Session 1 - Units and Dimensional Analysis

Session 1 - Units and Dimensional Analysis - Module 1:...

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Module 1: Units and Significant Figures 1.1 The Speed of Light When we observe and measure phenomena in the world, we try to assign numbers to the physical quantities with as much accuracy as we can possibly obtain from our measuring equipment. For example, we may want to determine the speed of light, which we can calculate by dividing the distance a known ray of light propagates over its travel time, distance speed of light = . (1.1.1) time In 1983 the General Conference on Weights and Measures defined the speed of light to be c = 299, 792, 458 meters/second . (1.1.2) This number was chosen to correspond to the most accurately measured value of the speed of light and is well within the experimental uncertainty. 1.2 International System of System of Units The three quantities – time, length, and the speed of light – are directly intertwined. Which quantities should we consider as “base” and which ones as “derived” from the base quantities? For example, are length and time base quantities while speed is a derived quantity? This question is answered by convention. The basic system of units used throughout science and technology today is the internationally accepted Système International (SI). It consists of seven base quantities and their corresponding base units: Mechanics is based on just the first three of these quantities, the MKS or meter- kilogram-second system. An alternative metric system to this, still widely used, is the so- called CGS system (centimeter-gram-second). So far as distance and time measurements are concerned, there is also wide use of British Imperial units (especially in the USA) based on the foot (ft), the mile (mi), etc., as units of length, and also making use of the minute, hour, day and year as units of time.
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Base Quantity Base Unit Length meter (m) Mass kilogram (kg) Time second (s) Electric Current ampere (A) Temperature Kelvin (K) Amount of Substance mole (mol) Luminous Intensity candela (cd) We shall refer to the dimension of the base quantity by the quantity itself, for example dim length ! length ! L, dim mass ! mass ! M, dim time ! time ! T. (1.2.1) 1.3 The Atomic Clock and the Definition of the Second Isaac Newton, in the Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), distinguished between time as duration and an absolute concept of time, “Absolute true and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year. ” 1 .
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Session 1 - Units and Dimensional Analysis - Module 1:...

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