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Physics · common notesQuick study package · 44 pages

Quick study package · prep review

Physics · quick study package

44 content pages · 60–90s per stem · flip or print

Notes hub
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Study package

Physics · quick study package

Depth-upgraded prep review · 60–90s templates · multi-concept ready

  • Advanced Physics is currently lengthiest when Mechanics and Electrodynamics join constraints, fields and circuits. Train cross-topic chains, not isolated formula recall.
  • Mechanics is FBD-plus-constraint; Fluids & Waves is assumptions-plus-boundary; Thermal is path-plus-state; EM is field-law-plus-circuit; Optics & Modern is sign/path/quantum equation. Keep styles separate, then practise deliberate joins.
  • First 15 seconds name every chapter the stem touches and the ask; the next 20–60 seconds only execute known templates. Write one-line reasons for every MC/MATCH statement.
  • Open chapter topic pages for full methods, samples, and families — this hub is the routing layer.
  • This deck pulls live hub banks — re-print after notes depth updates.
  • Flip or print — stay on package until the close checklist.

Full package (44 pages). Use Print package for a desk handout.

01 / 44 · Package

Study package

Physics · quick study package

Depth-upgraded prep review · 60–90s templates · multi-concept ready

  • Advanced Physics is currently lengthiest when Mechanics and Electrodynamics join constraints, fields and circuits. Train cross-topic chains, not isolated formula recall.
  • Mechanics is FBD-plus-constraint; Fluids & Waves is assumptions-plus-boundary; Thermal is path-plus-state; EM is field-law-plus-circuit; Optics & Modern is sign/path/quantum equation. Keep styles separate, then practise deliberate joins.
  • First 15 seconds name every chapter the stem touches and the ask; the next 20–60 seconds only execute known templates. Write one-line reasons for every MC/MATCH statement.
  • Open chapter topic pages for full methods, samples, and families — this hub is the routing layer.
  • This deck pulls live hub banks — re-print after notes depth updates.
  • Flip or print — stay on package until the close checklist.

02 / 44 · Package

How to use

How to use this package (30–60 min)

  • Heavy hub first (Mechanics or EM), then one light hub.
  • On every page: name the model (FBD / energy / field law / path) before formulas.
  • Mark 3 topic cards that scare you — those open tomorrow’s notes pages.
  • Close with 2 timed multi-concept stems from notes or /mixed.

03 / 44 · Subject

Protocol

Physics · master 60–90s protocol

  • 0–15s: name every chapter the stem touches + the ask.
  • Write assumptions (smooth?, e=?, pure rolling?, path?).
  • Execute FBD / field-law / path template only.
  • MC: one-line T/F per option before selecting.

04 / 44 · Mechanics

Hub review

Mechanics · hub overview

Bank ~30–35 /100 Phys (~full Mechanics share) · ~32% of Physics tags (2020–2026)

  • Mechanics full marks = name the model in ≤15s (Newton / energy / COM / rotation / SHM / gravity), then run a fixed FBD–constraint–check template — including multi-concept joins that make Advanced Mechanics lengthy.
  • Mechanics is often ~30%+ of Advanced Physics and the #1 rank separator when rotation and constraints densify. Cover units/errors, kinematics, Newton+friction, work–energy, COM/collisions, rigid body, SHM and gravitation. 100% means named templates (FBD set, energy gate, a=Rα, ẍ+ω²x=0, orbit energy) plus the discipline to combine them under time pressure. Mechanics bank marks come from diagrams and conservation choice, not longer algebra.

05 / 44 · Mechanics

Protocol

Mechanics · timed protocol

  • 0–15s: Name the family: Units-Error / Kinematics / Newton-Friction / Energy / COM-Collision / Rotation / SHM / Gravitation. Circle what is asked (a, T, v, ω, e, E, …) and any constraint (string, no-slip, level ground).
  • 15–35s: Draw FBDs or axes; write governing laws only — no story. State assumptions (smooth?, e=?, pure rolling?, small angle?).
  • 35–75s: Solve the linear system or energy/momentum equations. For MC: compute once, then check each option as T/F against that model.
  • 75–90s: Sanity: units, limiting cases (μ→0, e→1, θ→0), friction ≤ μN if rolling claimed. Bubble and leave — do not re-derive.

06 / 44 · Mechanics

Methods

Mechanics · methods

One FBD per body · Friction threshold first

One FBD per body

  • Applies: Newton, friction, pulleys, wedges
  • Move: Isolate every mass; same T on a light string; write ΣF=ma on chosen axes; add constraint a-links.
  • Why: Stops double-counting forces and invented single-body shortcuts.

Friction threshold first

  • Applies: Static/kinetic, impending motion, rolling check
  • Move: Compute f_needed for the proposed motion; compare with μ_s N before writing sliding equations.
  • Why: Avoids using μ_k when the block never slips.

