Lecture 1 Units and Physical Quantities

8/15/2019 Lecture 1 Units and Physical Quantities

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Lecture 1: Units,

Physical Quantities

Chapter 1: University Physics

by Young and Freedman


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Physics : ExperimentalScience

• requires measurement

• use o numbers to describe result

Physical Quantity - !ny number that describe physical

phenomenon quantitatively

" measurable# calculable rom other

measurable quantities

examples:

mass# $eight# height# length# etc%


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• &any la$s o physics are expressed

as mathematical relationship amongphysical quantities

• 'o understand better the physicalquantities or phenomenon# $e musthave some standard# and hence aunit% – MKS

– CGS

– International System (or SI, formSysteme International)


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&ap o Systems

om (mescience%com


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)ength: meter

• Units beore – Yard *distance rom the tip o the nose o

+ing o England to the end o

outstretched arm, – Foot *length o oot o +ing )ouis -./,

– meter *1 0 1 o distance

bet$een 2orth Pole to the Equator#passing through Paris,

• distance travelled by light invacuum during a time of 1 / 299792 458 s.


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Some o the typical lengths


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'ime: seconds

• de3ned beore as o amean solar day

• dened to be the 9 192 !"1 77#times the $eriod of vibration of a%esium atom transitioning fromone energy state to another.

1 1 1

60 60 24

÷ ÷ ÷


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ome typical timescales

&aboratory housing %esium atom


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P!4"!S!: time 5eeper ngPilipinas

"# million years for it go o( by a second)


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&ass: +g

• dened to be amass of a certain

platinum-iridium

alloy cylinder eptat International!ureau of "ei#$ts

and Measures(Se%res, &rance,')

! photo o the alloy de3ning 1+g


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• bound to change

soon – 2umber o Silicon

atoms in somesphere


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6uantiying standards:Pre3xes


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Unit consistency andconversion

• physical quantities can only beadded only i they have the sameunit

• . not# conversion is necessary*changing units,

• logic behind conversion – . a * b# then % 7ut any +uantities

multiplied by ' is e+ual to itself ence,

1a

b=

1 a

c c cb

= × = ×


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Examples• Convert 1% inches to mm

1 in 8 9%; cm• ! certain area has an area o %

m9% Convert it to yards9% –

1 yd 8


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Uncertainties

• Every measurements have

uncertainties – small uncertainty# more accurate

measurement

– big uncertainty# less accurate

– depends on measuring technique 0device used

• !ccuracy = ho$ close to the true

value – >?;%>@ A %1 cm or >?;%>@*1, means

the value could be any$here bet$een

>?;%> mm to >?;%>? mm


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Examples

• 'he length o a certain rectangle is

given by . / l# $hile the $idth isgiven by " / 0 Bhat is theuncertainty o the area *!ssume

that the uncertainties l and 0 arevery small such that the product l0 can be ignored%,


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Pics o errors


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Signi3cant Figures

• 7ecause sometimes uncertainties arenot speci3ed most o the times

• .ndicates reliability o themeasurement

•

2umbers to loo5 at%

S 4 id li Si i3 Fi


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Some 4uidelines Signi3cant Figures

1% 2on"(ero digits are signi3cant%

ex% >; cm have D SF

9% eroes bet$een non(eros are signi3cant%

ex% >< > cm have @ SF

D% .ntegers have in3nite values o SF%

ex% 9 goes li5e 9%%

;% .n decimal orm#

a% (eroes at the let o the 3rst non(ero digit

are not signi3cant%ex% %;D9 have D SF

b% the (eroes at the right o last non(ero digitare signi3cant%

ex% %?>


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Scienti3c 2otation

• convenient $ay to $rite very largeand very small number in aconvenient $ay%

• !llo$s us to preserve the signi3cant3gures in the calculation

example

D m 8 D x 1@ m% ;@


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&ost physical quantities can be expressed interms o undamental dimensions I J:

I)engthJ )I'imeJ '

I&assJ &

ICurrentJ !I'emperatureJ o

I!mountJ 2

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DIMENSIONAL ANALYSIS" chec5 i the equation is dimensionally correct

" 5no$ the units or the dimension o a physical quantity


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Examle: Dimensi!nal Analysis

Chec5 $hether the ollo$ing equations is

correct:

Use: m * Mass

•

9D

Lsubstitute dimensions o thephysical quantitiesLsimpliy the dimension o the )MSand NMS o the equation

Lchec5 i the dimension is consistent


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Exercise: Dimensi!nal Analysis

C$ec 0$et$er t$e follo0in# e+uations is

correct:

1

•

NMS:8 )ength

)MS:s 8 )ength

)MS:

NMS:

9;


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Lecture 1 Units and Physical Quantities