Physical Quantities And Measurement
Unit 1: Physical Quantitiesand MeasurementUnit 1: Physical Quantitiesand MeasurementUnit - 1Physical QuantitiesAnd MeasurementNature is described as a pragmaticset of rules followed by all the thingsaround us. It is something which ismuch greater than the imaginationof humans. It is observable, it issurprising but it is somehowexplainable, its architecture has beendesigned with very beautifulpatterns, strict rules but withsimplicity. A science which exploresthe nature is Physics.Students Learning Outcomes (SLOs)After learning this unit students should be able to:l Describe the crucial role of Physics in Science,Technology and Societyl List with brief description of various branchesllllllof physicsChoose a proper instrument (meter rule,Vernier calipers, screw gauge, physical balancestop watch, measuring cylinder) for themeasurement of length, diameter, mass, timeand volume in daily life activities.Interconvert the prefixes and their symbols toindicate multiple and sub-multiple for bothbase and derived unitsWrite the answer in scientific notation inmeasurements and calculationsDefine term density with S.I unitDetermine density of solids and liquidsDescribe the need of using significant figuresfor recording and stating results in laboratory.
Unit 1: Physical Quantitiesand MeasurementQuoteWhy do we study physics? Which device willyou choose to measure the length of a small cylinder?How will you determine the thickness of a piece ofwire? How will you find the volume of small stone?why ice floats while a coin sinks in the water? Afterlearning this unit you will be answer these and othersimilar questions.“No one undertakesresearch in physics with 1.1 INTRODUCTION TO PHYSICSthe intention of winningOne of the most basic and ancient science is thea prize. It is the joy ofPhysics. The word science refers to the study of a fact bydiscovering somethingcollecting information through observation, presentingno one knew before.”it in a mathematical way, justifying the idea withStephen Hawkingexperiment and finally making a conclusion about thefact. Thus physics can be defined as:Physics is the branch of science which observesthe nature represents it mathematically and concludewith the experiment.It basically deals with the behavior and structureof matter and the energy that derives the matter.Do You Know!Physics is the branch of natural science that studiesPhysics Derived from matter, its motion, its behavior through space and timeA n c i e n t G r e e k and the related entities of energy and force. Physics is‘physicos’ meaning one of the most fundamental scientific disciplines, and‘knowledge of nature’. its main goal is to understand how the universebehaves.It is a matter of fact that Physics can beconsidered as the mother of all sciences. The beauty ofphysics lies in its Laws that govern this whole universefrom an atom to large scale galaxies and in itsexperiments from home to large scale experiment labs.Physicist are categorized into two categories: those whoobserve the nature solve its mysteries with available2
Unit 1: Physical Quantitiesand Measurementand missing information, present their theories withmathematical approach. They are known as theoreticalphysicist and other are more interested to test thosetheories with experiments are known as experimentalphysicists.Since from the beginning of the universe, thestructure of universe is very straight forward, theclassification of physics was not that much easy but asthe physicist explained the universe, they classifiedPhysics into many branches. These branches show thespectrum and scope of Physics around us and helpscientist to describe ideas in a well-organized way.Fig. 1.1MechanicsThe main branches of Physics are as follows.Fig 1.2 ThermodynamicsMechanicsThis branch of physics is mainly concerned withthe laws of motion and gravitation.ThermodynamicsThermodynamics deals with heat andtemperature and their relation to energy and work.ElectricityElectricity is the study of properties of charges inrest and motionFig 1.3ElectricityMagnetismMagnetism is the study of magnetic propertiesof materialsAtomic PhysicsAtomic physics deals with the compositionstructure and properties of the atomFig 1.4 Magnetism3
