomic unit of mass = mass of an electron 9.109534 X 10-31 kg = 5.485803 X 10-4 U 1 u 1 universal atomic mass unit = one twelfth the mass of a 12c atom 1.6605655 x lo-27 kg = 1822.887 me time 1 t Eh 1 = 1 atomic unit of time = 2.418884 x l0-17 s 1 s = 1 second = 4.134137 x 1016 t/Eh temperature 1 K = 1 Kelvin amount of substance 1 mol = 1 mole 6.022045 x 1023 atoms, molecules, or formula units energy 1 cm-1 = 1 wavenumber 1 kayser 1.986477 x lo-23 J 4.556335 x 10-6 Eh 857 858 APPENDIX: UNITS 1 kcal/mol = 1 kilocalorie per mole 4.184 kJ/mol = 1.593601 x 10-3 Eh 1 eV 1 electron volt = 1.602189 x lo-19 J 3.674902 X 10-2 Eh 1 Eh 1 hartree = 4.359814 x lo-18 J Since so many different energy units are used in the book, it is helpful to have a conversion table. Such a table was calculated from the recommended values of Cohen and Taylor3 for the physical censtants and is given in Table 1. REFERENCES 1. "Standard for Metric Practice", American Society for Testing and Materials, Philadelphia (1976).
[Show full text]
Relationships of the SI Derived Units with Special Names and Symbols and the SI Base Units
Relationships of the SI derived units with special names and symbols and the SI base units Derived units SI BASE UNITS without special SI DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS names Solid lines indicate multiplication, broken lines indicate division kilogram kg newton (kg·m/s2) pascal (N/m2) gray (J/kg) sievert (J/kg) 3 N Pa Gy Sv MASS m FORCE PRESSURE, ABSORBED DOSE VOLUME STRESS DOSE EQUIVALENT meter m 2 m joule (N·m) watt (J/s) becquerel (1/s) hertz (1/s) LENGTH J W Bq Hz AREA ENERGY, WORK, POWER, ACTIVITY FREQUENCY second QUANTITY OF HEAT HEAT FLOW RATE (OF A RADIONUCLIDE) s m/s TIME VELOCITY katal (mol/s) weber (V·s) henry (Wb/A) tesla (Wb/m2) kat Wb H T 2 mole m/s CATALYTIC MAGNETIC INDUCTANCE MAGNETIC mol ACTIVITY FLUX FLUX DENSITY ACCELERATION AMOUNT OF SUBSTANCE coulomb (A·s) volt (W/A) C V ampere A ELECTRIC POTENTIAL, CHARGE ELECTROMOTIVE ELECTRIC CURRENT FORCE degree (K) farad (C/V) ohm (V/A) siemens (1/W) kelvin Celsius °C F W S K CELSIUS CAPACITANCE RESISTANCE CONDUCTANCE THERMODYNAMIC TEMPERATURE TEMPERATURE t/°C = T /K – 273.15 candela 2 steradian radian cd lux (lm/m ) lumen (cd·sr) 2 2 (m/m = 1) lx lm sr (m /m = 1) rad LUMINOUS INTENSITY ILLUMINANCE LUMINOUS SOLID ANGLE PLANE ANGLE FLUX The diagram above shows graphically how the 22 SI derived units with special names and symbols are related to the seven SI base units. In the ﬁrst column, the symbols of the SI base units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the associated base quantity shown in italic type below the rectangle.
[Show full text]
The Kelvin and Temperature Measurements
Volume 106, Number 1, January–February 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 105–149 (2001)] The Kelvin and Temperature Measurements Volume 106 Number 1 January–February 2001 B. W. Mangum, G. T. Furukawa, The International Temperature Scale of are available to the thermometry commu- K. G. Kreider, C. W. Meyer, D. C. 1990 (ITS-90) is defined from 0.65 K nity are described. Part II of the paper Ripple, G. F. Strouse, W. L. Tew, upwards to the highest temperature measur- describes the realization of temperature able by spectral radiation thermometry, above 1234.93 K for which the ITS-90 is M. R. Moldover, B. Carol Johnson, the radiation thermometry being based on defined in terms of the calibration of spec- H. W. Yoon, C. E. Gibson, and the Planck radiation law. When it was troradiometers using reference blackbody R. D. Saunders developed, the ITS-90 represented thermo- sources that are at the temperature of the dynamic temperatures as closely as pos- equilibrium liquid-solid phase transition National Institute of Standards and sible. Part I of this paper describes the real- of pure silver, gold, or copper. The realiza- Technology, ization of contact thermometry up to tion of temperature from absolute spec- 1234.93 K, the temperature range in which tral or total radiometry over the tempera- Gaithersburg, MD 20899-0001 the ITS-90 is defined in terms of calibra- ture range from about 60 K to 3000 K is [email protected] tion of thermometers at 15 fixed points and also described.
