State the First and Second Laws of Thermodynamics and the equations for Isothermal, Isobaric, Isochoric, and Adiabatic gas processes and Carnot Efficiency (HL B.4).

Internal energy of an ideal monatomic gas: U = (3/2)nRT = (3/2)Nk_B T. First Law of Thermodynamics: Q = ΔU + W, where work done BY the gas is W = PΔV (area under a P–V diagram). 1) Isochoric (constant V): W = 0, so Q = ΔU. 2) Isobaric (constant P): W = PΔV. 3) Isothermal (constant T): ΔU = 0, so Q = W. 4) Adiabatic (no heat exchange, rapid/insulated): Q = 0, so ΔU = −W and PV^(5/3) = constant (steeper than isothermals on P–V graph). Entropy change: ΔS = ΔQ / T and S = k_B ln Ω. Maximum Carnot heat engine efficiency: η_Carnot = 1 − (T_cold / T_hot).

Compare Standing Waves in strings fixed at both ends, open pipes (open at both ends), and closed pipes (closed at one end, open at the other) (C.4).

Displacement Nodes (N) occur at fixed ends/closed pipe ends; Antinodes (A) occur at open pipe ends. 1) String fixed at both ends OR Pipe open at both ends: ALL integer harmonics are present (n = 1, 2, 3, ...), with λ_n = 2L / n and f_n = n × (v / 2L). 2) Pipe closed at one end and open at the other: ONLY ODD harmonics are present (n = 1, 3, 5, ...), with λ_n = 4L / n and f_n = n × (v / 4L) (fundamental L = ¼λ₁).

In HL Electromagnetic Induction, write the equations for an AC Generator's sinusoidal EMF (ε = N BAω sin(ωt)) and how changing rotation speed ω affects peak EMF and period.

As a coil of N turns and area A rotates at constant angular velocity ω in a uniform magnetic field B, flux linkage is NΦ = NBA cos(ωt). By Faraday's Law, the induced EMF is the negative derivative: ε(t) = −d(NΦ)/dt = NBAω sin(ωt), so peak EMF is ε₀ = NBAω. If the rotational speed ω is DOUBLED, the peak induced EMF (ε₀) DOUBLES AND the period of the AC output (T = 2π/ω) HALVES (frequency doubles).

State the Doppler Effect equations for Sound (moving source vs moving observer) and Electromagnetic Waves (SL & HL C.5).

For Electromagnetic waves (when Δv ≪ c): Δf / f = Δλ / λ ≈ v / c. For Sound waves (speed v in air, HL): 1) Moving source (speed u_s): f' = f [ v / (v ∓ u_s) ] (use MINUS for source moving TOWARDS observer so frequency increases, PLUS for moving away); 2) Moving observer (speed u_o): f' = f [ (v ± u_o) / v ] (use PLUS for observer moving TOWARDS source, MINUS for moving away).

State the Single-Slit Diffraction equation (θ = λ / b), Rayleigh Criterion for Resolution, and Multiple-Slit / Diffraction Grating effects (HL C.3).

Single-slit diffraction: angular half-width of the central bright maximum (from centre to first minimum) is θ = λ / b (in radians, where b is slit width). When a double-slit pattern is modulated by single-slit diffraction, bright fringes of spacing s = λD / d lie inside the single-slit envelope. Increasing the number of slits N (towards a diffraction grating, d sin θ = nλ) makes the primary maxima much SHARPER (narrower) and much MORE INTENSE (I ∝ N²), while secondary maxima become negligible.

How do parallel-plate Capacitors behave when connected in Parallel vs in Series, and what happens when a dielectric (ε_r) is inserted?

Note that capacitor combination formulas are the OPPOSITE of resistor formulas: 1) Capacitors in Parallel (same V across each): C_total = C₁ + C₂ + ...; 2) Capacitors in Series (same Q on each plate): 1 / C_total = 1 / C₁ + 1 / C₂ + ... Inserting a dielectric material of relative permittivity ε_r > 1 polarises its molecules, creating an opposing internal electric field that increases capacitance (C = ε_r ε₀ A / d). If isolated (Q constant), V drops and E_stored = ½Q²/C decreases; if connected to a battery (V constant), Q increases and E_stored = ½CV² increases.

How do you propagate fractional/percentage uncertainties for powers and products in IB Physics Topic A (Data Booklet rules)?

If y = a ± b, absolute uncertainties add: Δy = Δa + Δb. If y = (a × b) / c, fractional uncertainties add: Δy / y = Δa / a + Δb / b + Δc / c. If y = a^n, fractional uncertainty is multiplied by |n|: Δy / y = |n| (Δa / a) (e.g., for period squared T², % uncertainty = 2 × %ΔT; for √L, % uncertainty = ½ × %ΔL).

Compare the roles of the Moderator, Control Rods, Heat Exchanger, and Shielding inside a pressurized water Nuclear Fission Reactor (E.4).

1) Moderator (water, heavy water D2O, or graphite): slows down fast fission neutrons (~2 MeV) via elastic collisions to thermal energies (~0.025 eV) so they have a high cross-section for capture by Uranium-235 nuclei (without absorbing them). 2) Control Rods (boron or cadmium): raised or lowered into the reactor core to absorb excess neutrons and keep the reaction self-sustaining at criticality (1 neutron per fission triggers 1 further fission). 3) Heat Exchanger: transfers thermal energy from the pressurized primary coolant loop to boil water into high-pressure steam for turbines.

Derive the Orbital Speed (v_orb), Escape Speed (v_esc), and Total Mechanical Energy of an orbiting satellite of mass m at radius r around planet M (HL D.1).

