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transcript
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