07 / 44 · Mechanics

Methods

Mechanics · methods

Energy gate before forces · Smart axis + a=Rα

Energy gate before forces

  • Applies: Variable force, springs, loops, heights
  • Move: If only speeds/heights matter, use ΔME = W_nc; reserve Newton for when a or T is asked mid-path.
  • Why: Cuts multi-step force integrations on Advanced energy stems.

Smart axis + a=Rα

  • Applies: Rigid body, rolling, impulse on rods
  • Move: Pick fixed or CM axis; write I; impose rolling constraint or conserve L when external impulse torque is zero.
  • Why: One correct axis replaces messy point-by-point kinetics.

08 / 44 · Mechanics

Methods

Mechanics · methods

Reduce to ẍ+ω²x=0 · Independent T/F on relations

Reduce to ẍ+ω²x=0

  • Applies: SHM, pendulums, torsional systems
  • Move: Write restoring F or τ; cast as ẍ=−ω²x; read T=2π/ω and energy ½mω²A².
  • Why: Avoids solving full DEs when only T, A, or v_max is asked.

Independent T/F on relations

  • Applies: Multi-correct Mechanics + MATCH
  • Move: Each statement is a separate check against your FBD/energy/orbit equation — never force consistency with another option.
  • Why: Protects partial marks; matching stays clean.

09 / 44 · Mechanics

Mental bank

Mechanics · mental bank

  • Projectile (level): R=u²sin2θ/g; T=2u sinθ/g; H=u²sin²θ/(2g)
  • Friction: f_s ≤ μ_s N; kinetic f_k=μ_k N opposite relative velocity
  • W–K: ΔK = W_all; mechanical: Δ(K+U)=W_nc
  • 1D collision: p conserve + e=(v₂−v₁)/(u₁−u₂)
  • Rolling no slip: a=Rα; K=½mv²+½Iω²; a=g sinθ/(1+I/mR²) on incline
  • SHM: ω=√(k/m); E=½kA²; v=ω√(A²−x²)
  • Orbit: v=√(GM/r); E=−GMm/(2r); v_esc=√(2GM/r)
  • Error: for f=xᵃyᵇ, δf/f = |a|δx/x + |b|δy/y
  • FBD + axes before equations
  • Energy bookkeeping: W_nc = ΔE_mech
  • Rolling: a = Rα only with the right contact story

10 / 44 · Mechanics

Topic cards

Mechanics · topic cards

Units · Errors · Kinematics · Projectiles · Newton · Friction · Work–Energy · Power

Units · Errors · Kinematics · Projectiles (Base + every-year kinematics)

  • Trigger: See dimensions/% error/vernier or a–t/projectile → dimension table or axes first.
  • Step: Units: write [ ] for each symbol; equate powers.
  • Step: Errors: logarithmic differential of the working formula.
  • Step: Kinematics: piecewise integrate; match v,x at junctions.
  • Step: Projectile: choose ground or incline axes; apply landing condition.
  • Automate: Relative-error powers
  • Automate: Vernier/screw least count
  • Automate: R, T, H and incline-range forms
  • Trap: Reporting more digits than limiting significant figures
  • Trap: Mixing horizontal and incline-axis formulas
  • Drill: Daily: 1 error NUM + 1 projectile/relative-velocity stem

Newton · Friction · Work–Energy · Power (High every-year)

  • Trigger: See blocks/pulleys/μ or spring/loop → FBD set or energy gate.
  • Step: Draw one FBD per body; mark constraints.
  • Step: Friction: f_need vs μN before choosing static/kinetic.
  • Step: If only speed/height: energy; if T or a mid-path: Newton.
  • Step: Power: P=F·v instantaneous; average ΔW/Δt.
  • Automate: Connected-body a and T in ≤40s
  • Automate: Pseudo-force in uniformly accelerating frames
  • Automate: Loop critical speeds and spring–friction stops
  • Trap: Using kinetic friction before checking impending motion
  • Trap: Forgetting nonconservative work in energy statements
  • Drill: Daily: 1 multi-body Newton + 1 energy NUM

11 / 44 · Mechanics

Topic cards

Mechanics · topic cards

COM · Collisions · Rigid Body · SHM · Oscillations · Gravitation

COM · Collisions · Rigid Body (Highest Mechanics yield)

  • Trigger: See collision/e or rolling/rod impulse → momentum+e or axis+I.
  • Step: COM: track R_cm and P_cm = M V_cm; only F_ext changes P_cm.
  • Step: Collision: n–t axes; p along normal + e; tangential if smooth.
  • Step: Rotation: choose axis; I; Στ=Iα or L conserve.
  • Step: Rolling: a=Rα then verify f≤μN.
  • Automate: Elastic 1D final speeds
  • Automate: Parallel/perpendicular axis shifts
  • Automate: Pure-rolling acceleration on incline
  • Trap: Conserving energy in clearly inelastic sticks
  • Trap: Wrong I about the chosen axis
  • Trap: Claiming pure rolling without friction check
  • Drill: Daily: 1 collision + 1 rolling/angular-momentum stem