1) Orbital speed: equate gravitational force to centripetal force (GMm / r² = mv² / r) → v_orb = √(GM / r), so Kinetic Energy Ek = ½mv² = +GMm / (2r). 2) Gravitational Potential Energy: Ep = −GMm / r. 3) Total Mechanical Energy: E_total = Ek + Ep = +GMm/(2r) − GMm/r = −GMm / (2r) (if atmospheric drag reduces E_total, orbital radius r decreases and speed v_orb actually INCREASES!). 4) Escape speed (where Ek + Ep = 0 at infinity): ½mv_esc² − GMm/R = 0 → v_esc = √(2GM / R) = √2 v_orb.

Explain Stellar Parallax (d in parsecs = 1 / p in arcseconds) and why standard candles (Cepheid variables and Type Ia supernovae) are used for greater cosmic distances.

As Earth orbits the Sun (baseline = 1 AU), nearby stars shift against background stars by parallax angle p (in arcseconds): distance in parsecs d(pc) = 1 / p(arcsec) (1 pc = 3.26 light-years = 3.09 × 10¹⁶ m). Above ~100–1,000 pc, p becomes too small to measure accurately. Astronomers then use Standard Candles of known luminosity L (Cepheid variables via their Period–Luminosity relationship, or Type Ia supernovae peaking at L ≈ 10¹⁰ L_☉ when a white dwarf exceeds the 1.4 M_☉ Chandrasekhar limit) and calculate distance from b = L / (4πd²).

In IB Wave Behaviour (Theme C), state the equations for Simple Harmonic Motion (SHM) displacement, velocity, acceleration, and kinetic/potential energy (SL & HL C.1).

Defining SHM equation: a = −ω²x, where angular frequency ω = 2π / T = 2πf. For x = x₀ sin(ωt + φ): Velocity v = ωx₀ cos(ωt + φ) = ±ω√(x₀² − x²). Total Mechanical Energy in SHM (constant with no damping): E_total = ½mω²x₀². Potential Energy at displacement x: Ep = ½mω²x² (parabola); Kinetic Energy: Ek = ½mω²(x₀² − x²). Under light damping, amplitude decays exponentially while period remains nearly constant; in forced oscillations, resonance occurs when driving frequency equals natural frequency (f_d = f₀).

State the IB Physics equations for Work Done (W), Elastic Potential Energy, Power (P = Fv), and Efficiency (A.3).

Work done by a constant force at angle θ to displacement: W = Fs cos θ. Elastic potential energy stored in a spring of constant k: E_H = ½k(Δx)². Mechanical power output of a force moving an object at constant velocity v: P = ΔW / Δt = Fv. Efficiency: η = E_useful / E_total = P_useful / P_total.

How do you read a Minkowski Spacetime Diagram (ct vs x) and use the Spacetime Interval Invariant in HL Special Relativity (A.5)?

On a spacetime diagram (vertical axis = ct, horizontal axis = x): light worldlines always have gradient ±1 (angle 45°), and the worldline of an object moving at speed v has gradient = c / v = 1 / tan θ (where tan θ = v / c; the moving frame's x' and ct' axes scissor symmetrically towards the 45° light line by angle θ). Between any two events, the Spacetime Interval is invariant across all inertial frames: (Δs)² = (cΔt)² − (Δx)² = (cΔt')² − (Δx')².

In IB Astrophysics / Stellar Processes (E.5), explain Hydrostatic Equilibrium, the Proton–Proton Chain, the Hertzsprung–Russell (H–R) Diagram, and the Chandrasekhar & Oppenheimer–Volkoff Limits.

Main sequence stars are in hydrostatic equilibrium: inward gravitational pressure balances outward thermal/radiation pressure from core hydrogen fusion (p–p chain or CNO cycle; for main sequence stars, Luminosity L ∝ M^3.5). On the H–R Diagram (Luminosity vs Decreasing Surface Temperature OBAFGKM): Main Sequence runs diagonally from hot/luminous top-left to cool/dim bottom-right; Red Giants/Supergiants are top-right (cool but huge R in L = σ4πR²T⁴); White Dwarfs are bottom-left (hot but tiny R). Stellar remnants: if core remnant mass < 1.4 M_☉ (Chandrasekhar limit), electron degeneracy pressure halts collapse to form a White Dwarf; if 1.4 M_☉ < M_core < ~2.5–3 M_☉ (Oppenheimer–Volkoff limit), neutron degeneracy pressure forms a Neutron Star; above ~3 M_☉, it collapses into a Black Hole.

How do you linearize a power-law relationship y = a x^n or an exponential relationship y = a e^(bx) for IB Physics Paper 1B and Internal Assessment?

1) Power law y = a x^n: take logs of both sides → log(y) = n log(x) + log(a). Plot log(y) on the vertical axis against log(x) on the horizontal axis to get a straight line with gradient = n and y-intercept = log(a). 2) Exponential relationship y = a e^(bx): take natural logs → ln(y) = bx + ln(a). Plot ln(y) against x to get a straight line with gradient = b and y-intercept = ln(a).

In IB Physics Theme D.3 & D.4, state the magnetic force on a current (F = BIL sin θ), on a moving charge (F = qvB sin θ), and Faraday's Law of Induction (HL).

Magnetic force on wire of length L carrying current I at angle θ to magnetic field B: F = BIL sin θ. Force on charge q moving at velocity v: F = qvB sin θ (circular radius r = mv / qB; in a velocity selector with crossed electric and magnetic fields, undeflected particles satisfy qE = qvB → v = E / B). Motional EMF induced in a straight rod of length L moving at speed v perpendicular to B: ε = BvL. Faraday's & Lenz's Law: ε = −N ΔΦ / Δt, where magnetic flux Φ = BA cos θ.

State the Phase Change and Phase Difference equations for travelling waves, and distinguish Refractive Index n₁ / n₂ = sin θ₂ / sin θ₁ = v₂ / v₁ = λ₂ / λ₁.

