IB DP Physics SL Study Notes

First Assessment 2025

A. Space, Time and Motion

A.1 Kinematics

• Position, Displacement, and Distance: Position is a vector coordinate. Displacement is the change in position (vector). Distance is the actual length of the path (scalar).
• Velocity and Speed: Velocity is the rate of change of position (vector), whereas speed is a scalar. Average velocity = displacement / time.
• Acceleration: Rate of change of velocity (vector).
• Equations of Uniformly Accelerated Motion:
  • s = (u + v)t / 2
  • v = u + at
  • s = ut + 1/2 at²
  • v² = u² + 2as
• Graphs of Motion:
  • Position-time graph: Gradient = velocity.
  • Velocity-time graph: Gradient = acceleration, Area = displacement.
  • Acceleration-time graph: Area = change in velocity.
• Projectile Motion: Motion in horizontal and vertical planes can be analyzed separately. Horizontal acceleration is 0 (constant horizontal velocity), vertical acceleration is g downwards.
• Fluid Resistance: Opposes motion (e.g., F = kv or F = kv²). Affects projectiles by reducing range and maximum height, breaking the parabolic symmetry. Objects falling in a fluid eventually reach a constant terminal speed when fluid resistance balances weight.

A.2 Forces and Momentum

• Newton's First Law: A body remains in a state of rest or uniform motion unless acted upon by a net external force. (Translational equilibrium: net force = 0).
• Newton's Second Law: Net force is proportional to the rate of change of momentum. For constant mass, F = ma.
• Newton's Third Law: When body A exerts a force on body B, body B exerts an equal and opposite force on body A.
• Common Forces:
  • Weight: F_g = mg
  • Normal Contact Force: Perpendicular to the surface.
  • Friction: Static friction F_f ≤ μ_s F_N. Dynamic friction F_f = μ_d F_N.
  • Tension: Force within a stretched string.
  • Hooke's Law: Elastic restoring force F_H = -kx.
  • Viscous Drag: F_d = 6πηrv (Stoke's Law).
  • Buoyancy: F_b = ρV_f (where V_f is displaced fluid volume).
• Linear Momentum and Impulse: p = mv. Impulse J = FΔt = Δp. In a force-time graph, impulse is the area under the curve.
• Collisions:
  • Momentum is always conserved in a closed system.
  • Elastic collisions: Kinetic energy is conserved.
  • Inelastic collisions: Kinetic energy is not conserved (completely inelastic when bodies stick together).
• Circular Motion: Constant speed in a circle requires a centripetal force perpendicular to velocity. Centripetal acceleration a = v² / r = ω² r = 4π² r / T². Angular velocity v = 2πr / T = ωr.

A.3 Work, Energy and Power

• Work Done: W = F s cos θ. It represents energy transfer.
• Principle of Conservation of Energy: In the absence of non-conservative forces, total mechanical energy is conserved.
• Types of Mechanical Energy:
  • Kinetic Energy: E_k = 1/2 mv² = p² / (2m)
  • Gravitational Potential Energy: ΔE_p = mgΔh
  • Elastic Potential Energy: E_H = 1/2 k(Δx)²
• Power and Efficiency: Power P = ΔW / Δt = Fv. Efficiency η = (useful work/power out) / (total work/power in).

B. The Particulate Nature of Matter

B.1 Thermal Energy Transfers

• Kinetic Theory: Describes differences between solids, liquids, and gases based on particle arrangements and motion. Kelvin temperature is a measure of average kinetic energy: E_k_avg = 3/2 k_B T.
• Internal Energy: The sum of total intermolecular potential energy and total random kinetic energy of particles.
• Phase Changes: Occur at constant temperature, representing changes in potential energy without changing kinetic energy.
• Specific Heat & Latent Heat: Q = mcΔT and Q = mL.
• Energy Transfer Mechanisms: Conduction, convection, and thermal radiation. Rate of conduction: ΔQ/Δt = kA(ΔT/Δx).
• Black Body Radiation: Emits EM waves. Stefan-Boltzmann law L = σAT⁴. Apparent brightness b = L / (4πd²). Wien's displacement law λ_max T = 2.9 × 10^-3 m K.

B.2 Greenhouse Effect

• Albedo & Emissivity: Albedo = scattered power / incident power. Emissivity = power radiated per unit area / σT⁴.
• Solar Constant (S): Incoming mean radiation intensity on Earth's surface cross-section is S/4.
• Greenhouse Gases: CH_4, H_2O, CO_2, N_2O absorb infrared radiation emitted by the Earth and re-radiate it in all directions, increasing the equilibrium temperature.

B.3 Gas Laws

• Pressure and Moles: P = F/A. Amount of substance n = N / N_A.
• Ideal Gas Law: Derived from empirical laws for constant P, V, or T. PV = nRT and PV = N k_B T.
• Kinetic Model: Relates macroscopic pressure to microscopic collisions: P = 1/3 ρ v². Internal energy of monatomic ideal gas U = 3/2 N k_B T = 3/2 nRT.
• Real vs Ideal: Ideal gases are good approximations of real gases under conditions of high temperature and low pressure/density.