SHM · Oscillations · Gravitation (High — recurring numerical)

  • Trigger: See spring/pendulum or satellite/escape → ω from restoring law or GM/r.
  • Step: SHM: write restoring law → ω → T, A, energy.
  • Step: Angular/torsional: τ=−κθ → ω=√(κ/I).
  • Step: Gravity: classify r≷R for sphere/shell; write E,V.
  • Step: Orbits: force balance or E=−GMm/(2a); compare escape.
  • Automate: Vertical spring period with mg shift
  • Automate: Energy at intermediate SHM position
  • Automate: Circular orbit v, T, E and transfer ΔE
  • Trap: Using sinθ≈θ outside small-angle stems
  • Trap: Applying outside-sphere formulas inside a shell
  • Drill: Alt days: SHM NUM / orbit energy NUM

12 / 44 · Fluids · Waves

Hub review

Fluids & Waves · hub overview

Bank ~10–14 /100 Phys (~full Fluids+Waves share) · ~12% of Physics tags (fluids ~2% + waves/SHM-sound ~10%, 2020–2026)

  • Fluids & Waves full marks = state assumptions and boundaries in ≤15s, then run Bernoulli/continuity, modulus, or standing-wave/Doppler templates inside 60–90 seconds.
  • This portion is fluid statics/dynamics, elasticity/surface tension, and waves & sound. 100% means you stamp ideal/incompressible for Bernoulli, drop vs soap for ΔP, and nodes/antinodes before harmonics — never invent a formula mid-stem. Fluids & Waves reward assumption honesty and boundary clarity.

13 / 44 · Fluids · Waves

Protocol

Fluids & Waves · timed protocol

  • 0–15s: Classify: hydrostatic/buoyancy, Bernoulli/continuity, viscosity/terminal, elasticity/surface, progressive/standing wave, beats, Doppler. Mark densities, open/closed ends, and what is asked.
  • 15–35s: Write assumptions (steady, inviscid, incompressible) or boundary sketch (nodes/antinodes). Pick the governing equation set only.
  • 35–75s: Execute template: P=ρgh + Archimedes, Bernoulli+continuity, Y/B/η definitions, f_n from boundaries, or Doppler with a fixed sign convention.
  • 75–90s: Check gauge vs absolute pressure, drop vs soap surfaces, open vs closed harmonic set, Doppler signs. Bubble.

14 / 44 · Fluids · Waves

Methods

Fluids & Waves · methods

Pressure map + buoyancy FBD · Assumptions → continuity → Bernoulli

Pressure map + buoyancy FBD

  • Applies: Hydrostatics, floating, apparent weight
  • Move: Write P at key depths; draw weight and buoyant force = weight of displaced fluid; solve immersed fraction.
  • Why: Replaces density folklore with one equilibrium equation.

Assumptions → continuity → Bernoulli

  • Applies: Venturi, Torricelli, streamline speed/pressure
  • Move: State ideal steady incompressible; A₁v₁=A₂v₂; then P+ρgh+½ρv² between two points.
  • Why: Stops mixing viscous losses into ideal Bernoulli stems.

15 / 44 · Fluids · Waves

Methods

Fluids & Waves · methods

Modulus definition first · Boundary sketch for standing waves

Modulus definition first

  • Applies: Y, bulk, shear, elastic energy
  • Move: Identify which modulus; write stress/strain ratio; add ½ factor only for gradual loading energy.
  • Why: Prevents Y/B/η formula swaps under time pressure.

Boundary sketch for standing waves

  • Applies: Strings, organ pipes, resonance
  • Move: Mark nodes/antinodes from end conditions; write allowed λ_n; then f=v/λ with v=√(T/μ) or sound speed.
  • Why: Closed-pipe odd-harmonic mistakes die at the sketch.

16 / 44 · Fluids · Waves

Methods

Fluids & Waves · methods

One Doppler sign convention · Independent T/F

One Doppler sign convention

  • Applies: Moving source/observer, wind, reflection
  • Move: Write f′=f(v±v_o)/(v±v_s) with signs stated once; for echoes apply Doppler twice.
  • Why: Sign chaos is the #1 Doppler time sink.

Independent T/F

  • Applies: Multi-correct Fluids & Waves
  • Move: Prove each statement from the stamped assumptions or boundary conditions — never from another option.
  • Why: Protects clusters of marks on wave MC.