[Show full text]
TECHNICAL Nbte D-626
NASA TN D-626 LIBRARY COPY NOV 16 1960 SPACE FLIGHT LANGLEY FIELD, VIRGINIA t TECHNICAL NbTE D-626 SATELLITE ATTDUDE CONTROL USING A COMBINATION OF INERTIA WHEELS AND A BAR MAGNET By James J. Adams and Roy F. Brissenden Langley Research Center Langley Field, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON November 1960 . NATIONAL AERONAUTICS AND SPACE ADMINISTRATION TECHNICAL NOTE D-626 SATELLITE ATTITUDE CONTROL USING A COMBINATION OF INERTIA WHEELS AND A BAR MAGNET By James J. Adams and Roy F. Brissenden SUMMARY The use of inertia wheels to control the attitude of a satellite has currently aroused much interest. The stability of such a system has been studied in this investigation. A single-degree-of-freedom analysis indicates that a response with suitable dynamic characteristics and pre- cise control can be achieved by commanding the angular velocity of the inertia wheel with an error signal that is the sum of the attitude error, the attitude rate, and the integral of the attitude error. A digital computer was used to study the three-degree-of-freedom response to step displacements, and the results indicate that the cross-coupling effects of inertia coupling and precession coupling had no effect on system sta- bility. A study was also made of the use of a bar magnet to supplement the inertia wheels by providing a means of removing any momentum intro- duced into the system by disturbances such as aerodynamic torques. A study of a case with large aerodynamic torques, with a typical orbit, indicated that the magnet was a suitable device for supplying the essen- tial trimming force.
[Show full text]
The Kibble Balance and the Kilogram
C. R. Physique 20 (2019) 55–63 Contents lists available at ScienceDirect Comptes Rendus Physique www.sciencedirect.com The new International System of Units / Le nouveau Système international d’unités The Kibble balance and the kilogram La balance de Kibble et le kilogramme ∗ Stephan Schlamminger , Darine Haddad NIST, 100 Bureau Drive, Gaithersburg, MD 20899, USA a r t i c l e i n f o a b s t r a c t Article history: Dr. Bryan Kibble invented the watt balance in 1975 to improve the realization of the unit Available online 25 March 2019 for electrical current, the ampere. With the discovery of the Quantum Hall effect in 1980 by Dr. Klaus von Klitzing and in conjunction with the previously predicted Josephson effect, Keywords: this mechanical apparatus could be used to measure the Planck constant h. Following a Unit of mass proposal by Quinn, Mills, Williams, Taylor, and Mohr, the Kibble balance can be used to Kilogram Planck constant realize the unit of mass, the kilogram, by ﬁxing the numerical value of Planck’s constant. Kibble balance In 2017, the watt balance was renamed to the Kibble balance to honor the inventor, who Revised SI passed in 2016. This article explains the Kibble balance, its role in the redeﬁnition of the Josephson effect unit of mass, and attempts an outlook of the future. Quantum Hall effect Published by Elsevier Masson SAS on behalf of Académie des sciences. This is an open access article under the CC BY-NC-ND license Mots-clés : (http://creativecommons.org/licenses/by-nc-nd/4.0/).
[Show full text]
CHAPTER 2: Radiometric Measurements Principles REFERENCE: Remote Sensing of the Environment John R
CHAPTER 2: Radiometric Measurements Principles REFERENCE: Remote Sensing of the Environment John R. Jensen (2007) Second Edition Pearson Prentice Hall Energy-matter interactions in the atmosphere at the study area and at the remote sensor detector RADIANT ENERGY (Q): is the energy carried by a photon. Unit: Joules (J) RADIANT FLUX (Φ): is the time rate of flow of radiant energy. Unit: watts (W = J s-1) Φ = dQ = Joules = Watts dt seconds A derivative is the instantaneous rate of change of a function. RADIANT INTENSITY (I): Is a measure of the radiant flux proceeding from the source per unit solid angle in a specified direction. Unit: watts steradian-1 I = dΦ = watts dω steradian Solid Angle (ω ó Ω): Is equal to the spherical surface area (A) divided by the square of the radius (r). Unit: steradian Ω = A/r2 Radiance (L) Radiance in certain wavelengths (L)is: -the radiant flux (Φ) -per unit solid angle () -leaving an extended source area L in a given direction () Acos -per unit projected source area (A) Units: watts per meter squared per steradian (W m-2 sr -1 ) L is a function of direction, therefore the zenith and azimuth angles must be considered. The concept of radiance leaving a specific projected source area on the ground, in a specific direction, and within a specific solid angle. FIELD RADIOMETRY Lλ Radiance (L) REFLECTANCE Sample Radiation () R() = __________________ Reference Radiation () x100 = Reflectance Percent REFLECTANCE RADIANCE FLUX DENSITY Irradiance is a measure of the amount of radiant flux incident upon a surface per unit area of the surface measured in watts m-2.
[Show full text]