B.5 Current and Circuits

• Charge and Current: Direct current I = Δq / Δt.
• Potential Difference (V): Work done per unit charge moving a positive test charge: V = W / q.
• Resistance: R = V / I. Resistivity ρ = RA / L. Ohmic conductors maintain constant R at constant temperature.
• Electrical Power: P = IV = I² R = V² / R.
• Circuits: Series: I is constant, V = V1 + V2 + ..., Rs = R1 + R2 + .... Parallel: V is constant, I = I1 + I2 + ..., 1/Rp = 1/R1 + 1/R2 + ....
• Electromotive Force (emf): For real cells with internal resistance r, ε = I(R + r).

C. Wave Behaviour

C.1 Simple Harmonic Motion (SHM)

• Defining Equation: a = -ω² x. Acceleration is proportional and opposite to displacement.
• Parameters: Period T = 1/f = 2π/ω.
• Systems: Mass-spring system T = 2π√(m/k). Simple pendulum T = 2π√(l/g).
• Energy: Continuous interchange between kinetic and potential energy; total energy remains constant.

C.2 Wave Model

• Characteristics: Waves transfer energy without net displacement of the medium. Includes transverse and longitudinal waves.
• Wave Equation: v = fλ = λ/T.
• Electromagnetic vs Mechanical: Mechanical waves require a medium; EM waves can travel through a vacuum.

C.3 Wave Phenomena

• Behaviours: Reflection, refraction, transmission, and diffraction. Represented using wavefronts and rays.
• Refraction: Snell's Law n1/n2 = sin(θ_2)/sin(θ_1) = v_2/v_1. Includes critical angle and total internal reflection.
• Superposition & Interference: Constructive interference: path difference = nλ. Destructive interference: path difference = (n + 1/2)λ.
• Young's Double Slit: Fringe spacing s = λD / d.

C.4 Standing Waves and Resonance

• Standing Waves: Formed by the superposition of two identical waves traveling in opposite directions. Characterized by nodes (zero amplitude) and antinodes (maximum amplitude).
• Strings & Pipes: Dependent on boundary conditions (fixed/free ends). Able to form various harmonics.
• Resonance & Damping: Driving an oscillator at its natural frequency results in resonance (maximum amplitude). Damping reduces the maximum amplitude and shifts the resonant frequency slightly.

C.5 Doppler Effect

• Principle: Change in observed frequency or wavelength due to relative motion between source and observer.
• Electromagnetic Waves: For speeds much less than c, Δf/f = Δλ/λ ≈ v/c. Applied in determining stellar/galactic velocities via spectral shifts.

D. Fields

D.1 Gravitational Fields

• Newton's Universal Law: F = G m1 m2 / r² for point masses.
• Field Strength (g): Force per unit mass experienced by a test mass: g = F/m = GM / r².
• Orbital Motion: Governed by Kepler's Third Law. The field provides the centripetal force.

D.2 Electric and Magnetic Fields

• Electric Charge: Quantized (Millikan's experiment) and conserved. Like charges repel, opposite charges attract.
• Coulomb's Law: F = k q1 q2 / r², where k = 1 / (4πε_0).
• Electric Field (E): Force per unit positive charge: E = F/q. Uniform field between parallel plates: E = V/d.
• Magnetic Fields: Patterns mapped via magnetic field lines (e.g., around a bar magnet or current-carrying wire).

D.3 Motion in Electromagnetic Fields

• Magnetic Force on Charge: F = qvB sin θ (causes circular motion because force is perpendicular to velocity).
• Magnetic Force on Wire: F = BIL sin θ.
• Force Between Parallel Wires: F/L = μ_0 I1 I2 / (2πr).

E. Nuclear and Quantum Physics

E.1 Structure of the Atom

• Discovery of Nucleus: Geiger-Marsden-Rutherford scattering experiment.
• Nuclear Notation: Standard notation indicating nucleon number (A) and proton number (Z).
• Energy Levels: Emission and absorption spectra provide evidence for discrete atomic energy levels. Photon energy E = hf.

E.3 Radioactive Decay

• Mass and Energy: Mass defect occurs because nuclear mass is less than sum of nucleon masses. E = mc².
• Strong Nuclear Force: Short-range, attractive force binding nucleons.
• Decay Types: Alpha, beta (β-, β+), and gamma decay. Accompanied by neutrinos/antineutrinos (in beta decay). Random and spontaneous process.
• Half-Life: Time taken for half the radioactive nuclei to decay. Relates to activity and count rate.

E.4 Fission

• Nuclear Fission: Splitting of heavy nuclei into lighter products, releasing energy (both spontaneous and neutron-induced).
• Chain Reactions: Sustained in nuclear power plants using control rods, moderators, and heat exchangers.

E.5 Fusion and Stars

• Stellar Stability: Equilibrium between inward gravitational collapse and outward radiation pressure from fusion.
• Conditions for Fusion: Extremely high density and temperature to overcome electrostatic repulsion.
• Stellar Evolution: Mass determines the evolutionary path. The Hertzsprung-Russell (HR) diagram classifies stars (main sequence, giants, white dwarfs) based on luminosity and temperature.
• Distances: Stellar parallax formula d(parsec) = 1 / p(arc-second).