17 / 44 · Fluids · Waves

Mental bank

Fluids & Waves · mental bank

  • Hydrostatic: P=P₀+ρgh; buoyant force = ρ_fluid V_imm g
  • Bernoulli: P+ρgh+½ρv² = const (ideal streamline)
  • Continuity: A₁v₁=A₂v₂ (incompressible)
  • Stokes terminal: 6πηrv = (ρ−σ)V g
  • ΔP drop = 2σ/r; soap bubble = 4σ/r; capillary h=2σ cosθ/(ρgr)
  • Y=(F/A)/(ΔL/L); U=½ F ΔL for gradual load
  • String fixed ends: f_n = n v/(2L); closed pipe: odd harmonics
  • Doppler: f′=f(v±v_o)/(v±v_s); beats |f₁−f₂|
  • Bernoulli assumptions spoken first
  • Open/closed pipe harmonics from boundary
  • Doppler: which source/observer moves

18 / 44 · Fluids · Waves

Topic cards

Fluids & Waves · topic cards

Fluid Mechanics · Properties of Matter · Surface Tension

Fluid Mechanics (Lower frequency — high conversion if templated)

  • Trigger: See pressure/float/Venturi/viscosity → hydrostatic FBD or Bernoulli assumptions.
  • Step: Statics: pressure map + Archimedes FBD.
  • Step: Dynamics: stamp assumptions; continuity; Bernoulli.
  • Step: Viscosity: weight = buoyancy + Stokes drag at terminal speed.
  • Step: MC: check gauge/absolute and ideal-flow claims separately.
  • Automate: Fraction submerged = ρ_body/ρ_liquid (floating)
  • Automate: Torricelli v=√(2gh) with surface-speed caveat
  • Automate: Terminal velocity force balance
  • Trap: Using Bernoulli through a viscous valve without stating loss
  • Trap: Wrong displaced volume for partially immersed bodies
  • Drill: 3×/week: 1 buoyancy + 1 Bernoulli NUM

Properties of Matter · Surface Tension (Medium — elasticity + capillarity)

  • Trigger: See wire stretch, ΔV, shear, drop/bubble, capillary → modulus or surface count.
  • Step: Identify Y vs B vs η.
  • Step: Write defining ratio; solve ΔL, ΔV, or θ.
  • Step: Surface: drop (2σ/r) vs soap (4σ/r); capillary with cosθ.
  • Step: Energy: include ½ for elastic; γΔA for surface.
  • Automate: Y numerical with area in m²
  • Automate: Bulk modulus from % volume change
  • Automate: Drop vs soap excess pressure
  • Trap: Soap counted as one surface
  • Trap: Thermal–elastic mismatch solved without length constraint
  • Drill: Weekly: 2 modulus + 1 capillarity/surface stem

19 / 44 · Fluids · Waves

Topic cards

Fluids & Waves · topic cards

Waves & Sound

Waves & Sound (High inside this portion)

  • Trigger: See y(x,t), harmonics, beats, Doppler → match form or boundary sketch.
  • Step: Progressive: read A, ω, k, direction; v=ω/k.
  • Step: Standing: boundaries → λ_n → f_n.
  • Step: Beats: |f₁−f₂|; amplitude bounds if asked.
  • Step: Doppler: fix signs; double application for reflection.
  • Automate: Open vs closed pipe spectra
  • Automate: End correction elimination via successive resonances
  • Automate: Doppler echo / moving-wall pattern
  • Trap: Even harmonics on a closed pipe
  • Trap: Inconsistent Doppler signs between echo legs
  • Drill: Daily: 1 standing-wave + 1 Doppler/beats stem

20 / 44 · Thermal

Hub review

Thermal Physics · hub overview

Bank ~10–14 /100 Phys (~full Thermal share) · ~12% of Physics tags (2020–2026)

  • Thermal full marks = label the process or heat path in ≤15s, then run expansion/calorimetry, kinetic averages, first-law cycle, or radiation templates inside 60–90 seconds.
  • Thermal in Advanced is expansion/calorimetry/conduction, kinetic theory, thermodynamics cycles, and radiation. 100% means path before w/q, phase-feasible calorimetry, and kelvin before T⁴ — never start from a random formula. Thermal full marks are process labels + correct state variables.

21 / 44 · Thermal

Protocol

Thermal Physics · timed protocol

  • 0–15s: Name the family: Expansion / Calorimetry / Kinetic / First-law process / Cycle / Conduction / Radiation/Wien. Circle T units and what is asked (Q, W, ΔU, η, H, λ_max).
  • 15–35s: Stamp path (isochoric/isobaric/isothermal/adiabatic) or phase hypothesis; write governing relations only (ΔU=nC_vΔT, ΣQ=0, R=L/(kA), σAT⁴).
  • 35–75s: Plug carefully; for cycles fill a leg table and verify ΣΔU=0; for radiation convert °C→K before powers.
  • 75–90s: Sanity: sign convention, Carnot bound, phase feasibility, kelvin check. Bubble.

22 / 44 · Thermal

Methods

Thermal Physics · methods

Path label before w and q · Phase-feasible calorimetry

Path label before w and q

  • Applies: Ideal-gas first-law numericals
  • Move: Name the process; ΔU=nC_vΔT always; then path rule for w; q from first law with the paper’s sign convention.
  • Why: Stops using isothermal w on isochoric stems.

Phase-feasible calorimetry

  • Applies: Ice/steam mixtures, latent heat
  • Move: Guess final phase; write ΣQ=0 with mcΔT and mL; reject roots outside the assumed range.
  • Why: Avoids long wrong algebra after an impossible T_f.