Unit 1: Physical Quantitiesand MeasurementHydrogenOpticsHeliumOptics studies physical aspects of light and itsproperties with the help of optical instruments.NeonSodiumMercuryFig. 1.5 Atomic PhysicsSoundSound is the study of production, propertiesand applications of sound waves.Nuclear physicsNuclear physics deals with the constituents,structure, behavior and interactions of atomic nuclei.Particle physicsParticle Physics studies the elementaryconstituents of matter and radiation, and theinteractions between them.Fig. 1.6 OpticsAstrophysicsThe study of celestial objects with the help oflaws of physics is known as Astrophysics.Plasma physicsThe study of ionized state of mater and itsproperties is known as Plasma Physics.Fig. 1.7 SoundGeo physicsThe study of internal structure of earth is knownas Geo physics.Importance of Physics in Science Technologyand SocietySociety’s reliance on technology represents theFig. 1.8 Nuclear Physics importance of physics in daily life. Many aspects ofmodern society would not have been possible without4
Unit 1: Physical Quantitiesand Measurementthe important scientific discoveries made in the past.These discoveries became the foundation on whichcurrent technologies were developed.Discoveries such as magnetism, electricity,conductors and others made modern conveniences,such as television, computers, smart phones, medicalFig. 1.9 Particle Physicsinstruments, other business and home technologiespossible. Moreover, modern means of transportation,such as aircraft and telecommunications, have drawnpeople across the world closer together all rely onconcepts of physics.1.2 MEASURING INSTRUMENTSPhysics is much concerned with matter and Fig. 1.10 Astro Physicsenergy and the interaction between them which isexplained with the help of describing the mathematicalrelations between various physical quantities. Allphysical quantities are important for describing thenature around us. A physical quantity is a physicalproperty of a phenomenon, body, or substance that canbe quantified by measurement.A physical quantity can be expressed as thecombination of a magnitude expressed by a number –usually a real number – and a unit. Physical quantities Fig. 1.11 Plasma Physicsare classified into two categories:u Fundamental quantitiesu Derived physical quantities.Physical quantities which cannot be explainedby other physical quantities are called fundamentalphysical quantities.There are seven fundamental physical quantities andare listed in table 1.1 along with their units.5Fig. 1.12 Geo Physics
Unit 1: Physical Quantitiesand MeasurementTable 1.1 Fundamental quantities and their S.I unitsFundamental quantitiesS.I UnitSymbol of UnitmetermMassKilogramkgTimesecondsElectric tureDo You Know!Some Physicalquantities are unitless. Such as Elasticmodulus, Plane angleand solid angleDo You Know!The notion ofphysical dimensionof a physical quantitywas introduced byJoseph Fourier in1822 by convention,physical quantitiesare organized in adimensional systembuilt upon basequantities, each ofwhich is regarded ashaving its owndimension.Amount of substanceLuminous intensityPhysical quantities which are explained on thebasis of fundamental physical quantities are calledderived physical quantities.Table1.2 derived quantities and their celerationS.I Unitcubic metermeter per secondNewtonkilogram per cubic metermeter per second squareSymbol ofUnitm3m-1sNkg/m3m/s2All physical quantities are either calculatedmathematically or measured through an instrument.Scientist, Engineers, Doctors and others likeblacksmith, carpenter, and goldsmith even the workersand ordinary human's measure those physicalquantities with the help of instruments. For instance,your doctor uses a thermometer to tell your bodytemperature, a carpenter uses the inch tape to measurethe length of woods required for furniture.6
Unit 1: Physical Quantitiesand MeasurementA puncture mender uses air gauges to check theair pressure in the tyre. Similarly, a chemical engineeruses hydrometer for describing the density of a liquid.Measuring the physical quantity correctly withinstrument is not an easy task for scientist andengineers. Scientist are seriously concerned with theaccuracy of the instrument and its synchronization.Moreover, the instrument they design mostly for theirown sake of research which readably goes on tocommercial market. Many of the instruments we usetoday are inventions of pioneers of science. Usually, thebasic physical quantities that we use in our daily life aremeasured with basic and simple instruments.The Standard of LengthIf there is any measurement that has proven to bethe most useful to humanity, it is length. For examplesunits of length include the inch, foot, yard, mile,meter etc.The length is defined as the minimum distancebetween two points lying on same plane.The meter (m) is the SI unit of length and is defined as:Do You Know!Use of every instrumentis restricted by smallestmeasurement that itcan perform which iscalled least count.Do You Know!1000m 1km100cm 1m1cm 10mm1inch 2.53cm12 inch 1 ft1 yard 3ftThe length of the path traveled by light invacuum during the time interval of 1/299 792 458 of asecond.The basic measurement of length can beobtained with the help of a meter rod or an inch tape.Meter RuleA meter rule is a device which is used tomeasure length of different objects. A meter rule oflength 1m is equal to 100 centimeters (cm). On meterrule each cm is divided further in to 10 divisions which7Fig 1.13 Meter Rule
