page 48 ACKNOWLEDGEMENTS Question 1 – Figure 1A – CG Stocker/Shutterstock.com Question 3 – Figure 3A – dashadima/Shutterstock.com Question 15 – Figure 15A – Luciano Cosmo/shutterstock.com © National Qualications 2018 AH X757/77/11 Physics Relationships Sheet TUESDAY, 8 MAY 9:00 AM – 11:30 AM A/PB page 02 Relationships required for Physics Advanced Higher ds v dt = 2 2 dv d s a dt dt = = v u at = + 2 1 2 s ut at = + 2 2 2 v u as = + dθ ω dt = 2 2 dω d θ α dt dt = = o ω ω αt = + 2 1 2 o θ ω t αt = + 2 2 2 o ω ω αθ = + s rθ = v rω = ta rα = 2 2 r v a rω r = = 2 2 mv F mrω r = = T Fr = T Iα = 2 L mvr mr ω = = L Iω = 2 1 2 K E Iω = 2 Mm F G r = GM V r = − 2GM v r = 2 apparent brightness, 4 L b πr = 4 Power per unit area σT = 2 4 4 L πr σT = 2 2 Schwarzschild GM r c = E hf = h λ p = 2 nh mvr π = 4 x h x p π Δ Δ ≥ 4 h E t π Δ Δ ≥ F qvB = 2 ω πf = 2π ω T = page 03 cos sin or y A ωt y A ωt = = ( ) 2 2 v ω A y = ± − ( ) 2 2 2 1 2 K E mω A y = − 2 2 1 2 P E mω y = sin ( ) 2 x y A π ft λ = − 2 E kA = 2πx λ = φ , , .... 1 optical path difference or 2 where 0 1 2 mλ m λ m ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ = 2 λl x d Δ = 4 λ d n = λD x d Δ = tan P n i = 1 2 2 4 o Q Q F πε r = 2 4 o Q E πε r = 4 o Q V πε r = F QE = V Ed = sin F IlB θ = 2 oμ I B πr = 1 o o c ε μ = t RC = C V X I = 1 2 C X πfC = dI L dt ε = − 2 1 2 E LI = L V X I = 2 L X πfL = 2 2 2 W X Y Z W X Y Z Δ Δ Δ Δ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ = + + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 2 2 W X Y Z Δ = Δ + Δ + Δ 2 2 2 d y a ω y dt = = − page 04 d vt = s vt = v u at = + 2 1 2 s ut at = + 2 2 2 v u as = + ( ) 1 2 s u v t = + W mg = F ma = W E Fd = P E mgh = 2 1 2 K E mv = E P t = p mv = Ft mv mu = − 2 Mm F G r = ( ) 2 1 t t vc ′ = − ( ) 2 1 v l l c ′ = − o s s v f f v v ⎛ ⎞ = ⎜ ⎟ ± ⎝ ⎠ observed rest rest λ λ z λ − = v z c = 0 v H d = W QV = 2 E mc = E hf = 0 K E hf hf = − 2 1 E E hf − = 1 T f = v fλ = sin d θ mλ = sin sin 1 2 θ n θ = sin sin 1 1 1 2 2 2 θ λ v θ λ v = = sin 1 cθ n = 2 k I d = P I A = , , ... 1 path difference or where 0 1 2 2 mλ m λ m ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ = max. value min. value random uncertainty number of values − = 2 peak rms V V = 2 peak rms I I = Q It = V IR = 2 2 V P IV I R R = = = .... 1 2 T R R R = + + .... 1 2 1 1 1 T R R R = + + E V Ir = + 1 1 1 2 S R V V R R ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ 1 1 2 2 V R V R = 2 2 1 1 1 2 2 2 Q E QV CV C = = = Q C V = 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 ( ) f x ( ) f x ′ sin ax cos a ax cosax sin a ax − Table of standard integrals ( ) f x ( ) f x dx ∫ sin ax cos 1 ax C a − + cosax sin 1 ax C a + circumference 2πr = 2 area πr = 2 area 4πr = 3 4 3 volume πr = sin opposite hypotenuse θ = cos adjacent hypotenuse θ = tan opposite adjacent θ = sin cos 2 2 1 θ θ + = 2 I mr = 2 1 12 I ml = 2 1 3 I ml = 2 1 2 I mr = 2 2 5 I mr = page 06 Electron Arrangements of Elements Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 0 (1) (18) 1 H 1 Hydrogen Key Atomic number Symbol Electron arrangement Name 2 He 2 Helium (13) (14) (15) (16) (17) (2) 3 Li 2,1 Lithium 4 Be 2,2 Beryllium 5 B 2,3 Boron 6 C 2,4 Carbon 7 N 2,5 Nitrogen 8 O 2,6 Oxygen 9 