23 / 44 · Thermal

Methods

Thermal Physics · methods

Mole-weighted kinetic averages · Cycle leg table

Mole-weighted kinetic averages

  • Applies: Mixtures, C_v, γ, partial pressures
  • Move: Average C_v (and M) by moles; never average γ linearly; Dalton for partial pressures.
  • Why: Mixture MC dies without expanding every molecule story.

Cycle leg table

  • Applies: PV loops, engines, refrigerators
  • Move: List each process’s ΔU, W, Q; sum; η=W_net/Q_in only (heat absorbed).
  • Why: Prevents counting |Q_out| inside efficiency.

24 / 44 · Thermal

Methods

Thermal Physics · methods

Thermal resistance network · Kelvin before T⁴ / Wien

Thermal resistance network

  • Applies: Composite slabs, steady conduction
  • Move: R=L/(kA); series add R; parallel add conductances; H=ΔT/R_eq.
  • Why: Turns layered-wall stems into circuit algebra.

Kelvin before T⁴ / Wien

  • Applies: Stefan, Newton cooling, λ_max T=b
  • Move: Convert temperatures; use net σA(T⁴−T₀⁴) when surroundings matter; keep Wien separate from Stefan.
  • Why: Celsius-in-T⁴ is the classic radiation trap.

25 / 44 · Thermal

Mental bank

Thermal Physics · mental bank

  • ΔL=LαΔT; γ≈3α; thermal stress ≈ YαΔT if fully constrained
  • Ideal gas: PV=nRT; ΔU=nC_vΔT
  • C_v=(f/2)R; C_p=C_v+R; γ=1+2/f
  • Isothermal reversible: w=−nRT ln(V₂/V₁) (paper sign)
  • Adiabatic: PV^γ, TV^{γ−1}; q=0
  • Carnot: η=1−T_C/T_H (kelvin)
  • v_rms=√(3RT/M); P=(1/3)ρ v_rms²
  • H=kAΔT/L; P_net=eσA(T⁴−T₀⁴); λ_max T=b
  • Lock sign convention for first law
  • Ideal-gas ΔU depends on T only
  • Carnot is a bound, not a default engine

26 / 44 · Thermal

Topic cards

Thermal Physics · topic cards

Thermal Properties · Calorimetry · Conduction · Kinetic Theory · Thermodynamics

Thermal Properties · Calorimetry · Conduction (Medium–High)

  • Trigger: See gap/α, mixture/latent, or composite slab → expansion law, ΣQ=0, or R network.
  • Step: Expansion: free vs constrained; include vessel for liquids.
  • Step: Calorimetry: phase hypothesis → ΣQ=0 → feasibility check.
  • Step: Conduction: draw R=L/(kA); combine; H=ΔT/R.
  • Step: Electrical heating: VIt = mcΔT when relevant.
  • Automate: Apparent expansion of liquid in vessel
  • Automate: Ice–water–steam heat accounting
  • Automate: Series slab interface temperature
  • Trap: Latent heat applied away from the phase-change temperature
  • Trap: Parallel slabs treated as series resistances
  • Drill: Daily: 1 calorimetry or expansion + 1 conduction stem

Kinetic Theory · Thermodynamics (Highest Thermal yield)

  • Trigger: See v_rms/C_v or w/q/cycle → f→C_v or path label.
  • Step: Kinetic: identify which speed; use √(RT/M) factor; mixture by moles.
  • Step: First law: path → ΔU → w → q.
  • Step: Adiabatic/polytropic: correct invariant.
  • Step: Cycle: leg table; η vs Carnot bound.
  • Automate: Mono/dia C_v, C_p, γ
  • Automate: Isochoric/isobaric/isothermal/adiabatic quick set
  • Automate: Carnot η and refrigerator COP definitions
  • Trap: Averaging γ of a mixture linearly
  • Trap: Using °C in Carnot formula
  • Trap: Efficiency with |Q_cold| in the denominator
  • Drill: Daily: 1 kinetic ratio + 1 first-law/cycle NUM

27 / 44 · Thermal

Topic cards

Thermal Physics · topic cards

Heat Transfer · Radiation

Heat Transfer · Radiation (Medium — easy if kelvin-safe)

  • Trigger: See cooling rate, Stefan, Wien → net T⁴ or λ_max T=b.
  • Step: Newton cooling: θ=T−T₀; exponential fit.
  • Step: Stefan: kelvin; net power if enclosure given.
  • Step: Wien: λ_max T=b independent of Stefan power.
  • Step: MC: separate spectral peak from total power claims.
  • Automate: Net Stefan numerical
  • Automate: Wien temperature from peak shift
  • Automate: e factor on power only (not on Wien b)
  • Trap: Forgetting surroundings temperature in net radiation
  • Trap: Using Wien to replace Stefan
  • Drill: 3×/week: 1 Stefan + 1 Wien/cooling stem