Phase difference Δφ (in radians) for path difference Δx: Δφ = (2π / λ) Δx. Constructive interference occurs when path difference Δx = nλ (Δφ = 2nπ); Destructive interference occurs when Δx = (n + ½)λ (Δφ = (2n + 1)π). When a wave refracts from medium 1 into medium 2, its frequency f stays CONSTANT while speed and wavelength change proportionally: n₁ / n₂ = sin θ₂ / sin θ₁ = v₂ / v₁ = λ₂ / λ₁.

Explain Radioactive Decay (N = N₀e^(−λt)), Why Beta-Minus Decay Produces a Continuous Energy Spectrum, and how Nuclear Binding Energy per Nucleon drives Fission and Fusion (E.3 & E.4).

In Alpha decay, emitted α particles have discrete energies because it is a 2-body decay. In Beta-minus decay (n → p + e⁻ + ν̄_e), the released decay energy is shared in variable proportions between three bodies (daughter nucleus, beta particle, and electron antineutrino ν̄_e), giving β⁻ particles a continuous energy spectrum up to a maximum endpoint energy (which led Pauli to postulate the neutrino). Activity A = λN = λN₀e^(−λt) with t₁/₂ = ln 2 / λ.

Explain Archimedes' Principle of Buoyancy (F_b = ρ_f V_f g) and Stokes' Law of Viscous Drag (F_d = 6πηrv) for a sphere falling at terminal velocity.

Archimedes' Buoyancy Force (upthrust) equals the weight of fluid displaced: F_b = ρ_fluid V_submerged g. Stokes' Law viscous drag on a small sphere of radius r moving slowly (laminar flow) through a fluid of viscosity η: F_d = 6πηrv. At terminal velocity v_t, downward weight balances upward buoyancy + viscous drag: mg = F_b + F_d → (4/3)πr³ρ_sphere g = (4/3)πr³ρ_fluid g + 6πηrv_t, so v_t = [2r²g(ρ_sphere − ρ_fluid)] / (9η).

State the two Postulates of Einstein's Special Relativity and the equations for Time Dilation and Length Contraction using the Lorentz Factor γ (HL A.5).

Postulates: 1) The laws of physics are identical in all inertial (non-accelerating) reference frames; 2) The speed of light in a vacuum (c = 3.00 × 10⁸ m s⁻¹) is constant for all inertial observers regardless of the motion of the source or observer. Lorentz factor: γ = 1 / √(1 − v²/c²) (always ≥ 1). Time Dilation: Δt = γ Δt₀ (where proper time Δt₀ is measured in the frame where the two events occur at the same spatial point—moving clocks run slow). Length Contraction: L = L₀ / γ (where proper length L₀ is measured at rest relative to the object—contracted only parallel to motion). Muon decay at Earth's surface confirms both.

Define Linear Impulse (J = FΔt = Δp) and distinguish between Elastic, Inelastic, and Totally Inelastic Collisions (IB Physics A.2).

Impulse J = F_net Δt = Δp (equal to the area under a Force–Time graph). In ALL isolated collisions (zero external resultant force), Total Linear Momentum is conserved (Σp_before = Σp_after). In an Elastic collision, Total Kinetic Energy is ALSO conserved (and relative speed of approach equals relative speed of separation). In an Inelastic collision, some kinetic energy is converted to thermal/sound/deformation energy (maximum Ek loss occurs when objects stick together in a totally inelastic collision).

Compare Gravitational Fields and Electrostatic Fields in IB Physics Theme D (SL & HL D.1 & D.2).

Gravitational (always attractive): Force F_g = Gm₁m₂ / r²; Field strength g = GM / r²; Potential V_g = −GM / r (J kg⁻¹); Potential energy Ep = mV_g = −GMm / r; Field strength equals negative potential gradient: g = −ΔV_g / Δr; Equipotential surfaces are perpendicular to field lines (zero work done moving along an equipotential: W = mΔV_g). Electrostatic (attractive or repulsive): F_e = kq₁q₂ / r² (k = 1 / 4πε₀ = 8.99 × 10⁹ N m² C⁻²); E = kQ / r²; V_e = kQ / r (V = J C⁻¹); E = −ΔV_e / Δr; Work done W = qΔV_e.

State Hubble's Law (v = H₀d), show how 1 / H₀ estimates the Age of the Universe, and state the two key observations supporting the Big Bang Model.

Hubble's Law: the recession speed v of a distant galaxy (found from cosmological redshift z = Δλ / λ₀ ≈ v / c) is directly proportional to its distance d: v = H₀d (where H₀ ≈ 70 km s⁻¹ Mpc⁻¹). Assuming constant expansion rate, Hubble Time (Age of the Universe) is T ≈ d / v = 1 / H₀ ≈ 13.8 billion years. Two pillars of the Big Bang: 1) Cosmological Redshift of galaxies (expansion of space itself: z = R / R₀ − 1); 2) Cosmic Microwave Background (CMB) radiation—isotropic black-body radiation at T = 2.73 K (λ_max ≈ 1.1 mm) left over from recombination.

How do you find the maximum and minimum gradients (uncertainty in slope and y-intercept) on a graph with error bars in IB Physics?

Draw the line of best fit through the data points. Then draw two worst-fit lines passing through all error bars: 1) Maximum gradient line (m_max): from the bottom of the first error bar to the top of the last error bar; 2) Minimum gradient line (m_min): from the top of the first error bar to the bottom of the last error bar. Uncertainty in gradient: Δm = (m_max − m_min) ÷ 2; Uncertainty in y-intercept: Δc = (c_max − c_min) ÷ 2.

State the equations for DC Circuits: Kirchhoff's Laws, Potential Divider, and Electric Cells with Internal Resistance (B.5).

