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JEE Advanced · Cheatsheet

Physics Quick Revision

Deep mechanics, EM theorems, waves, thermodynamics & modern insights.

Problem-solving toolkit

Draw FBD; label every force + direction.
Choose smart axes (along incline / motion).
Try conservation (E, p, L) before Newton.
Check limits: g→0, m→∞, μ→0, for sanity.
Dimensional check every formula you derive.

Constraint & pulleys

String inextensible: components of velocities along string equal.
Wedge–block constraint: relative acceleration along contact surface = 0.
Pulley: T same throughout massless string; N = length constraint gives a-relations.

Centre of mass & momentum

COM

Σmᵢrᵢ/Σmᵢ

v_cm

Σmᵢvᵢ/M

a_cm

F_ext/M

Impulse

J = ∫F dt = Δp

Reduced mass

μ = m₁m₂/(m₁+m₂)

Rotation — advanced

τ_ext = dL/dt; L conserved if τ_ext = 0.
Pure rolling: v_cm = Rω, a_cm = Rα.
Rolling on incline a = g sinθ/(1 + I/mR²).
Angular impulse = ΔL.
Precession of top ω_p = τ/L.

Fluid mechanics

Equation of continuity Av = const.
Bernoulli P + ½ρv² + ρgh = const.
Torricelli v = √(2gh).
Viscous force F = ηA(dv/dy).
Reynolds Re = ρvd/η (>2000 turbulent).
Excess P: drop 2T/r; bubble 4T/r.
Capillary rise h = 2T cosθ/(ρgr).

Thermo — deep cuts

For polytropic PVⁿ=const: W = (P₁V₁−P₂V₂)/(n−1).
Free expansion of ideal gas: ΔU=0, W=0, Q=0.
Entropy dS = dQ_rev/T.
For ideal gas ΔS = nCv ln(T₂/T₁) + nR ln(V₂/V₁).
Second law: ΔS_universe ≥ 0.

EM — deep cuts

Gauss E

∮E·dA = q_enc/ε₀

Gauss B

∮B·dA = 0

Ampere

∮B·dl = μ₀I_enc

Faraday

∮E·dl = −dΦ_B/dt

Solenoid B

μ₀nI

Toroid B

μ₀NI/(2πr)

Mutual ind

M = μ₀N₁N₂A/l

AC & LCR

√(R² + (X_L − X_C)²)

tanφ

(X_L − X_C)/R

P_avg

V_rms I_rms cosφ

Q-factor

ω_r L / R = (1/R)√(L/C)

Bandwidth

R/L

Waves & interference

Standing wave: nodes at fixed ends (string); antinodes at open ends (pipe).
String modes: fₙ = n v/2L; pipe open fₙ = n v/2L; pipe closed fₙ = (2n−1)v/4L.
YDSE: β=λD/d; missing orders when d sinθ = mλ and a sinθ = nλ coincide.
Thin film: 2μt cosr = (m+½)λ for constructive reflection.
Newton's rings: r² = mλR (dark), (m+½)λR (bright).
Doppler (light, relativistic): f' = f √((c−v)/(c+v)) receding.

Modern physics — deep

X-rays: characteristic Kα, Kβ (Moseley √ν = a(Z−b)).
Compton effect Δλ = (h/mc)(1−cosθ).
Nuclear BE per nucleon peaks at Fe (56).
Q-value = (Δm)c² = (products − reactants)c².
Radioactive equilibrium: N₁λ₁ = N₂λ₂ (secular).
Meson theory (Yukawa) — strong force via π meson.