Unit 1: Physical Quantitiesand Measurementare called millimeters (mm). So, a meter rule canmeasure up to 1mm as smallest reading. It is made up ofa long rigid piece of wood or steel(Fig 1.13).The zero-end of the meter rule is first alignedwith one end of the object and the reading is takenwhere the other end of the object meets the meter rule.Vernier CaliperFig 1.14 Vernier CalipersFig 1.15 Digital verniercalipersThe Vernier Caliper is a precision instrumentthat can be used to measure internal and externaldistance extremely accurate. It has both an imperial andmetric scale. A Vernier caliper has main jaws that areused for measuring external diameter, as well assmaller jaws that are used for measuring the internaldiameter of objects. Some models also have a depthgauge. The main scale is fixed in place, while theVernier scale is the name for the sliding scale that opensand closes the jaws (Fig1.14).Reading a Vernier CaliperStep 1Step 2Place the object between the Note the main scale reading bycounting lines before the zerojaws of the Vernier caliperline of Vernier scaleVernier Scale readingMain scale reading 2.8mmVernier scale reading 0.6mmTotal reading 3.4mmMain scale readingStep 3Step 4Count the next line of Vernier scaleafter zero coinciding main scaleAdd the two readingfor total8
Unit 1: Physical Quantitiesand MeasurementCHECKING FOR ZEROERROR0Main scaleOBSERVED READING31CORRECTEDREADINGMain scale 43.14cm0 Vernierscale100Two zero markscoincideNo Zero error.00Main scalezero mark onvernier scale isslightly to the rightZero error is 0.0300Main scaleReading 3.14cm31Vernier scale1Vernier scale10Main scale 43.17cm( 0.03) 3.14cm100Vernier scale10Reading 3.17cm3(The positive zeroerror issubtracted fromreading)Main scale 43.11cm -(-0.07) 3.18cm10Vernier scaleZero mark on vernierscale is slightly to theleft. zero error of -0.07(No zero errorNo correctionrequired)0Vernier scale10(Negative zeroerror is added toReading 3.11cm the reading)Micrometer Screw GaugeScrew gauge in extensively used in engineeringfield for obtaining precision measurements.Micrometer screw gauge is used for measuringextremely small dimensions.A screw gauge can even measure dimensionssmaller than those measured by a Vernier Caliper.Micrometer Screw gauge works on the simple principleof converting small distances into larger ones by9
Unit 1: Physical Quantitiesand Measurementmeasuring the rotation of the screw. This “screw"principle facilitates reading of smaller distances on ascale after amplifying them (Fig 1.16).Reading A Micrometer Screw GaugeFig 1.16 Screw GaugeStep 1Step 2Turn the thimbleuntil the anvil andthe spindle gentlygrip the object. Thenturn the ratchet untilit starts to click.Take the main scalereading at the edge ofthe e treading 4.5mmThimble reads twelve division 0.12mmTotal reading 4.62mmStep 3Step 4Take the thimble scalereading opposite thedatum line of themain scale. Multiplythis reading with leastcount i.e., 0.01mmNow add mainscale reading tothimble reading.This will be thediameter of theobject.10
Unit 1: Physical Quantitiesand MeasurementChecking For Zero ErrorObserved reading105035302.00.000Corrected Reading0.2525452015402.25mmNo zero errorNo Correctionis requiredZero mark on thimble scalecoincides with the datum lineon the main scale and reading Reading 2.0 0.25 2.25mmon the main scale is zero.No zero error1501052.040350.073000.2525Zero on datum line can beseen.Positive Zero ErrorReading 0.07 mm(Count from Zero.)4500.022.030250.23204015Zero mark on datumline cannot be seennegative zero errorReading -0.02mm(count down from 0)The kilogram,originally defined as:The mass of one cubicdecimeter of water atthe temperature ofmaximum density.Itwas replaced after theInternational MetricConvention in 1875 bythe InternationalPrototype Kilogram.Reading 2.0 0.32 2.32mm502.32 - ( 0.07) 2.25mmDo You Know!2.23 - (-0.02) 2.25mmReading 2.0 0.23 2.23mmThe Standard Of MassThe kilogram is the SI unit of mass and is equalto the mass of the international prototype of thekilogram, a platinum-iridium standard that is kept atthe International Bureau of Weights and Measures(Fig1.17).11Fig 1.17 Kilo gram