Kirchhoff's First Law (conservation of charge at a junction): ΣI_in = ΣI_out. Kirchhoff's Second Law (conservation of energy around any closed loop): ΣV = 0 (sum of EMFs = sum of IR drops). Terminal voltage of a cell with EMF ε and internal resistance r: V = ε − Ir. Potential divider with resistors R₁ and R₂ in series across V_in: V_out (across R₂) = V_in × [R₂ / (R₁ + R₂)].

State the four SUVAT equations and explain how air resistance (fluid drag) alters the trajectory of a projectile (IB Physics A.1).

SUVAT (constant acceleration only): 1) v = u + at; 2) s = ut + ½at²; 3) v² = u² + 2as; 4) s = ½(u + v)t. With air resistance (acting opposite to instantaneous velocity v): 1) Maximum height is LOWER; 2) Horizontal range is SHORTER; 3) Peak of trajectory is reached earlier in horizontal distance, and the descent path is steeper than the ascent (asymmetric trajectory).

State the Stefan–Boltzmann Law, Wien's Displacement Law, Albedo, and the Solar Constant in IB Thermal & Greenhouse Physics (B.1 & B.2).

Black-body radiation power: L = σAT⁴ (Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴). Wien's Displacement Law: λ_max T = 2.9 × 10⁻³ m K (hotter stars peak at shorter, bluer wavelengths). Apparent brightness / Intensity at distance d: b = L / (4πd²) (at Earth's orbit, Solar Constant S ≈ 1360 W m⁻²; average incident intensity across Earth's spherical surface is S/4 ≈ 340 W m⁻²). Albedo α = Total scattered/reflected power ÷ Total incident power; Emissivity e = Power radiated by surface ÷ Power radiated by a black body of same A and T.

How do you determine the Half-Life of a short-lived vs a very long-lived radioactive isotope in IB Physics E.3?

1) Short-lived isotope (minutes/hours): measure count rate with a Geiger–Müller (GM) tube, subtract the background count rate to get corrected activity A, and plot ln(A) against time t; the gradient equals −λ, and t₁/₂ = ln 2 / λ. 2) Extremely long-lived isotope (millions/billions of years, where activity appears constant over a lab session): measure the mass of the pure sample to find the number of nuclei N = (m / M_r) N_A, measure the corrected activity A, calculate λ = A / N, and then find t₁/₂ = ln 2 / λ.

State the HL Rotational Mechanics equations for Torque (τ), Moment of Inertia (I), Angular Momentum (L), and Rotational Kinetic Energy (A.4).

Rotational equivalents of linear mechanics: Angular kinematics: ω_f = ω_i + αt; θ = ω_i t + ½αt²; ω_f² = ω_i² + 2αθ (with v = ωr and a_t = αr). Torque: τ = Fr sin θ = Iα. Moment of Inertia: I = Σmr² (resistance to angular acceleration). Angular Momentum: L = Iω (conserved when net external torque τ_ext = 0, e.g., ice skater pulling arms in decreases I so ω increases, and ΔL = τΔt). Rotational Kinetic Energy: Ek_rot = ½Iω² = L² / (2I) (a rolling sphere/cylinder has total Ek = ½mv² + ½Iω²).

What happens to the phase of a wave upon reflection at a fixed boundary (or higher refractive index medium) vs a free boundary?

When a mechanical wave reflects at a fixed boundary (or when light reflects off a medium of HIGHER refractive index n₂ > n₁), it undergoes a phase change of π radians (180° inversion, equivalent to a half-wavelength ½λ path difference). When a wave reflects at a free boundary (or off a medium of lower refractive index n₂ < n₁), there is zero phase change (0 rad).

Compare the three mechanisms of Thermal Energy Transfer: Conduction (Fourier's Law), Convection, and Radiation.

1) Conduction: transfer of kinetic energy through lattice vibrations (phonons) and collisions of delocalised free electrons in metals without bulk movement of matter; rate of heat transfer through area A and thickness Δx is ΔQ / Δt = kA(ΔT / Δx), where k is thermal conductivity. 2) Convection: bulk movement of fluids driven by density differences (heated fluid expands, becomes less dense, and rises). 3) Thermal Radiation: electromagnetic infrared waves requiring no medium (L = eσAT⁴).

In IB Quantum & Nuclear Physics (Theme E), explain Rutherford's Closest Approach / Deviations, Compton Scattering, and Bohr's Angular Momentum Quantisation (HL E.1 & E.2).

1) Rutherford Alpha Scattering: at closest head-on approach d to a gold nucleus (Z=79), initial kinetic energy Ek of the alpha particle (q = 2e) converts entirely to electrostatic potential energy: Ek = k(2e)(Ze) / d → estimates upper bound of nuclear radius (~10⁻¹⁴ m); deviations from Rutherford scattering at very high alpha energies occur because the alpha particle gets close enough (<10⁻¹⁵ m) for the attractive Strong Nuclear Force to act. 2) Bohr model quantisation condition (standing de Broglie electron wave around orbit 2πr = nλ): mvr = nh / (2π), giving E_n = −13.6 / n² eV for Hydrogen. 3) Compton Scattering (particle nature of photons): X-ray photon scatters off a stationary electron, losing energy and shifting to a longer wavelength: Δλ = λ' − λ = (h / m_e c)(1 − cos θ).

IB Physics HL/SL: Space, Time & Motion, Particulate Nature of Matter, Wave Behaviour, Fields & Nuclear/Quantum Physics

Complete IBDP Physics (Themes A–E, 2023+ syllabus) revision: kinematics, work/power, rigid body rotational mechanics, special relativity, thermal/greenhouse physics, SHM & wave phenomena, Doppler effect, gravitational/electric/magnetic fields, and quantum/nuclear physics.

