As Physics Chap 1

8/2/2019 As Physics Chap 1

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ADVANCED LEVEL PHYSICS (AS LEVEL)

Physical Quantities and Units

1.

Physical Quantity:

Aysiclquniycomissnumiclmgniudnduni.

Exml:infocofnNwon,focisysiclquniy,nisnumiclmgniudnd

Nwonisuni.Insymbol

Uni

F=10N

Pysiclquniy Numiclmgniud

Note: When stating a physical quantity, two items needed to be mentioned; the first

is its numerical value and second is the unit.

Fundamental Unit (Base Unit):

Wn ysicl quniy is ndd o msu, sndd siz of quniy is quid. Tis

snddsizisknowns unitfoiculysiclquniy.

) Pysiclquniisdmindbycomingmosnddsiz ouniof

ysiclquniy.

Exml: Iflngofodis5m,ysiclquniyislng.Tunifolngism.

Bsidsmounisoflngsucs

i) Fooii) Ydsiii)

Mils

Hnc scinis fmili o on uni find difficulis wn ncouns o sysms of unis

(loug on uni cn b convdino no by convsion fco) so unis of ll diffn

ysiclquniiscnbldobsofundmnlunis.Scinissgdovcommon

sysmuniclld System Internationalofmsumnswicusssvnbsunisfosvnbs

quniissummizdblow.

Base Quantity Unit

Name Symbol

Mss Kilogm Kg

Lng M MTim Scond S

Elcicun Am A

Tmu Klvin K


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Amounofsubsnc Mol Mol

Luminousinnsiy ndl cd

Note: dvngofsysminnionlisysiclquniysonlyonuni.

) T Meter isunioflngndisqulo1/299792458ofdisncvlldbyliginvcuuminonscond.

b) The kilogram is uni of mss nd is qul o mss of international prototypekilogram (linum-iidiumcylind ) ksvs,Pis.

c) The Secondisuniofimndisduionofxcly9192631770iodsofdiioncosondingonsiionbwnwoyfinlvlsofgoundsofcsium

133om.

Derived Quantities:Pysicl quniis o n bsic quniis clld Derived quantities. A divd quniy is

combinionofviousbsicquniis,-gwok=Focxdislcmnc.

Derived Unit:

T divd uni fo divd quniy cn b obind fom lionsi bwn

divd quniis wi bsic quniis. Ts unis obind using oduc o

quoin of on o mo bsic unis wiou inclusion of ny numicl fcos (on

coulomb=onmXonscond)

Note:

i) Afomdinndsdin(uniofnglisdinnduniofsolid

ngl,sdin,officillydsignds subsidiaryunisndcnbdsbso

divd s convninc dics) ll o unis usd in sysm clld derived

unis.

ii) Som divd unis livly comlx wn xssd in bsic uni nd fo

convnincgivnscilnms(-gkgm2

s-3

A-2

gisclldom,).

iii) Tsymbolfouniwicisnmdfsonscill.

The derived units with special names:

Derived quantity Unit

Name Symbol

Foc Nwon N=Kgms-2

Pssu Pscl P=kgm-1

s-2

Engy,wok Joul J=kgm2s

-2

Pow W W=kgm-2s-3

Fquncy Hz Hz=s-1

g oulomb =As

Elcomoivfoc Vol V=kgm2

s-3

A-1

Rsisnc Om =kgm2s-3A-2

onducnc Simns S=kg-1m-2s3A2

Inducnc Hny H=kgm2s-2A-2


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cinc Fd F=kg-1m-2s4A2

Mgnicflux Wb Wb=kgm2s-2A-1

MgnicFluxdnsiy Tsl T=kgs-2A-1

Power of Ten and Prefixes:

Iisvycommoninysicsoncounquniiswicvybigndvysmll.Tdiusis,foxml,vybigvlu,simsob6400,000m.Ononddiusofydogn

nuclus is vy smll quniy, oximly 0.000 000 000 000 0013 m. H i is vy sy o

clsslyndunwiinglyddoomionomozos.Toovcomisoblm,sciniscndo

nywomods

) Usofscinificnoions(snddfom)b) Pfixs.

Scientific Notation:Tdiusof,6400000mcnbwins6.4X10

6m.Rdiusofydognnuclus,0.000000000

0000013m,cnbwins1.310-15

m.

Prefixes:

Pfixs usd wi unis symbols o indic dciml mulils o submulils. Mos of

snddfixs

Submulils Pfix Symbol Mulil Pfix Symbol

10-24 yoco y yo 1024 y

10-21 Zo z z 1021 z

10-18

o x 1018

10-15 fmo f 1015

10-12

Pico T 1012

10-09 nno n Gig 109 g

10-6

Mico Mg 106 M

10-3

mili m Kilo 103 k

Dimensions:Tdimnsionsofysiclquniisindicowiisldobsicquniis.Tdimnsions

ofysiclquniycnbwins(ysiclquniy).

Base Quantity Base unit Dimension

Lng M L

Mss Kg M

Tim S T

Elciccun A A

Tmu K

Amounofsubsnc Mol N

Luminousinnsiy cd I

Example: A is obind by mulilying on lng by no (ms suc s bd, wid,

disnc,diusomlyconvninwysofsyinglng)ndfodimnsionsofos

oflngsqud

i) [A]=[lngXbd]=LXL=L2


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ii) [Vlociy]=[dislcmn/im]=L/T=LT-1

iii) [Acclion]=[cnginvlociy]=LT-1

/T=LT-2

iv) [Foc]=[mssXcclion]=MLT-2

v) [Wok]=[focXdislcmn]=MLT-2

XL=ML2

T-2

vi) [Elciccg]=[unXTim]=AT

vii) [Fquncy]=[1/iod]=[1/T]=T-1

viii) [Sin]=[xnsion/oiginllng]=L/L(wicisnondimnsionlodimnsionlss)

Andoxmls

i) [ScificHcciy]=L2T-2-1

ii) [MolHciy]=ML2

T-2

-1

N-1

iii) [Tmlconduciviy]=MLT

-3

-1

iv) [ElcicPonil]=ML2T-3I-1

v) [Elcicsisnc]=ML2T-3I-2

Dimensionless or Unit-less Quantities:

Ts quniis wic in ios of quniis ving sm dimnsions o unis.