28 / 44 · EM

Hub review

Electromagnetism · hub overview

Bank ~22–28 /100 Phys (~full EM share) · ~24% of Physics tags (electro ~11% + current ~3% + mag/EMI/AC ~10%, 2020–2026)

  • EM full marks = pick the field law or circuit constraint in ≤15s (Gauss / superposition / Kirchhoff / Faraday / phasor), then execute — Advanced Electrodynamics is often the longest Physics block.
  • EM spans electrostatics+Gauss+capacitance, current electricity, magnetism, EMI, and AC/EM waves (~20–25% of Advanced Physics in recent papers). 100% means symmetry before Gauss, battery-vs-isolated before dielectrics, Lenz before |ε|, and one impedance triangle for LCR — plus the stamina for multi-step field–circuit joins. EM speed is choosing the right language (E, V, Φ, circuit) in the first 15s.

29 / 44 · EM

Protocol

Electromagnetism · timed protocol

  • 0–15s: Classify: E/V superposition, Gauss, capacitor/dielectric, resistor network, Biot/Ampere/Lorentz, Faraday/motional, LR/RC transient, LCR/EM wave. Circle fixed Q vs fixed V and what is asked.
  • 15–35s: Write the governing law only: superposition, Φ=q_enc/ε₀, C=κC₀, KVL/KCL, B law, ε=−dΦ/dt, Z=√[R²+(X_L−X_C)²].
  • 35–75s: Compute with directions (right-hand, Lenz). For MC: independent T/F against the same law. For LCR: one phasor triangle yields I, φ, P.
  • 75–90s: Sanity: conductor E=0 inside, series capacitor Q same, Lenz opposes change, rms vs peak. Bubble.

30 / 44 · EM

Methods

Electromagnetism · methods

Vector E, scalar V · Symmetry → Gauss surface

Vector E, scalar V

  • Applies: Point charges, dipoles, conductors
  • Move: Superpose E as vectors and V as scalars with a fixed reference; use conductor rules (E=0 inside, V constant).
  • Why: Kills component and reference mistakes early.

Symmetry → Gauss surface

  • Applies: Line, sheet, sphere, shell, uniform ρ
  • Move: Name symmetry; pick Gaussian surface; only q_enc enters; solve E from Φ.
  • Why: Avoids Biot-style integrals on high-symmetry electrostatics.

31 / 44 · EM

Methods

Electromagnetism · methods

Battery vs isolated dielectric · Loop currents + internal r

Battery vs isolated dielectric

  • Applies: Capacitance, energy, slab insertion
  • Move: Connected: V fixed, Q→κQ; isolated: Q fixed, V→V/κ for full fill; recompute U.
  • Why: Wrong constraint is the #1 capacitor trap.

Loop currents + internal r

  • Applies: Kirchhoff networks, cell packs
  • Move: Assign loop currents; write KVL with Ir; reduce series/parallel packs before load.
  • Why: Turns spaghetti circuits into a small linear system.

32 / 44 · EM

Methods

Electromagnetism · methods

Flux then Lenz · One LCR phasor triangle

Flux then Lenz

  • Applies: EMI, motional emf, inductance
  • Move: Write Φ(t) or Bℓv; get |ε|; fix direction with Lenz before I=ε/R.
  • Why: Direction MC resolves without redoing magnitude.

One LCR phasor triangle

  • Applies: Series LCR, power factor, resonance
  • Move: Compute X_L, X_C; Z and φ; I₀=V₀/Z; P=V_rms I_rms cosφ.
  • Why: One diagram answers amplitude, phase, and power together.

33 / 44 · EM

Mental bank

Electromagnetism · mental bank

  • E point: kq/r²; V: kq/r; dipole axial ≈ 2kp/r³; U=−p·E
  • Gauss: ∮E·dA = q_enc/ε₀; line E=λ/(2πε₀r); sheet σ/(2ε₀)
  • C=ε₀A/d; series 1/C=Σ1/C_i; U=½CV²=Q²/(2C)
  • Ohm + Kirchhoff; shunt S=I_g G/(I−I_g)
  • Long wire B=μ₀I/(2πa); F=q(v×B); F=I ℓ×B
  • ε=−dΦ/dt; motional ε=Bℓv (⊥); U=½LI²
  • Z=√[R²+(X_L−X_C)²]; cosφ=R/Z; resonance X_L=X_C
  • EM wave: c=1/√(μ₀ε₀); E/B=c in vacuum
  • Symmetry gate before Gauss
  • Kirchhoff: mark currents and loop directions
  • ε = −dΦ/dt with Lenz direction spoken

34 / 44 · EM

Topic cards

Electromagnetism · topic cards

Electrostatics · Gauss · Capacitance · Current Electricity

Electrostatics · Gauss · Capacitance (High (~11% electro share))