Unit 1: Physical Quantitiesand MeasurementDo You Know!1000g 1kg1g 1000mg1g 1000000mg1g 1000000000ng1g 0.002lbFig 1.18 Physical BalanceThe kilogram is a cylinder of special metal about39 millimeters wide by 39 millimeters tall that serves asthe world's mass standard.Each country that subscribed to theInternational Metric Convention was assigned one ormore copies of the international standards; these areknown as National Prototype Meter and Kilogram.The Physical BalanceThe Physical balance is an instrument used formeasurement of mass. It is mostly used in laboratory. Itworks on the principle of moments. It consists of a lightand rigid beam of brass, a metallic pillar, a woodenbase, two pans, a metallic pointer and an ivory scale(Fig 1.18). The plumb line indicates whether the balanceis horizontal. In ideal condition the plumb line isaligned with the end of the knob fixed with the pillar.When the beam is horizontal the pointer remains onzero mark on the ivory scale. The whole box hasleveling screws at the bottom to set it to horizontal. Thedevice is enclosed in a glass box to avoid wind effects.BeamAgate knifeand agate OIn 20 CWeightsArrestment knob12Levelingscrew
Unit 1: Physical Quantitiesand MeasurementThe Electronic BalanceThe digital mass meter is an electronicinstrument configured with integrated circuits and itworks on the principal of balancing the forces.The device is turned on and set to zero then object isplaced on the plate. The reading on the screen gives themass of object. The electronic balance (Fig 1.19) is Fig 1.19 Electronic Balanceavailable in different ranges of measurement such as Fig 1.19 Electronic Balancemicro gram, milligram and kilogram etc.The Standard of TimeBefore 1960, the standard of time was defined interms of the mean solar day for the year 1900. Therotation of the Earth is now known to vary slightly withtime, this motion is not a good one to use for defining atime standard.In 1967, the second was redefined to takeadvantage of the high precision attainable in a deviceknown as an atomic clock(Fig 1.20), which uses thecharacteristic frequency of the cesium-133 atom as the“reference clock”.The second is now defined as 9 192 631 770 timesthe period of vibration of radiation from the cesiumatom.Stop WatchFig 1.20 Atomic ClockA stopwatch is used to measure the time intervalbetween two events. There are two types of stopwatch :Mechanical stopwatch and Digital stopwatch.Mechanical / Analogue StopwatchA mechanical stop watch can measure a timeinterval up to 0.1 second (Fig1.21). It has a knob that is13Fig. 1.21 Stop Watch
Unit 1: Physical Quantitiesand Measurementused to wind the spring that powers the watch. It canalso be used as a start stop and reset button. The watchstarts when the knob is pressed once. When pressedsecond time, the watch stops While the third pressbrings the needle back to zero.Digital StopwatchA digital stop watch can measure a time intervalup to 0.01 second (fig 1.22). It starts to indicate the timelapsed as the start/stop button is pressed. As soon asstart/stop button is pressed again, it stops and indicatesthe time interval recorded by it between start and stopof an event. A reset button restores its initial zeroFig. 1.22 Digital stop watch setting. Now a days almost the mobile phones have astopwatch function.Human Reaction TimeAs analogue or digital or watch is operated byhuman manually i.e., they have to be started or stoppedby hand. This causes a random error in measurementof time i.e called human reaction time. For most peoplehuman reaction time is about 0.3- 0.5 s. Therefore formore accurate measurement of time intervals lightgates (Fig1.23) can be used.Light gates0.00 sTimer 20.00 sTimer 1Fig 1.23 Light gates14
