AH

*S8577711*©

National

Quali cationsSPECIMEN ONLY

S857/77/11 PhysicsRelationships sheet

Date — Not applicable

Duration — 3 hours

page 02

Relationships required for Physics Advanced Higher

dsvdt

=

2

2

dv d sdt dt

= =

v t= +

212

s t t= +

2 2 2v s= +

ddt

=

2

2

d ddt dt

= =

t= +

212

t t= +

2 2 2= +

s =

v =

t =

22v= =

22v= =

2v= =

=

= −

2 44=

2

2s d =

=

=

2v =

4∆ ∆ ≥

4t∆ ∆ ≥

v=

2=

2=

= = −

( )k rotationalE Iω= 212

τ Fr=

τ Iα=

I mr=∑ 2

( ) ( )P k translational k rotationalE E E= +

GMm mv πF mrω mrr r T

= = = =22

22

2

escGMvr

=2

Lbπd

= 24

P σTA= 4

mvFr

=2

GMmFr

= 2

page 03

cos sinory A t y A t= =

2 212

=

2E kA=

2=φ

2d∆ =

4d =

d∆ =

n=

1 224

=

24=

4=

=

d=

sin=

2=

1=

=

12

=

212

=

=

2=

2 2 2∆ ∆ ∆ ∆⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

2 2 2∆ = ∆ + ∆ + ∆

22

2

ddt

= = −

F ky= −

πω πfT

= =2

2

( )v ω A y= ± −2 2

( )kE mω A y= −2 2 212

sin xy A π ftλ

= −2

opd n gpd= ×

W QV=

kE mv= 212

F qvB=

τ RC=

Δ Δn

n

W WnW W

=

1or where 0 1 2

2 , , ...opd mλ m λ m= + =

dIε Ldt

= −

page 04

d vt=

s vt=

v t= +

212

s t t= +

2 2 2v s= +

12

s v t= +

=

=

d=

=

212

v=

t=

v=

t v= −

2=

( )21

ttv

′ =−

( )21 v′ = −

ss

vv v

⎛ ⎞= ⎜ ⎟±⎝ ⎠

s v d st

st

−=

v=

0v d=

=

2=

=

0= −

2 1− =

1=

v =

sind =

sinsin

1

2

=

sinsin

1 1 1

2 2 2

vv

= =

sin 1=

2d=

PIA

=

1path difference or where 0 1 22

⎛ ⎞= +⎜ ⎟⎝ ⎠

=

max. value min. valuerandom uncertainty

number of values−=

2 s=

2 s=

t=

=

22= = =

1 2= + +

1 2

1 1 1= + +

= +

11

1 2

⎛ ⎞= ⎜ ⎟⎜ ⎟+⎝ ⎠

1 1

2 2

=

221 1 1

2 2 2= = =

=

page 05

Additional relationships

Circle

Sphere

Trigonometry

Moment of inertia

point mass

rod about centre

rod about end

disc about centre

sphere about centre

Table of standard derivatives

′

sin cos

cos sin−

Table of standard integrals

d

sin cos1− +

cos sin1 +

circumference 2=

2area =

2area =

343volume =

sin oppositehypotenuse

=

cos adjacenthypotenuse

=

n oppositeadjacent

=

sin cos2 2 1+ =

2=

2112=

213=

212=

225=

page 06

Electron arrangements of elem

entsG

roup 1G

roup 2G

roup 3G

roup 4G

roup 5G

roup 6G

roup 7G

roup 0

(1)(18)

1H1

Hydrogen

KeyAtom

ic number

Symbol

Electron arrangement

Nam

e

2He2

Helium

(13)(14)

(15)(16)

(17)(2)

3Li2,1

Lithium

4Be2,2

Beryllium

5B2,3

Boron

6C2,4

Carbon

7N2,5

Nitrogen

8O2,6

Oxygen

9F2,7

Fluorine

10

Ne

2,8

Neon

11

Na

2,8,1

Sodium

12

Mg

2,8,2

Magnesium

Transition elements

13Al2,8,3

Aluminium

14Si2,8,4

Silicon

15P2,8,5

Phosphorus

16S2,8,6

Sulfur

17Cl2,8,7

Chlorine

18

Ar2,8,8

Argon(3)

(4)(5)

(6)(7)

(8)(9)

(10)(11)

(12)