  • Trigger: See charges/E/V, symmetry flux, or capacitor/κ → superposition, Gauss, or Q/V constraint.
  • Step: Discrete charges: superpose E and V.
  • Step: Symmetry: Gaussian surface → E.
  • Step: Capacitor network: reduce C_eq; back-substitute Q,V.
  • Step: Dielectric: stamp battery vs isolated; apply κ.
  • Automate: Dipole τ and U in uniform E
  • Automate: Classic Gauss trio (line, sheet, sphere)
  • Automate: Series–parallel C and dielectric energy change
  • Trap: Using Gauss without sufficient symmetry
  • Trap: Isolated capacitor treated as constant V
  • Drill: Daily: 1 E/V or Gauss + 1 capacitor stem

Current Electricity (Medium (~3%) — quick bank)

  • Trigger: See network, cells, heating, galvanometer → R_eq or loop currents.
  • Step: Simplify series/parallel to R_eq.
  • Step: Multi-loop: KVL with internal r.
  • Step: Cell packs: reduce emf and r first.
  • Step: Instruments: shunt vs multiplier formula.
  • Automate: Two-loop Kirchhoff in ≤90s
  • Automate: Terminal voltage with internal r
  • Automate: Galvanometer → ammeter/voltmeter
  • Trap: Ignoring internal resistance
  • Trap: Power with peak instead of rms in AC crossover stems
  • Drill: Alt days: 2 network NUM

35 / 44 · EM

Topic cards

Electromagnetism · topic cards

Magnetism · EMI · AC · EM Waves

Magnetism · EMI · AC · EM Waves (High (~10%))

  • Trigger: See B field/force, changing flux, or LCR → Biot/Ampere, Faraday+Lenz, or phasor.
  • Step: Magnetism: choose Biot vs Ampere; right-hand direction; F=q(v×B) or Iℓ×B.
  • Step: EMI: Φ(t) → |ε| → Lenz → I.
  • Step: Transients: τ=L/R or RC; match continuity.
  • Step: AC: X_L, X_C, Z, φ, P_avg; EM wave relation set.
  • Automate: Wire/loop/solenoid B formulas
  • Automate: Motional emf on rails
  • Automate: Series LCR numerical + power factor
  • Trap: Lenz direction opposite the physical opposition
  • Trap: Using X_L+X_C instead of X_L−X_C
  • Trap: Averaging power without cosφ
  • Drill: Daily: 1 B/force or EMI + 1 LCR/EM-wave stem

36 / 44 · Optics · Modern

Hub review

Optics & Modern Physics · hub overview

Bank ~18–22 /100 Phys (~full Optics+Modern share) · ~20% of Physics tags (optics ~13% + modern ~7%, 2020–2026)

  • Optics & Modern full marks = stamp sign convention or path difference / quantum equation in ≤15s, then finish ray, YDSE, photoelectric, Bohr, X-ray, or nuclear templates — including concept-driven Modern blends.
  • This portion is ray optics, wave optics (YDSE-only interference), photoelectric/Bohr, X-rays/matter waves, and nuclear. Advanced Optics punishes silent sign flips; Modern is often tricky rather than lengthy. 100% means one sign convention per ray solution, path difference before intensity, Einstein before graphs, MeV conversion before nuclear arithmetic, and refusal of out-of-syllabus interference setups. Optics & Modern rewards convention locks and unit discipline.

37 / 44 · Optics · Modern

Protocol

Optics & Modern Physics · timed protocol

  • 0–15s: Classify: mirror/lens/prism, YDSE/slab/diffraction/polarisation, photoelectric/Bohr, X-ray/de Broglie, decay/BE/Q-value. Circle signs, λ, V, Z, and the ask.
  • 15–35s: Stamp sign convention or write Δ path / Einstein / E_n / λ_min / decay law. No option reading yet for MC.
  • 35–75s: Execute imaging chain, fringe shift, K_max=hν−φ, level ΔE, Duane–Hunt, or N=N₀e^{−λt}. Independent T/F on statements.
  • 75–90s: Check real/virtual sign, bright/dark condition, threshold vs intensity, u↔MeV, α/β ΔA ΔZ. Bubble.

38 / 44 · Optics · Modern

Methods

Optics & Modern Physics · methods

Sign convention once · Path difference first

Sign convention once

  • Applies: Mirrors, thin lenses, combinations
  • Move: State Cartesian (or New Cartesian) signs once; apply 1/v−1/u=1/f (lens) or mirror form; m=−v/u; chain images.
  • Why: Most optics errors are sign flips, not concept gaps.

Path difference first

  • Applies: YDSE, slab, thin-film style path inserts
  • Move: Write Δ; φ=2πΔ/λ; β=λD/d; slab OPD=(μ−1)t → fringe shift ΔN=OPD/λ.
  • Why: Intensity formulas without Δ are dead ends.

39 / 44 · Optics · Modern

Methods

Optics & Modern Physics · methods

Einstein then graph · Level difference for Bohr

Einstein then graph

  • Applies: Photoelectric numericals and graphs
  • Move: K_max=hc/λ−φ; eV₀=K_max; separate intensity→i_sat from frequency→K_max.
  • Why: Stops reading graphs before the equation.