Unit 1: Physical Quantitiesand MeasurementSELF ASSESSMENT QUESTIONS:Q1: What instrument will you choose to measure heightof your friend?Q2: Can you describe how many seconds are there in ayear?Q3: Which instrument will you choose to measure yourmass?1.3 PREFIXESThe Physical quantities are described by thescientist in terms of magnitudes and units. Units play avital role in expressing a quantity either base orderived. Prefixes are useful for expressing units ofphysical quantities that are either very big or verysmall.A unit prefix is a specifier. It indicates multiples orfractions of the units.Units of various sizes are commonly formed bythe use of such prefixes. The prefixes of the metricsystem, such as kilo and milli , represent multiplicationby powers of ten. Historically, many prefixes have beenused or proposed by various sources, but only a narrowset has been recognized by standards 0,000100,000,000ggBiAtomsr? Edge ofthe 000? 000,000,000,000,000,000,000,000? seCellsDNASmerMoon10010,000NucleusElectron ?Neutrino 000,000,000,000,000,000,000,000Planck ?Scale by 100’STable 1.3 SI pre fixes15Do You Know!1 hour 60 min1 hour 3600 sec1min 60sec1sec 1000ms1sec 1000000ms
Unit 1: Physical Quantitiesand MeasurementSI mmnpfaMeaningGreater than 1trillionbillionmillionthousandhundredtenLess than Multiplier(Exponential)1 000 000 000 0001 000 000 0001 000 0001 0001001010121091061031021010.10.010.0010.000 0010.000 000 0010.000 000 000 0010.000 000 000 000 0010.000 000 000 000 000 00110-110-210-310-610-910-1210-1510-18SELF ASSESSMENT QUESTION:Q4: Can you tell if the size of a nucleus is up to 10-15m.What prefix shall we use to describe its size?1.4 SCIENTIFIC NOTATIONScientific NotationExponentm x 10 ncoefficientbaseScientific notation or the standard form is asimple method of writing very large numbers or verysmall numbers. In this method numbers are written aspowers of ten. Thus calculation of very large or verysmall numbers becomes easy.Numbers in Scientific Notation are made up of threeparts: The coefficient, the base and the exponent.u The coefficient must be equal to or (Not zero)greater than oneu The base must be 10u The exponent can be negative or positive.16
Unit 1: Physical Quantitiesand MeasurementWorked Example 1Convert mass of Sun 2 000 000 000 000 000 000 000 000000 000 kg. into Scientific Notation.SolutionStep 1: Since, MSun 2 000 000 000 000 000 000 000 000 000000 kgIt's obvious that in this value decimal lies at the end.Step 2: Converting into scientific notationMove the decimal to left writing in terms of base of tenMsun 2.00 1030kg.Note: power of exponent is taken as positive not to beconfused as we have displaced decimals but notnumbers.Worked Example 2Convert mass of an electron 9.11 x 10-31 kg intostandard form.SolutionStep 1: The decimal lies in the middle of the value.Since, melectron 9.11 10-31 kgStep 2: Move the decimal 31 steps towards leftmelectron 0.000 000 000 000 000 000 000 000 000 000911 kgQuick LabFill a tub with water to certainlevel and mark.Put some ice in it and observethe water level carefully aswell as floating or sinking.Remove the ice from the tubwithout being melt and put aballoon in it and then observe.Likewise, put a spoon in thattub and observe.Again put an empty can ofcoke and observe.Can you tell which of all fourhas more density? And whichhas more volume?1.5 DENSITY AND VOLUMEThe three common phases or states of matter aresolid, liquid and gas. A solid maintains a fixed shapeand a fixed size, even if same force is applied it notreadily change its volume. A liquid does not maintain afixed shape it takes on the shape of its container. But,like a solid it is not readily compressible, and its volumecan be changed significantly only by a large force.17Do You Know!31 liter 1000cm1m3 1000 litr
Unit 1: Physical Quantitiesand MeasurementHowever, a gas has neither a fixed shape nor a fixedvolume- it will expand to fill its container.Often we find the large weight woods floating on thesurface of water. However, an iron needle sinks into thewater. We say iron is “heavier” than wood. This cannotreally be true rather we should say like iron is “denser”than wood. Physicist are concerned with a physicalquantity, a property of matter which may help to definethe nature of matter in terms of its mass and space.Measuring the VolumeFor density to be measured or calculated we firstneed to find the volume of substances. Most of solidgeometrical shapes have formulae for their volumewhich is obtained through different parameters such asradius, height, depth, width, base and length, but forirregular objects, liquids and gases this approach isunusual. The volume of liquids can be measured withthe help of Cylinders, and Beakers.Measuring CylinderEye levelMeniscusFig. 1.24Measuring CylinderMeasuring cylinder is a glass or plastic cylinderwith a scale-graduated in cubic centimeters ormilliliters (ml)(fig1.24). It is used to find the volume ofliquids. When a liquid is poured, it rises to a certainheight in the cylinder. The level of liquid in the cylinderis noted and volume of the liquid is obtained.In order to read the volume correctly we should keepthe eye in level with the bottom of the meniscus of theliquid surface as you learned in previous grade.18