Level: intermediate
Languages: en → en
Cards: 32
Markdown: IB Physics HL/SL: Space, Time & Motion, Particulate Nature of Matter, Wave Behaviour, Fields & Nuclear/Quantum Physics (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	State the First and Second Laws of Thermodynamics and the equations for Isothermal, Isobaric, Isochoric, and Adiabatic gas processes and Carnot Efficiency (HL B.4).	Internal energy of an ideal monatomic gas: U = (3/2)nRT = (3/2)Nk_B T. First Law of Thermodynamics: Q = ΔU + W, where work done BY the gas is W = PΔV (area under a P–V diagram). 1) Isochoric (constant V): W = 0, so Q = ΔU. 2) Isobaric (constant P): W = PΔV. 3) Isothermal (constant T): ΔU = 0, so Q = W. 4) Adiabatic (no heat exchange, rapid/insulated): Q = 0, so ΔU = −W and PV^(5/3) = constant (steeper than isothermals on P–V graph). Entropy change: ΔS = ΔQ / T and S = k_B ln Ω. Maximum Carnot heat engine efficiency: η_Carnot = 1 − (T_cold / T_hot).
2	Compare Standing Waves in strings fixed at both ends, open pipes (open at both ends), and closed pipes (closed at one end, open at the other) (C.4).	Displacement Nodes (N) occur at fixed ends/closed pipe ends; Antinodes (A) occur at open pipe ends. 1) String fixed at both ends OR Pipe open at both ends: ALL integer harmonics are present (n = 1, 2, 3, ...), with λ_n = 2L / n and f_n = n × (v / 2L). 2) Pipe closed at one end and open at the other: ONLY ODD harmonics are present (n = 1, 3, 5, ...), with λ_n = 4L / n and f_n = n × (v / 4L) (fundamental L = ¼λ₁).
3	In HL Electromagnetic Induction, write the equations for an AC Generator's sinusoidal EMF (ε = N BAω sin(ωt)) and how changing rotation speed ω affects peak EMF and period.	As a coil of N turns and area A rotates at constant angular velocity ω in a uniform magnetic field B, flux linkage is NΦ = NBA cos(ωt). By Faraday's Law, the induced EMF is the negative derivative: ε(t) = −d(NΦ)/dt = NBAω sin(ωt), so peak EMF is ε₀ = NBAω. If the rotational speed ω is DOUBLED, the peak induced EMF (ε₀) DOUBLES AND the period of the AC output (T = 2π/ω) HALVES (frequency doubles).
4	State the Doppler Effect equations for Sound (moving source vs moving observer) and Electromagnetic Waves (SL & HL C.5).	For Electromagnetic waves (when Δv ≪ c): Δf / f = Δλ / λ ≈ v / c. For Sound waves (speed v in air, HL): 1) Moving source (speed u_s): f' = f [ v / (v ∓ u_s) ] (use MINUS for source moving TOWARDS observer so frequency increases, PLUS for moving away); 2) Moving observer (speed u_o): f' = f [ (v ± u_o) / v ] (use PLUS for observer moving TOWARDS source, MINUS for moving away).
5	State the Single-Slit Diffraction equation (θ = λ / b), Rayleigh Criterion for Resolution, and Multiple-Slit / Diffraction Grating effects (HL C.3).	Single-slit diffraction: angular half-width of the central bright maximum (from centre to first minimum) is θ = λ / b (in radians, where b is slit width). When a double-slit pattern is modulated by single-slit diffraction, bright fringes of spacing s = λD / d lie inside the single-slit envelope. Increasing the number of slits N (towards a diffraction grating, d sin θ = nλ) makes the primary maxima much SHARPER (narrower) and much MORE INTENSE (I ∝ N²), while secondary maxima become negligible.
6	How do parallel-plate Capacitors behave when connected in Parallel vs in Series, and what happens when a dielectric (ε_r) is inserted?	Note that capacitor combination formulas are the OPPOSITE of resistor formulas: 1) Capacitors in Parallel (same V across each): C_total = C₁ + C₂ + ...; 2) Capacitors in Series (same Q on each plate): 1 / C_total = 1 / C₁ + 1 / C₂ + ... Inserting a dielectric material of relative permittivity ε_r > 1 polarises its molecules, creating an opposing internal electric field that increases capacitance (C = ε_r ε₀ A / d). If isolated (Q constant), V drops and E_stored = ½Q²/C decreases; if connected to a battery (V constant), Q increases and E_stored = ½CV² increases.
7	How do you propagate fractional/percentage uncertainties for powers and products in IB Physics Topic A (Data Booklet rules)?	If y = a ± b, absolute uncertainties add: Δy = Δa + Δb. If y = (a × b) / c, fractional uncertainties add: Δy / y = Δa / a + Δb / b + Δc / c. If y = a^n, fractional uncertainty is multiplied by \|n\|: Δy / y = \|n\| (Δa / a) (e.g., for period squared T², % uncertainty = 2 × %ΔT; for √L, % uncertainty = ½ × %ΔL).
8	Compare the roles of the Moderator, Control Rods, Heat Exchanger, and Shielding inside a pressurized water Nuclear Fission Reactor (E.4).	1) Moderator (water, heavy water D2O, or graphite): slows down fast fission neutrons (~2 MeV) via elastic collisions to thermal energies (~0.025 eV) so they have a high cross-section for capture by Uranium-235 nuclei (without absorbing them). 2) Control Rods (boron or cadmium): raised or lowered into the reactor core to absorb excess neutrons and keep the reaction self-sustaining at criticality (1 neutron per fission triggers 1 further fission). 3) Heat Exchanger: transfers thermal energy from the pressurized primary coolant loop to boil water into high-pressure steam for turbines.