19K2,8,8,1

Potassium

20

Ca2,8,8,2

Calcium

21Sc2,8,9,2

Scandium

22Ti2,8,10,2

Titanium

23V2,8,11,2

Vanadium

24

Cr2,8,13,1

Chromium

25

Mn

2,8,13,2

Manganese

26

Fe2,8,14,2

Iron

27

Co2,8,15,2

Cobalt

28Ni

2,8,16,2

Nickel

29

Cu2,8,18,1

Copper

30

Zn2,8,18,2

Zinc

31

Ga

2,8,18,3

Gallium

32

Ge

2,8,18,4

Germ

anium

33

As2,8,18,5

Arsenic

34

Se2,8,18,6

Selenium

35

Br2,8,18,7

Bromine

36

Kr2,8,18,8

Krypton

37

Rb2,8,18,8,1

Rubidium

38Sr2,8,18,8,2

Strontium

39Y2,8,18,9,2

Yttrium

40Zr2,8,18,

10,2Zirconium

41

Nb

2,8,18,12,1

Niobium

42

Mo

2,8,18,13,1

Molybdenum

43Tc2,8,18,13,

2Technetium

44

Ru2,8,18,15,

1Ruthenium

45

Rh2,8,18,16,

1Rhodium

46

Pd2,8,18,

18,0Palladium

47

Ag2,8,18,

18,1Silver

48

Cd2,8,18,

18,2Cadm

ium

49In2,8,18,

18,3Indium

50

Sn2,8,18,

18,4Tin

51

Sb2,8,18,

18,5Antim

ony

52

Te2,8,18,

18,6Tellurium

53I2,8,18,

18,7Iodine

54

Xe2,8,18,

18,8Xenon

55

Cs2,8,18,18,

8,1Caesium

56

Ba2,8,18,18,

8,2Barium

57

La2,8,18,18,

9,2Lanthanum

72

Hf

2,8,18,32,10,2

Hafnium

73

Ta2,8,18,32,11,2Tantalum

74W2,8,18,32,

12,2Tungsten

75

Re2,8,18,32,

13,2Rhenium

76

Os

2,8,18,32,14,2

Osm

ium

77Ir2,8,18,32,

15,2Iridium

78Pt2,8,18,32,

17,1Platinum

79

Au2,8,18,32,18,1

Gold

80

Hg

2,8,18,32,18,2M

ercury

81Tl2,8,18,32,18,3Thallium

82

Pb2,8,18,32,18,4

Lead

83Bi2,8,18,32,18,5Bism

uth

84

Po2,8,18,32,18,6Polonium

85

At2,8,18,32,18,7Astatine

86

Rn2,8,18,32,18,8Radon

87Fr2,8,18,32,

18,8,1Francium

88

Ra2,8,18,32,

18,8,2Radium

89

Ac2,8,18,32,

18,9,2Actinium

104

Rf2,8,18,32,

32,10,2Rutherfordium

105

Db

2,8,18,32,32,11,2D

ubnium

106

Sg2,8,18,32,

32,12,2Seaborgium

107

Bh2,8,18,32,

32,13,2Bohrium

108

Hs

2,8,18,32,32,14,2H

assium

109

Mt

2,8,18,32,32,15,2

Meitnerium

110

Ds

2,8,18,32,32,17,1

Darmstadtium

111

Rg2,8,18,32,

32,18,1Roentgenium

112

Cn2,8,18,32,

32,18,2Copernicium

57

La2,8,18,18,9,2

Lanthanum

58

Ce2,8,18,20,8,2Cerium

59Pr2,8,18,21,

8,2Praseodym

ium

60

Nd

2,8,18,22,8,2

Neodym

ium

61

Pm2,8,18,23,

8,2Prom

ethium

62

Sm2,8,18,24,

8,2Sam

arium

63

Eu2,8,18,25,

8,2Europium

64

Gd

2,8,18,25,9,2

Gadolinium

65

Tb2,8,18,27,

8,2Terbium

66

Dy

2,8,18,28,8,2

Dysprosium

67

Ho

2,8,18,29,8,2

Holm

ium

68Er2,8,18,30,

8,2Erbium

69

Tm2,8,18,31,

8,2Thulium

70

Yb2,8,18,32,

8,2Ytterbium

71

Lu2,8,18,32,

9,2Lutetium

89

Ac2,8,18,32,

18,9,2Actinium

90

Th2,8,18,32,

18,10,2Thorium

91

Pa2,8,18,32,

20,9,2Protactinium

92U2,8,18,32,

21,9,2U

ranium

93

Np

2,8,18,32,22,9,2

Neptunium

94

Pu2,8,18,32,

24,8,2Plutonium

95

Am2,8,18,32,

25,8,2Am

ericium

96

Cm2,8,18,32,

25,9,2Curium

97

Bk2,8,18,32,

27,8,2Berkelium

98Cf2,8,18,32,

28,8,2Californium

99Es2,8,18,32,

29,8,2Einsteinium

100

Fm2,8,18,32,

30,8,2Ferm

ium

101

Md

2,8,18,32,31,8,2

Mendelevium

102

No

2,8,18,32,32,8,2

Nobelium

103

Lr2,8,18,32,

32,9,2Law

rencium

Lanthanides

Actinides