F 2,7 Fluorine 10 Ne 2,8 Neon 11 Na 2,8,1 Sodium 12 Mg 2,8,2 Magnesium Transition Elements 13 Al 2,8,3 Aluminium 14 Si 2,8,4 Silicon 15 P 2,8,5 Phosphorus 16 S 2,8,6 Sulfur 17 Cl 2,8,7 Chlorine 18 Ar 2,8,8 Argon (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) 19 K 2,8,8,1 Potassium 20 Ca 2,8,8,2 Calcium 21 Sc 2,8,9,2 Scandium 22 Ti 2,8,10,2 Titanium 23 V 2,8,11,2 Vanadium 24 Cr 2,8,13,1 Chromium 25 Mn 2,8,13,2 Manganese 26 Fe 2,8,14,2 Iron 27 Co 2,8,15,2 Cobalt 28 Ni 2,8,16,2 Nickel 29 Cu 2,8,18,1 Copper 30 Zn 2,8,18,2 Zinc 31 Ga 2,8,18,3 Gallium 32 Ge 2,8,18,4 Germanium 33 As 2,8,18,5 Arsenic 34 Se 2,8,18,6 Selenium 35 Br 2,8,18,7 Bromine 36 Kr 2,8,18,8 Krypton 37 Rb 2,8,18,8,1 Rubidium 38 Sr 2,8,18,8,2 Strontium 39 Y 2,8,18,9,2 Yttrium 40 Zr 2,8,18, 10,2 Zirconium 41 Nb 2,8,18, 12,1 Niobium 42 Mo 2,8,18,13, 1 Molybdenum 43 Tc 2,8,18,13, 2 Technetium 44 Ru 2,8,18,15, 1 Ruthenium 45 Rh 2,8,18,16, 1 Rhodium 46 Pd 2,8,18, 18,0 Palladium 47 Ag 2,8,18, 18,1 Silver 48 Cd 2,8,18, 18,2 Cadmium 49 In 2,8,18, 18,3 Indium 50 Sn 2,8,18, 18,4 Tin 51 Sb 2,8,18, 18,5 Antimony 52 Te 2,8,18, 18,6 Tellurium 53 I 2,8,18, 18,7 Iodine 54 Xe 2,8,18, 18,8 Xenon 55 Cs 2,8,18,18, 8,1 Caesium 56 Ba 2,8,18,18, 8,2 Barium 57 La 2,8,18,18, 9,2 Lanthanum 72 Hf 2,8,18,32, 10,2 Hafnium 73 Ta 2,8,18, 32,11,2 Tantalum 74 W 2,8,18,32, 12,2 Tungsten 75 Re 2,8,18,32, 13,2 Rhenium 76 Os 2,8,18,32, 14,2 Osmium 77 Ir 2,8,18,32, 15,2 Iridium 78 Pt 2,8,18,32, 17,1 Platinum 79 Au 2,8,18, 32,18,1 Gold 80 Hg 2,8,18, 32,18,2 Mercury 81 Tl 2,8,18, 32,18,3 Thallium 82 Pb 2,8,18, 32,18,4 Lead 83 Bi 2,8,18, 32,18,5 Bismuth 84 Po 2,8,18, 32,18,6 Polonium 85 At 2,8,18, 32,18,7 Astatine 86 Rn 2,8,18, 32,18,8 Radon 87 Fr 2,8,18,32, 18,8,1 Francium 88 Ra 2,8,18,32, 18,8,2 Radium 89 Ac 2,8,18,32, 18,9,2 Actinium 104 Rf 2,8,18,32, 32,10,2 Rutherfordium 105 Db 2,8,18,32, 32,11,2 Dubnium 106 Sg 2,8,18,32, 32,12,2 Seaborgium 107 Bh 2,8,18,32, 32,13,2 Bohrium 108 Hs 2,8,18,32, 32,14,2 Hassium 109 Mt 2,8,18,32, 32,15,2 Meitnerium 110 Ds 2,8,18,32, 32,17,1 Darmstadtium 111 Rg 2,8,18,32, 32,18,1 Roentgenium 112 Cn 2,8,18,32, 32,18,2 Copernicium 57 La 2,8,18, 18,9,2 Lanthanum 58 Ce 2,8,18, 20,8,2 Cerium 59 Pr 2,8,18,21, 8,2 Praseodymium 60 Nd 2,8,18,22, 8,2 Neodymium 61 Pm 2,8,18,23, 8,2 Promethium 62 Sm 2,8,18,24, 8,2 Samarium 63 Eu 2,8,18,25, 8,2 Europium 64 Gd 2,8,18,25, 9,2 Gadolinium 65 Tb 2,8,18,27, 8,2 Terbium 66 Dy 2,8,18,28, 8,2 Dysprosium 67 Ho 2,8,18,29, 8,2 Holmium 68 Er 2,8,18,30, 8,2 Erbium 69 Tm 2,8,18,31, 8,2 Thulium 70 Yb 2,8,18,32, 8,2 Ytterbium 71 Lu 2,8,18,32, 9,2 Lutetium 89 Ac 2,8,18,32, 18,9,2 Actinium 90 Th 2,8,18,32, 18,10,2 Thorium 91 Pa 2,8,18,32, 20,9,2 Protactinium 92 U 2,8,18,32, 21,9,2 Uranium 93 Np 2,8,18,32, 22,9,2 Neptunium 94 Pu 2,8,18,32, 24,8,2 Plutonium 95 Am 2,8,18,32, 25,8,2 Americium 96 Cm 2,8,18,32, 25,9,2 Curium 97 Bk 2,8,18,32, 27,8,2 Berkelium 98 Cf 2,8,18,32, 28,8,2 Californium 99 Es 2,8,18,32, 29,8,2 Einsteinium 100 Fm 2,8,18,32, 30,8,2 Fermium 101 Md 2,8,18,32, 31,8,2 Mendelevium 102 No 2,8,18,32, 32,8,2 Nobelium 103 Lr 2,8,18,32, 32,9,2 Lawrencium Lanthanides Actinides page 07 [BLANK PAGE] DO NOT WRITE ON THIS PAGE page 08 [BLANK PAGE] DO NOT WRITE ON THIS PAGE