Level difference for Bohr

  • Applies: Hydrogenic spectra
  • Move: E_n=−13.6 Z²/n²; photon = |E_i−E_f|; λ=hc/|ΔE|.
  • Why: Avoids treating a single level energy as the photon energy.

40 / 44 · Optics · Modern

Methods

Optics & Modern Physics · methods

Cutoff vs characteristic · Decay / mass-defect units

Cutoff vs characteristic

  • Applies: X-rays; de Broglie
  • Move: λ_min=hc/eV from tube voltage; characteristic from Z/Moseley; matter waves λ=h/p.
  • Why: Prevents mixing continuous cutoff with Kα claims.

Decay / mass-defect units

  • Applies: Radioactivity, BE, fission/fusion
  • Move: T½↔λ; exponential for N or A; Δm in u ×931.5 → MeV; balance A,Z for Q.
  • Why: Unit chaos is the main nuclear time sink.

41 / 44 · Optics · Modern

Mental bank

Optics & Modern Physics · mental bank

  • Mirror/lens: 1/v−1/u=1/f (watch sign convention); m=−v/u
  • Thin prism: δ=(μ−1)A; μ=sin((A+δ_m)/2)/sin(A/2)
  • YDSE: β=λD/d; bright d sinθ=mλ
  • Single slit minima: a sinθ=mλ; Brewster μ=tan i_p; Malus I=I₀ cos²θ
  • Photoelectric: K_max=hν−φ; V₀=K_max/e
  • Bohr: E_n=−13.6 Z²/n² eV; L=nħ
  • X-ray: λ_min=hc/eV; de Broglie λ=h/p
  • Decay: N=N₀ e^{−λt}; T½=ln2/λ; 1 u ↔ 931.5 MeV
  • Mirror/lens sign convention written once per page
  • YDSE: path difference → fringe shift templates
  • Photoelectric: K_max = hf − φ in consistent units

42 / 44 · Optics · Modern

Topic cards

Optics & Modern Physics · topic cards

Ray Optics · Wave Optics

Ray Optics (High inside optics)

  • Trigger: See mirror/lens/prism/TIR → stamp signs or Snell/critical angle.
  • Step: Draw sketch; assign signed u,v,f.
  • Step: Apply formula; find m.
  • Step: Combinations: image of first = object of second.
  • Step: Prism/TIR: thin δ or i_c=sin⁻¹(μ₂/μ₁).
  • Automate: Concave/convex mirror numerical
  • Automate: Thin-lens and silvered-lens combinations
  • Automate: Thin-prism deviation
  • Trap: Changing sign convention mid-solution
  • Trap: Virtual-object cases mishandled in combinations
  • Drill: Daily: 1 mirror/lens + 1 prism/TIR stem

Wave Optics (High — YDSE heavy)

  • Trigger: See fringes, slab, diffraction, polariser → path difference or Malus/Brewster.
  • Step: YDSE: Δ → β or position of fringe.
  • Step: Slab: OPD=(μ−1)t → shift.
  • Step: Single slit: a sinθ=mλ for minima.
  • Step: Polarisation: Malus chain or μ=tan i_p.
  • Automate: Fringe width numerical
  • Automate: Fringe shift with slab
  • Automate: Brewster angle
  • Trap: Confusing YDSE β with single-slit central width
  • Trap: Wrong direction of fringe shift
  • Drill: Daily: 1 YDSE + 1 diffraction/polarisation stem

43 / 44 · Optics · Modern

Topic cards

Optics & Modern Physics · topic cards

Modern Physics · Nuclear

Modern Physics · Nuclear (~7% modern + nuclear bank)

  • Trigger: See photo/Bohr, X-ray/λ, decay/BE → Einstein, Duane–Hunt, or exponential.
  • Step: Photoelectric: convert λ; K_max; V₀; intensity vs frequency split.
  • Step: Bohr: level difference → λ.
  • Step: X-ray/matter: λ_min or λ=h/p; Moseley if Z.
  • Step: Nuclear: decay law or Δm→MeV; balance reaction for Q.
  • Automate: Photoelectric graph reads
  • Automate: H-like transition energy
  • Automate: Activity after time t
  • Trap: Intensity changing K_max
  • Trap: Cutoff ascribed to target Z
  • Trap: Missing 931.5 MeV/u conversion
  • Drill: Alt days: photoelectric/Bohr / nuclear+X-ray NUM

44 / 44 · Close

Checklist

Physics package · close checklist

  • I can separate Mechanics / Fluids·Waves / Thermal / EM / Optics·Modern styles.
  • I check a=Rα only with pure rolling / stated link.
  • YDSE stays YDSE — no out-of-syllabus interference inventing.
  • Tomorrow: one join drill (rotation+constraint or EMI+circuit).

After this package: open Physics notes notes only for weak marked pages, or drill /mixed. Directions without content pages do not move marks.