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IB Physics Formula Sheet (from the Physics Data Booklet )
Topic 1: Measurement and uncertainties
1.1. Measurements in physics 1.3.Vectors and scalars A H = A cos θ 1.2. Uncertainties and errors A V = A sin θ If y = a ± b then ∆ y = ∆ a + ∆ b If y = ab/c then ∆ y/y = ∆ a/a + ∆ b/b + ∆ c/c If y = an^ then ∆ y/y = | n ∆ a/a |
Topic 2: Mechanics
2.1. Motion 2.2. Forces 2.3. Work, energy and power 2.4. Momentum and impulse v = u + at F = ma W = Fs cos θ p = mv s = ut + (1/2) at^2 F f ≤ μ s R E K = (1/2) mv^2 F = Δ p/ Δ t v^2 = u^2 + 2 as F f ≤ μ d R E P = (1/2) k Δ x^2 E K = p^2 /2 m s = (1/2)( v + u )/t Δ E P = mg Δ h power = Fv Efficiency = W out/ W in = P out/ P in
Topic 3: Thermal concepts
3.1. Thermal concepts 3.2. Modelling a gas Q = mc Δ t p = F / A Q = mL n = N / N A pV = nRT E K = (3/2) k B T = (3/2) RT / N A
Topic 4: Waves
4.1. Oscillations 4.2. Travelling waves 4.3. Wave characteristics T = 1/ f c = λ f I ∝ A^2 I ∝ x -‐^2 4.4. Wave behaviour 4.5. Standing waves I = I 0 cos θ
Topic 5: Electricity and magnetism
5.1. Electric fields 5.2. Electric currents 5.3. Electric cells 5.4. Magnetic effects I = Δ q /Δ t Σ V = 0 (loop) ε = I ( R + r ) F = qvB sin θ F = kq 1 q 2 / r^2 Σ I = 0 (junction) F = BIL sin θ k = 1/(4 πε 0 ) R = V / I V = W / q P = VI = I^2 R = V^2 / R E = F / q R total = R 1 + R 2 + … I = nAvq 1/ R total = 1/ R 1 + 1/ R 2 + … ρ = RA / L
A H
A V A
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Topic 6: Circular motion and gravitation
6.1. Circular motion 6.2. Newton’s law of gravitation v = ω r F = GMm / r^2 a = v^2 / r = 4π^2 r / T^2 g = F / m F = mv^2 / r = m ω^2 r g = GM / r^2
Topic 7: Atomic, nuclear and particle physics
7.1. Discrete energy and radioactivity 7.2. Nuclear reactions E = hf Δ E = Δ m c^2 λ = hc / E
7.3. The structure of matter Charge Quarks Baryon number (2/3) e u c t 1/ -‐(1/3) e d s b 1/ All quarks have a strangeness number of 0 except the strange quark that has a strangeness number of -‐ 1
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Topic 8: Energy production
8 .1. Energy sources 8 .2. Thermal energy transfer Power = energy / time P = e σ AT^4 Power = (1/2) A ρ v^3 λmax = 2.90× 10 -‐^3 / T I = power/ A albedo = total scattered power / total incident power
Topic 9: Simple harmonic motion
9.1. SHM 9.2. Single-‐slit 9.3. Interference ω = 2π/ T θ = λ/ b n λ = d sin θ a = -‐ω^2 x Constructive interference: 2 dn = ( m + ½)λ x = x 0 sin ω t ; x = x 0 cos ω t ; Destructive interference: 2 dn = m λ v = ω x 0 cos ω t ; v = -‐ω x 0 sin ω t ; v = ±ω sqrt ( x 02 – x^2 ) 9.4. Resolution 9.5. Doppler effect E K = (1/2) m ω^2 ( x 02 – x^2 ) θ = 1.22 λ/ b Moving source: f ‘^ = fv /( v ± u s) E T = (1/2) m ω^2 x 02 R = (λ/∆λ) = mN Moving observer: f ‘^ = f ( v ± u o)/ v Pendulum: T = 2π sqrt ( l / g ) ∆ f / f = λ/∆λ ≈ v / c Mass-‐spring: T = 2π sqrt ( m / k )
Charge Leptons -‐ 1 e e (^) μ τ (^0) ν (^) e νμ ντ All leptons have a lepton number of 1 and antileptons have a lepton number of -‐ 1 Gravitational Weak Electromagnetic Strong Particles experiencing All Quarks, leptons Charged Quarks, gluons Particles mediating Graviton W+, W-‐, Z^0 γ Gluons
E^2 = p^2 c^2 + m 02 c^4 qV = ∆ E K
Option B: Engineering physics
B.1. Rigid bodies and rotational dynamics B.2. Thermodynamics Γ = Fr sin θ ω = 2π f Q = Δ U + W pV5/3^ = const I = Σ mr^2 ωf = ωI + α t U = (3/2) nRT W = p Δ V Γ = I α ωf^2 = ωI^2 + 2 αθ Δ S = Δ Q / T η = W useful/ E input θ = ωI t + (1/2) α t^2 pV5/3^ = const η (^) carnot = 1 – T cold/ T hot L = I ω W = p Δ V E Krot = (1/2) I ω^2
B.3. Fluids and fluid dynamics (HL only) B.4. Forced vibrations and resonance (HL only) B = ρf V f g F D = 6π η rv Q = 2Π( E stored/ E dissipated/cycle) P = P 0 + ρf gd R = vr ρ/ η Q = 2Π× f res( E stored/ Pl oss) Av = constant (1/2) ρ v^2 + ρ gz + p = const
Option C: Imaging
C.1. Introduction to imaging C.2. Imaging instrumentation C.3. Fibre optics 1/ f = 1/ v + 1/ u M = θi/ θo M = f o/ f e n = 1/sin c P = 1/ f Mnear point = D / f + 1 attenuation = 10 log ( I / I 0 ) m = h i/ h o = -‐ v / u M infinity = D / f M = θi/ θo
C.4. Medical imaging (HL only) L f = 10 log ( I 1 / I 0 ) I = I 0 e -‐μ x^ μx 1/2 = ln 2 Z = pc
Option D: Astrophysics
D.1. Stellar quantities D.2. Stellar evolution D.3. Cosmology d (parsec) = 1/ p (arc-‐second) λmax = 2.9× 10 -‐^3 m K z = Δλ/λ 0 ≈ v / c L = σ AT^4 L ∝ M 3.5^ z = R / R 0 – 1 B = L /(4π d^2 ) v = H 0 d T ≈ 1/ H 0 D.4. Stellar processes (HL only) D.5. Further cosmology (HL only) v = sqrt(4π G ρ/3) r ρc = 3 H^2 /(8π G )