Quniis wic v no unis ssocid wi m dimnsionlss (-gfciv indx). Som

quniis(-gngl)dimnsionlssvnougyvnssociduni.

Exmlincludlivdnsiy,sin.

Uses of Units and Dimensions:

a) To check homogeneity of physical equations:

Aysiclquionisuiscivofsysmofunisusdfoysiclquniismniondin

quions.Ec m in quion ssm dimnsions ndunis.Tdimnsions ofn

quionis sido bomognousif llmsin ivsmdimnsionsounis(is ysicllycocquionmusvsmdimnsionounisonboigndsidndlf

ndsidofquion).

Note:Onlyquniiswismdimnsionscnbddd,subcdoqudinnquion.

Example: AsudnclimsiodofsimlndulumTisldoislngl,mssof

bobm,ndcclionduogviygbyfollowingfomul.

T=k wkisdimnsionlssquniy

LHS=UnisofT=s


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RHS=unisofk =(kgm/ms-2

)1/2

=(kgs2)

1/2

Tquniisonbosidsofquiondonvsmuni.Tquioncnnobcoc.

T quion is inhomogeneous nd fo ysiclly wong. In o wods quion is

dimensionally inconsistent.

Example: Ascondsudnclimsfollowingfomulfoiodofsimlndulum

T=k wsymbolsviusulmningiscoc.

LHS=unisofT=s

RHS=unisofk =(m/ms-2

)1/2

=s

Tquionisomognous.Iislsosidob dimensionally consistent.

Note: A igoous mmiclmnyilds vlu ofk ob 2.Tcoc ysicl

fomulfoiodisncT=2 .Ifinsd,iodiswinsT=3 ,icn b

sownquionissilldimnsionllyconsisnbuysicllywong.

conclusions:

i) EquionswicgovndbyLwsofysicsmusbdimnsionllyconsisn.

ii) Howv,dimnsionllyconsisnquionsndnoblwsofysics(isif

dimnsionsdbnsmoncofquion,wwouldknowonlyi

migbcoc,fomoddosnoovidcckonnynumiclfcos).

iii) Tmoddosnolluswquioniswong.

Cases where an equation can be homogeneous and yet incorrect:

) Incorrect coefficient:

Tcocquionlingfomulfomoionundunifomcclionis

s=u+1/22

ndnoquionwicsbnwinwongly

s=u+22

Issmunisfocminquion;buiswongbcuscofficinof

2nd

monigsidoffisquionisndcofficinofscondmon

igsidofscondquionis2insdof.

b) Missing Terms:


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Tlionsibwns,u,ndmybjuswins

s=1/22

wicisincomlndwong;lougquionisomognous.

c) Extra terms

Tbovquionmybwonglywinwinxmwicssmdimnsion

ounisoms,foxml,

s=u+v+1/22

cocnssofysiclquionisconfimdximnlly.

Deriving Physical Equations:

Dmining ysicl quniy usully dnds on numb of o ysiclly quniis. Foxmliodofsimlndulumdndsonislngndcclionduogviyg.using

unisodimnsions,nquioncnbdivdoliodTwilndg.Txmlisgivn

blow.

Dimensional Analysis:

Tfcnquionmusbdimnsionllyomognousnblsdicionsobmdwy

inwicysiclquniisldoco.

Example:Piodofsimlndulum

Eximnsows iodof siml ndulum indndn of mliud ofoscillion

ovidingiissmll.Tfoimybsonblybsuosdfosmlloscillionsiod

dndsonlyonmssmofbob,lnglofsingndcclionduogviyg,if

wxsslionsis

Piod=kmxlygz,wkisdimnsionlssndx,yndzunknownindics,nsinccsidof

quionmusvsmdimnsions,so

[Piod]=[mx][ly][gz]

T=MxLy(LT-2)z

T=MxL

y+zT

-2z

EquingindicsofM,LndToncsidofquiongivs

(foM) 0=x

(foL) 0=y+z

(foT) 1=-2z

Solvinggivsx=0,z=-1/2,y=1/2

Piod=km0l

1/2g

-1/2


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i-Piod=k

Note: dimnsionl nlysis dos no ovid vlu of dimnsionlss consn k;

mmiclly nlysis of y cid ou in oving (im iod of siml ndulum)

fomulT= 2 dos. Howv siuions wmmicl nlysis isoo difficul;

dimnsionlnlysisisicullyusfulinsuccsslikisuillsfomul(influidmcnics,wic

invsig sdy flow of liquid (w)oug i)nd Soks Lw(in fluid mcnics, A low

vlociis,ficionlfoconsiclbodymovingougfluidconsnvlociyisqulo

6imsoducofvlociy,fluidviscosiy,nddiusofs.)

-Tnd-(No:xmiloninnionlsysmunissslybnddd)i

iPdonAugus,2000nduddfofifiminJn2010

SiHbibU.S.0333-4382319(Islmbd,Pkisn)

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As Physics Chap 1