9	Derive the Orbital Speed (v_orb), Escape Speed (v_esc), and Total Mechanical Energy of an orbiting satellite of mass m at radius r around planet M (HL D.1).	1) Orbital speed: equate gravitational force to centripetal force (GMm / r² = mv² / r) → v_orb = √(GM / r), so Kinetic Energy Ek = ½mv² = +GMm / (2r). 2) Gravitational Potential Energy: Ep = −GMm / r. 3) Total Mechanical Energy: E_total = Ek + Ep = +GMm/(2r) − GMm/r = −GMm / (2r) (if atmospheric drag reduces E_total, orbital radius r decreases and speed v_orb actually INCREASES!). 4) Escape speed (where Ek + Ep = 0 at infinity): ½mv_esc² − GMm/R = 0 → v_esc = √(2GM / R) = √2 v_orb.
10	Explain Stellar Parallax (d in parsecs = 1 / p in arcseconds) and why standard candles (Cepheid variables and Type Ia supernovae) are used for greater cosmic distances.	As Earth orbits the Sun (baseline = 1 AU), nearby stars shift against background stars by parallax angle p (in arcseconds): distance in parsecs d(pc) = 1 / p(arcsec) (1 pc = 3.26 light-years = 3.09 × 10¹⁶ m). Above ~100–1,000 pc, p becomes too small to measure accurately. Astronomers then use Standard Candles of known luminosity L (Cepheid variables via their Period–Luminosity relationship, or Type Ia supernovae peaking at L ≈ 10¹⁰ L_☉ when a white dwarf exceeds the 1.4 M_☉ Chandrasekhar limit) and calculate distance from b = L / (4πd²).
11	In IB Wave Behaviour (Theme C), state the equations for Simple Harmonic Motion (SHM) displacement, velocity, acceleration, and kinetic/potential energy (SL & HL C.1).	Defining SHM equation: a = −ω²x, where angular frequency ω = 2π / T = 2πf. For x = x₀ sin(ωt + φ): Velocity v = ωx₀ cos(ωt + φ) = ±ω√(x₀² − x²). Total Mechanical Energy in SHM (constant with no damping): E_total = ½mω²x₀². Potential Energy at displacement x: Ep = ½mω²x² (parabola); Kinetic Energy: Ek = ½mω²(x₀² − x²). Under light damping, amplitude decays exponentially while period remains nearly constant; in forced oscillations, resonance occurs when driving frequency equals natural frequency (f_d = f₀).
12	State the IB Physics equations for Work Done (W), Elastic Potential Energy, Power (P = Fv), and Efficiency (A.3).	Work done by a constant force at angle θ to displacement: W = Fs cos θ. Elastic potential energy stored in a spring of constant k: E_H = ½k(Δx)². Mechanical power output of a force moving an object at constant velocity v: P = ΔW / Δt = Fv. Efficiency: η = E_useful / E_total = P_useful / P_total.
13	How do you read a Minkowski Spacetime Diagram (ct vs x) and use the Spacetime Interval Invariant in HL Special Relativity (A.5)?	On a spacetime diagram (vertical axis = ct, horizontal axis = x): light worldlines always have gradient ±1 (angle 45°), and the worldline of an object moving at speed v has gradient = c / v = 1 / tan θ (where tan θ = v / c; the moving frame's x' and ct' axes scissor symmetrically towards the 45° light line by angle θ). Between any two events, the Spacetime Interval is invariant across all inertial frames: (Δs)² = (cΔt)² − (Δx)² = (cΔt')² − (Δx')².
14	In IB Astrophysics / Stellar Processes (E.5), explain Hydrostatic Equilibrium, the Proton–Proton Chain, the Hertzsprung–Russell (H–R) Diagram, and the Chandrasekhar & Oppenheimer–Volkoff Limits.	Main sequence stars are in hydrostatic equilibrium: inward gravitational pressure balances outward thermal/radiation pressure from core hydrogen fusion (p–p chain or CNO cycle; for main sequence stars, Luminosity L ∝ M^3.5). On the H–R Diagram (Luminosity vs Decreasing Surface Temperature OBAFGKM): Main Sequence runs diagonally from hot/luminous top-left to cool/dim bottom-right; Red Giants/Supergiants are top-right (cool but huge R in L = σ4πR²T⁴); White Dwarfs are bottom-left (hot but tiny R). Stellar remnants: if core remnant mass < 1.4 M_☉ (Chandrasekhar limit), electron degeneracy pressure halts collapse to form a White Dwarf; if 1.4 M_☉ < M_core < ~2.5–3 M_☉ (Oppenheimer–Volkoff limit), neutron degeneracy pressure forms a Neutron Star; above ~3 M_☉, it collapses into a Black Hole.
15	How do you linearize a power-law relationship y = a x^n or an exponential relationship y = a e^(bx) for IB Physics Paper 1B and Internal Assessment?	1) Power law y = a x^n: take logs of both sides → log(y) = n log(x) + log(a). Plot log(y) on the vertical axis against log(x) on the horizontal axis to get a straight line with gradient = n and y-intercept = log(a). 2) Exponential relationship y = a e^(bx): take natural logs → ln(y) = bx + ln(a). Plot ln(y) against x to get a straight line with gradient = b and y-intercept = ln(a).
16	In IB Physics Theme D.3 & D.4, state the magnetic force on a current (F = BIL sin θ), on a moving charge (F = qvB sin θ), and Faraday's Law of Induction (HL).	Magnetic force on wire of length L carrying current I at angle θ to magnetic field B: F = BIL sin θ. Force on charge q moving at velocity v: F = qvB sin θ (circular radius r = mv / qB; in a velocity selector with crossed electric and magnetic fields, undeflected particles satisfy qE = qvB → v = E / B). Motional EMF induced in a straight rod of length L moving at speed v perpendicular to B: ε = BvL. Faraday's & Lenz's Law: ε = −N ΔΦ / Δt, where magnetic flux Φ = BA cos θ.
