PHYSICS FORMULA SPINE WALL CARD: 12 MASTER EQUATIONS

Official Study Room Broadsheet • 3-Tier Architecture • NEET 2027 (180 Compulsory Questions, 2:00–5:00 PM)

THE 12 REFLEX SPINES

TIER 1: THE 12 UNIVERSAL SPINE FORMULAS (INSTANT ZERO-LATENCY RECALL) 12 IRREDUCIBLE TRUNKS

#	Spine Equation	Domain	What It Derives On Demand	[T] [Q] [E]
1	W_net = ΔK	Mechanics	Stopping distance (s = v²/2μg), vertical circle critical speed (v = √5gR), spring compression	[ ] [ ] [ ]
2	F_net = dp/dt ⇒ J = Δp	Mechanics	Rocket propulsion, collision impulse, average force during impact, recoil velocities	[ ] [ ] [ ]
3	E = −dV/dr	Electro / Gravitation	Uniform field V = Ed, point charge potential V = kq/r, dipole potential, conservative field check	[ ] [ ] [ ]
4	L = Iω = const (τ_ext = 0)	Rotational Motion	Kepler areal velocity, collapsing rotating star spin rate, turntable dumbbell jumps	[ ] [ ] [ ]
5	P + ½ρv² + ρgh = const	Fluids	Torricelli efflux velocity v = √(2gh), Venturi pressure differential, siphon tube flow	[ ] [ ] [ ]
6	ΔQ = ΔU + ΔW (dW = PdV)	Thermal Physics	Isothermal work nRT ln(V₂/V₁), adiabatic PV^γ = const, Carnot efficiency η = 1 − T_c/T_h	[ ] [ ] [ ]
7	a = −ω²x ⇒ T = 2π√(m/k)	SHM & Oscillations	Simple pendulum T = 2π√(l/g), U-tube mercury oscillations, LC electrical oscillations ω = 1/√(LC)	[ ] [ ] [ ]
8	I = neAv_d (v_d = eEτ/m)	Current Electricity	Microscopic Ohm law J = σE, resistivity ρ = m/(ne²τ), wire stretching R ∝ l²	[ ] [ ] [ ]
9	F = q(v × B) + qE	Magnetism	Cyclotron radius r = mv/(qB), pitch p = v_\|\|T, velocity selector v = E/B, magnetic force on wire IlB	[ ] [ ] [ ]
10	ε = −dΦ/dt (Φ = B · A)	EMI & AC	Motional EMF ε = Bvl, mutual inductance ε = −M di/dt, self-inductance L = μ₀n²Al	[ ] [ ] [ ]
11	β = λD/d (Δx = d sinθ)	Wave Optics	Angular fringe width θ = λ/d, fringe shifts by mica sheet Δy = (μ−1)tD/d, central maxima position	[ ] [ ] [ ]
12	hν = φ₀ + K_max \| E_n = −13.6 Z²/n²	Modern Physics	de Broglie wavelength λ = h/p = 12.27/√V Å, stopping potential eV₀ = K_max, Rydberg transitions	[ ] [ ] [ ]

DIMENSIONAL SANITY FILTERS (ANTI-BLANK RULES) 3-SEC CHECK

Sound Velocity	v = √(γP/ρ) — Units: [N/m² / (kg/m³)]^1/2 = m/s. (Never flip to ρ/P).
Capacitor vs Resistor	Series: 1/C_s = 1/C₁ + 1/C₂ (Inverted relative to resistors!). Parallel: C_p = C₁ + C₂.
Carnot Temperature	η = 1 − T₂/T₁ — Always in Kelvin (K). Celsius substitution loses 5 marks instantly!
Unit Prefix Traps	cm → m: 10⁻² \| cm² → m²: 10⁻⁴ \| mm → m: 10⁻³ \| μF → F: 10⁻⁶.

Rule: If you doubt a formula denominator, run [M L T] dimensions on scratch paper.

HIGH-RISK BOUNDARY TRAPS (NTA FAVOURITES) MISTAKE FENCES

Solid vs Hollow Sphere	Solid Sphere I = 2/5 MR² \| Hollow Sphere I = 2/3 MR². Circle sphere type with pen!
Circular Coil B-Field	At Center: B = μ₀I / (2R) [No π in denominator!]. Straight wire has 2πr.
Dielectric Insertion	Battery connected: V = const, C × K, Q × K \| Disconnected: Q = const, V / K, C × K.
Angle with Normal vs Surface	Flux Φ = BA cosθ — θ is angle with area normal, not surface plane!

CRITICAL: Never bubble OMR before confirming unit prefixes and boundary condition labels.

THE 4-DAY ROLLING REVISION PROTOCOL (FOR HOSTEL ROOM WALL) 25 MIN DAILY

DAY 1: ENCODE & DUMP
Write 12 Spines on blank paper without looking. Re-derive 4 major anchors.

DAY 2: PROFILE SOLVING
Solve 20 questions chosen from Top 90 Numerical Profiles. Match formula to archetype.

DAY 3: ERROR LOGGING
Tag slips in Learnzy Mistake Notebook. Record One-Line Boundary Rule.

DAY 4: 90-SEC SPEED TEST
Write chapter equations under 90-second timer. If > 4s per formula, recycle to Day 1.