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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
99
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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