Unit 1: Physical Quantitiesand Measurement1. Volume of LiquidQuick LabA volume of about a liter or so can be measuredusing a measuring cylinder. When the liquid is pouredinto the cylinder the level on scale gives the volume.Most measuring cylinders have scales marked inmilliliters (ml) or cubic centimeters (cm3). It should benoted that while recording the value from cylinder theeyes should maintain the level with the value. Angularobservation may result a false reading of the volume.2. Regular solidIf an object has a regular shape its volume can becalculatedFor instance:Volume of a rectangular block length x width x heightVolume of a cylinder p radius2 heightTake a measuring cylinder of1 liter capacity at full place itin a beaker.Fill cylinder full with water.Pour a stone of irregular shapein it gradually.As you pour the stone in thecylinder, the water fromcylinder drops into thebeaker.Drop the stone in cylindercompletelyCalculate the volume of waterejected out of cylinder.Volume of water ejected is thevolume of the stone.3. Irregular solidRockFor an irregular solid its volume is calculated bylowering the object in a partially filled measuringcylinder (fig 1.25). The rise in the level on the volumescale gives the volume of that object. Thus the volumeof irregular solid is calculated by subtracting theoriginal volume of liquid from the raised volume ofliquid.The total volume is found. The volume of thesolid is measured in a separate experiment and thensubtracted from the total volume.RockFig 1.25. Volume Irregularshaped Solid19
Unit 1: Physical Quantitiesand MeasurementDensityDo You Know!During the Cold War betweenRussia and America. There wasa race of Astrophysics. Americawas facing the period of racism.A Black lady mathematiciannamed Katherine solved theproblem of putting the firstorbital satellite.Recommended!Watch movie “Hidden Figures”Observe the importance ofReliable Numbers.The term density of a substance is defined asmass of substance (m) per unit volume (V). It is denotedby Greek letter ρ (rho).mρ VDensity is characteristic property of any puresubstance. Objects made of a particular pure substancesuch as pure Gold can have any size or mass but itsdensity will be same for each.In accordance with the above equation mass of asubstance can be expressed asm ρVThe S.I unit for density is kg/m 3 kgm - 3 .Sometimes dens of substances is given in gm/ cm3. Thedensity of Aluminum is 2.70 gm/cm3 which is equal to2700 Kg/m3.Do You Know!In Jordan there is sea knownas 'Dead Sea'The humans in that sea whileswimming does not sink!This is because the water ofsea is much more salty thannormal, which raises thedensity of water.Measuring the DensityIt is to be noted that there are two ways offinding the density of a substance eithermathematically or experimentally by taking densityof water at 4oC as a reference which is sometimesknown as relative density or 'Specific gravity'. It hasno unit, it is a number whose value is the same as thatof the density in g/cm3.relative density 20density of substancedensity of water
Unit 1: Physical Quantitiesand MeasurementWorked Example 4What is the mass a solid iron wrecking ball of radius18cm. if the density of iron is 7.8 gm/cm3?Solution:Step 1: write known physical quantities with units andpoint out the quantity to be found.Density of iron ball ρ 7.8 gm/cm3 7.8 1000 kg/ m3Radius of iron ball is r 18cm 18 10-2 m 0.18mVolume of the iron ball is V (4/3) π r3 (1.33) 3.14 (0.18m)3 V 0.024m3Step 2: write down the formula and rearrange ifnecessarym ρ VStep 3: put the values in formula and calculateSince mass of iron ball is m ρ V (7.8 x 103) (0.024)m 187.2 kgSELF ASSESSMENT QUESTIONS:Q5: How can you identify which gas is denser amongthe gases?Q6: Can you tell how hot air balloon works?1.6 SIGNIFICANT FIGURESEngineers and scientist around the world workwith numbers either representing a large or smallmagnitude of a physical quantity. The engineers arehowever interested in the accuracy of a value as theymostly work on estimation but scientist especiallyphysicist are more concerned in the accuracy of thesenumbers. For instance, an engineer records the speed ofwind and explains it on an average. On the other hand,for the physicist, the speed of earth on its course, the21
