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IB physics formula sheet, Cheat Sheet of Physics

Formula sheet in measurements and uncertainties, mechanics, thermal concept, waves, electricity and magnetism, circular motion and gravitation.

Typology: Cheat Sheet

2021/2022
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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#
#AH#=#A#cos
θ
#
1.2.#Uncertainties#and#errors#AV#=#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)at2#Ff#≤#µsR' EK#=#(1/2)mv2
#F#=#Δp/Δt#
' v2#=#u2#+#2as' Ff#≤#µdR' EP#=#(1/2)kΔx2#EK#=#p2/2m#
' s#=#(1/2)(v#+#u)/t#ΔEP#=#mgΔh'
' ' ' power#=#Fv'
# # Efficiency#=#Wout/Win#=#Pout/Pin### #
_____________________________________________________________________________________#
Topic&3:&Thermal&concepts&
#
3.1.#Thermal#concepts###3.2.#Modelling#a#gas#
Q#=#mcΔt' p#=#F/A'
Q#=#mL' n#=#N/NA#
#pV#=#nRT'
' EK#=#(3/2)kBT#=#(3/2)RT/NA#
_____________________________________________________________________________________#
Topic&4:&Waves&
&
4.1.#Oscillations## 4.2.#Travelling#waves# # 4.3.#Wave#characteristics#
' T#=#1/f#c#=#λf' I##A2#
# # # I##xU2#
4.4.#Wave#behaviour###4.5.#Standing#waves'' I#=#I0#cos
θ
#
_____________________________________________________________________________________#
Topic&5:&Electricity&and&magnetism&
#
5.1.#Electric#fields#5.2.#Electric#currents#5.3.#Electric#cells#5.4.#Magnetic#effects#
' I#=#Δq/Δt' ΣV#=#0#(loop)#ε#=#I(R#+#r)# F#=#qvB'sin
θ
'
' F#=#kq1q2/r2#ΣI=#0#(junction)# # F#=#BIL'sin
θ
#
' k=#1/(4
πε
0)# R#=#V/I'
' V#=#W/q' P#=#VI#=#I2R#=#V2/R'
' E#=#F/q' Rtotal#=#R1#+#R2#+#…#
' I#=#nAvq'1/Rtotal#=#1/R1#+#1/R2#+#…#
# #
ρ
#=#RA/L'
_____________________________________________________________________________________#
AH'
AV'
A"
pf3
pf4
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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 = | na/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 IA^2 Ix -­‐^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 qt 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

_____________________________________________________________________________________

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

_____________________________________________________________________________________

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 LM 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 )