17	State the Phase Change and Phase Difference equations for travelling waves, and distinguish Refractive Index n₁ / n₂ = sin θ₂ / sin θ₁ = v₂ / v₁ = λ₂ / λ₁.	Phase difference Δφ (in radians) for path difference Δx: Δφ = (2π / λ) Δx. Constructive interference occurs when path difference Δx = nλ (Δφ = 2nπ); Destructive interference occurs when Δx = (n + ½)λ (Δφ = (2n + 1)π). When a wave refracts from medium 1 into medium 2, its frequency f stays CONSTANT while speed and wavelength change proportionally: n₁ / n₂ = sin θ₂ / sin θ₁ = v₂ / v₁ = λ₂ / λ₁.
18	Explain Radioactive Decay (N = N₀e^(−λt)), Why Beta-Minus Decay Produces a Continuous Energy Spectrum, and how Nuclear Binding Energy per Nucleon drives Fission and Fusion (E.3 & E.4).	In Alpha decay, emitted α particles have discrete energies because it is a 2-body decay. In Beta-minus decay (n → p + e⁻ + ν̄_e), the released decay energy is shared in variable proportions between three bodies (daughter nucleus, beta particle, and electron antineutrino ν̄_e), giving β⁻ particles a continuous energy spectrum up to a maximum endpoint energy (which led Pauli to postulate the neutrino). Activity A = λN = λN₀e^(−λt) with t₁/₂ = ln 2 / λ.
19	Explain Archimedes' Principle of Buoyancy (F_b = ρ_f V_f g) and Stokes' Law of Viscous Drag (F_d = 6πηrv) for a sphere falling at terminal velocity.	Archimedes' Buoyancy Force (upthrust) equals the weight of fluid displaced: F_b = ρ_fluid V_submerged g. Stokes' Law viscous drag on a small sphere of radius r moving slowly (laminar flow) through a fluid of viscosity η: F_d = 6πηrv. At terminal velocity v_t, downward weight balances upward buoyancy + viscous drag: mg = F_b + F_d → (4/3)πr³ρ_sphere g = (4/3)πr³ρ_fluid g + 6πηrv_t, so v_t = [2r²g(ρ_sphere − ρ_fluid)] / (9η).
20	State the two Postulates of Einstein's Special Relativity and the equations for Time Dilation and Length Contraction using the Lorentz Factor γ (HL A.5).	Postulates: 1) The laws of physics are identical in all inertial (non-accelerating) reference frames; 2) The speed of light in a vacuum (c = 3.00 × 10⁸ m s⁻¹) is constant for all inertial observers regardless of the motion of the source or observer. Lorentz factor: γ = 1 / √(1 − v²/c²) (always ≥ 1). Time Dilation: Δt = γ Δt₀ (where proper time Δt₀ is measured in the frame where the two events occur at the same spatial point—moving clocks run slow). Length Contraction: L = L₀ / γ (where proper length L₀ is measured at rest relative to the object—contracted only parallel to motion). Muon decay at Earth's surface confirms both.
21	Define Linear Impulse (J = FΔt = Δp) and distinguish between Elastic, Inelastic, and Totally Inelastic Collisions (IB Physics A.2).	Impulse J = F_net Δt = Δp (equal to the area under a Force–Time graph). In ALL isolated collisions (zero external resultant force), Total Linear Momentum is conserved (Σp_before = Σp_after). In an Elastic collision, Total Kinetic Energy is ALSO conserved (and relative speed of approach equals relative speed of separation). In an Inelastic collision, some kinetic energy is converted to thermal/sound/deformation energy (maximum Ek loss occurs when objects stick together in a totally inelastic collision).
22	Compare Gravitational Fields and Electrostatic Fields in IB Physics Theme D (SL & HL D.1 & D.2).	Gravitational (always attractive): Force F_g = Gm₁m₂ / r²; Field strength g = GM / r²; Potential V_g = −GM / r (J kg⁻¹); Potential energy Ep = mV_g = −GMm / r; Field strength equals negative potential gradient: g = −ΔV_g / Δr; Equipotential surfaces are perpendicular to field lines (zero work done moving along an equipotential: W = mΔV_g). Electrostatic (attractive or repulsive): F_e = kq₁q₂ / r² (k = 1 / 4πε₀ = 8.99 × 10⁹ N m² C⁻²); E = kQ / r²; V_e = kQ / r (V = J C⁻¹); E = −ΔV_e / Δr; Work done W = qΔV_e.
23	State Hubble's Law (v = H₀d), show how 1 / H₀ estimates the Age of the Universe, and state the two key observations supporting the Big Bang Model.	Hubble's Law: the recession speed v of a distant galaxy (found from cosmological redshift z = Δλ / λ₀ ≈ v / c) is directly proportional to its distance d: v = H₀d (where H₀ ≈ 70 km s⁻¹ Mpc⁻¹). Assuming constant expansion rate, Hubble Time (Age of the Universe) is T ≈ d / v = 1 / H₀ ≈ 13.8 billion years. Two pillars of the Big Bang: 1) Cosmological Redshift of galaxies (expansion of space itself: z = R / R₀ − 1); 2) Cosmic Microwave Background (CMB) radiation—isotropic black-body radiation at T = 2.73 K (λ_max ≈ 1.1 mm) left over from recombination.
24	How do you find the maximum and minimum gradients (uncertainty in slope and y-intercept) on a graph with error bars in IB Physics?	Draw the line of best fit through the data points. Then draw two worst-fit lines passing through all error bars: 1) Maximum gradient line (m_max): from the bottom of the first error bar to the top of the last error bar; 2) Minimum gradient line (m_min): from the top of the first error bar to the bottom of the last error bar. Uncertainty in gradient: Δm = (m_max − m_min) ÷ 2; Uncertainty in y-intercept: Δc = (c_max − c_min) ÷ 2.