Unit 1: Physical Quantitiesand Measurementspeed of light in vacuum the mass or charge on anelectron is just not a matter of numbers but accuratenumbers.The numbers of reliably known digits in a value areknown as significant figures.Table 1.4 Rules for determining significant figuresExampleRule1. All non-zeroes are 2.25 (3 significant figures)significant2. Leading zeroes are 0.00000034 (2 significantNOT significantfigures)3. Trailing zeroes are 200 (1 significant figure)significant ONLY if 200. (3 significant figures)an explicit decimal 2.00 (3 significant figures)point is present4. Trapped zeroes are 0.00509 (3 significant figures)2045 (4 significant figures)significantWorked example 5How many significant figures are there in the area of acylinder whose diameter is 5 cmSolution:Step 1: write known physical quantities and point out theunknown quantityDiameter of the cylinder is d 5cm 5 10-2 m 0.05mRadius of cylinder is r d/2 2.5 10-2 m 0.025mStep 2: write down formula and rearrange if necessaryThe area of the cylinder is A p r2 3.14 (0.025m)2 20.0019mStep 3: put value in formula and calculate2Thus area of cylinder can be written as A 1.9 mmThus, there are two significant numbers in the value 1and 9.22
Unit 1: Physical Quantitiesand MeasurementSELF ASSESSMENT QUESTIONS:Q7: Determine the number of significant figures in00.6022009SUMMARYu Physics is the branch of science which deals withuuuuuuuuuustudies of matter its composition, properties, andinteraction with energy.The branches of Physics are classified on the basis ofdifferent areas of study with different approaches.There are two types of physicist, theoretical andexperimental physicist.Physics define mathematical relation betweenphysical quantities. A physical quantity hasmagnitude and unit.Physical quantity are mainly classified into twocategorize
physical quantities are important for describing the nature around us. A physical quantity is a physical property of a phenomenon, body, or substance that can be quantified by measurement. Fig. 1.5 Atomic Physics Fig. 1.6 Optics Fig. 1.8 Nuclear Physics Fig. 1.7 Sound Fig. 1.10 Astro Physics Fig. 1.12 Geo Physics Fig. 1.9 Particle Physics
2-2 Physical Quantities and Units Reading Assignment: pp. 7-11 Electromagnetics (e.m.) requires . and, b) HO: Examples of Physical Quantities . 8/18/2005 section 2_2 Physical Quantities and Units.doc 2/2 Jim Stiles The Univ. of Kansas Dept. of EECS B. Vector Representation Use an arrow to symbolically represent a discrete vector quantity. .
Method of Measurement for Road Works Preparation of Bill of Quantities March 2011 3 Preambles to Bill of 9 The matters set out under the heading “Preambles to Bill of Quantities” Quantities (1-17) hereafter are always to be included as a preamble to the Bill of Quantities. Ad
single real number, these quantities are often called scalars. Other quantities, such as directed distances, velocities and forces , require for their complete specification both a magnitude and direction, these quantities are called vectors. Vectors
Page 1 Unit 1: Relationships Between Quantities UNIT 1: RELATIONSHIPS BETWEEN QUANTITIES Quantities and Units MGSE9-12.N.Q.1 Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems. MGSE9-12.N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
4 Physics data booklet. Adding/subtracting quantities: uncertainty in result will be sum of uncertainties of quantities. Multiplying/dividing quantities: % uncertainties of quantities are added together to obtain % uncertainty in result. Powers of quantities: % uncertainty of quantity is multiplied by power to obtain % uncertainty in result.
BASIC RADIATION PHYSICS 3 1.1.3. Physical quantities and units Physical quantities are characterized by their numerical value (magnitude) and associated unit. Symbols for physical quantities are set in italic type, while symbols for units are set in roman type (e.g. m 21 kg; E 15 MeV). The numerical va
two fundamental quantities are the magnetic induction, B , and the magnetic field, H, both of which are axial vector quantities. In many cases the induction and the field will be collinear (parallel) so that we can treat them as scalar quantities, B and H.2 In a vacuum, the magnetic induction, B , is related to the magnetic field, H : B ¼ m 0
Artificial Intelligence of December 2018 [5] and in the EU communication on Artificial Intelligence for Europe [6], including billions of Euros allocated in the Digital Europe Programme _ [7]. This is due to potential economic gains (e.g. see OECD reports on AI investments [8] and on AI patents [9]), as well as economic risks (such as the issue of liability – Liability for Artificial .