25	State the equations for DC Circuits: Kirchhoff's Laws, Potential Divider, and Electric Cells with Internal Resistance (B.5).	Kirchhoff's First Law (conservation of charge at a junction): ΣI_in = ΣI_out. Kirchhoff's Second Law (conservation of energy around any closed loop): ΣV = 0 (sum of EMFs = sum of IR drops). Terminal voltage of a cell with EMF ε and internal resistance r: V = ε − Ir. Potential divider with resistors R₁ and R₂ in series across V_in: V_out (across R₂) = V_in × [R₂ / (R₁ + R₂)].
26	State the four SUVAT equations and explain how air resistance (fluid drag) alters the trajectory of a projectile (IB Physics A.1).	SUVAT (constant acceleration only): 1) v = u + at; 2) s = ut + ½at²; 3) v² = u² + 2as; 4) s = ½(u + v)t. With air resistance (acting opposite to instantaneous velocity v): 1) Maximum height is LOWER; 2) Horizontal range is SHORTER; 3) Peak of trajectory is reached earlier in horizontal distance, and the descent path is steeper than the ascent (asymmetric trajectory).
27	State the Stefan–Boltzmann Law, Wien's Displacement Law, Albedo, and the Solar Constant in IB Thermal & Greenhouse Physics (B.1 & B.2).	Black-body radiation power: L = σAT⁴ (Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴). Wien's Displacement Law: λ_max T = 2.9 × 10⁻³ m K (hotter stars peak at shorter, bluer wavelengths). Apparent brightness / Intensity at distance d: b = L / (4πd²) (at Earth's orbit, Solar Constant S ≈ 1360 W m⁻²; average incident intensity across Earth's spherical surface is S/4 ≈ 340 W m⁻²). Albedo α = Total scattered/reflected power ÷ Total incident power; Emissivity e = Power radiated by surface ÷ Power radiated by a black body of same A and T.
28	How do you determine the Half-Life of a short-lived vs a very long-lived radioactive isotope in IB Physics E.3?	1) Short-lived isotope (minutes/hours): measure count rate with a Geiger–Müller (GM) tube, subtract the background count rate to get corrected activity A, and plot ln(A) against time t; the gradient equals −λ, and t₁/₂ = ln 2 / λ. 2) Extremely long-lived isotope (millions/billions of years, where activity appears constant over a lab session): measure the mass of the pure sample to find the number of nuclei N = (m / M_r) N_A, measure the corrected activity A, calculate λ = A / N, and then find t₁/₂ = ln 2 / λ.
29	State the HL Rotational Mechanics equations for Torque (τ), Moment of Inertia (I), Angular Momentum (L), and Rotational Kinetic Energy (A.4).	Rotational equivalents of linear mechanics: Angular kinematics: ω_f = ω_i + αt; θ = ω_i t + ½αt²; ω_f² = ω_i² + 2αθ (with v = ωr and a_t = αr). Torque: τ = Fr sin θ = Iα. Moment of Inertia: I = Σmr² (resistance to angular acceleration). Angular Momentum: L = Iω (conserved when net external torque τ_ext = 0, e.g., ice skater pulling arms in decreases I so ω increases, and ΔL = τΔt). Rotational Kinetic Energy: Ek_rot = ½Iω² = L² / (2I) (a rolling sphere/cylinder has total Ek = ½mv² + ½Iω²).
30	What happens to the phase of a wave upon reflection at a fixed boundary (or higher refractive index medium) vs a free boundary?	When a mechanical wave reflects at a fixed boundary (or when light reflects off a medium of HIGHER refractive index n₂ > n₁), it undergoes a phase change of π radians (180° inversion, equivalent to a half-wavelength ½λ path difference). When a wave reflects at a free boundary (or off a medium of lower refractive index n₂ < n₁), there is zero phase change (0 rad).
31	Compare the three mechanisms of Thermal Energy Transfer: Conduction (Fourier's Law), Convection, and Radiation.	1) Conduction: transfer of kinetic energy through lattice vibrations (phonons) and collisions of delocalised free electrons in metals without bulk movement of matter; rate of heat transfer through area A and thickness Δx is ΔQ / Δt = kA(ΔT / Δx), where k is thermal conductivity. 2) Convection: bulk movement of fluids driven by density differences (heated fluid expands, becomes less dense, and rises). 3) Thermal Radiation: electromagnetic infrared waves requiring no medium (L = eσAT⁴).
32	In IB Quantum & Nuclear Physics (Theme E), explain Rutherford's Closest Approach / Deviations, Compton Scattering, and Bohr's Angular Momentum Quantisation (HL E.1 & E.2).	1) Rutherford Alpha Scattering: at closest head-on approach d to a gold nucleus (Z=79), initial kinetic energy Ek of the alpha particle (q = 2e) converts entirely to electrostatic potential energy: Ek = k(2e)(Ze) / d → estimates upper bound of nuclear radius (~10⁻¹⁴ m); deviations from Rutherford scattering at very high alpha energies occur because the alpha particle gets close enough (<10⁻¹⁵ m) for the attractive Strong Nuclear Force to act. 2) Bohr model quantisation condition (standing de Broglie electron wave around orbit 2πr = nλ): mvr = nh / (2π), giving E_n = −13.6 / n² eV for Hydrogen. 3) Compton Scattering (particle nature of photons): X-ray photon scatters off a stationary electron, losing energy and shifting to a longer wavelength: Δλ = λ' − λ = (h / m_e c)(1 − cos θ).