Physics Quick Notes - JEE/NEET Essential Concepts

📋 Introduction

These physics quick notes contain essential concepts, formulas, and key points for rapid revision before JEE Advanced and NEET exams. Focus on understanding the concepts and their applications.

⚛️ Mechanics

Kinematics

🎯 Key Formulas:
v = u + at
s = ut + ½at²
v² = u² + 2as

💡 Important Points:
- Always specify coordinate system
- Sign convention crucial for vectors
- Graphical analysis: slope = velocity, area = displacement
- Relative velocity: v_AB = v_A - v_B

📌 Projectile Motion:
- Time of flight: T = 2u sin θ/g
- Range: R = u² sin 2θ/g
- Maximum height: H = u² sin²θ/2g
- Equation: y = x tan θ - (gx²/2u²cos²θ)

⚠️ Common Mistakes:
- Mixing up sign conventions
- Forgetting to resolve vectors
- Not checking units

Newton’s Laws

🎯 Key Formulas:
F = ma (second law)
F_AB = -F_BA (third law)

💡 Important Points:
- Free body diagrams essential
- Identify all forces acting
- Use proper sign convention
- Check equilibrium conditions

📌 Friction:
- Static: f_s ≤ μ_s N
- Kinetic: f_k = μ_k N
- Angle of friction: tan θ = μ
- Banking: tan θ = v²/rg

⚠️ Common Mistakes:
- Missing normal force calculations
- Wrong friction direction
- Not considering all forces

Work, Energy and Power

🎯 Key Formulas:
W = F·d·cosθ
KE = ½mv²
PE = mgh
Power = Work/time

💡 Important Points:
- Work-energy theorem: W_net = ΔKE
- Conservation of energy
- Power = F·v (instantaneous)
- Efficiency = Output/Input

📌 Collisions:
- Elastic: KE conserved
- Inelastic: KE not conserved
- Coefficient of restitution: e = (v₂ - v₁)/(u₁ - u₂)

⚠️ Common Mistakes:
- Sign errors in work calculations
- Missing potential energy terms
- Not considering friction losses

Rotational Motion

🎯 Key Formulas:
ω = v/r = 2π/T
τ = Iα
L = Iω

💡 Important Points:
- Parallel axis theorem: I = I_cm + Md²
- Perpendicular axis theorem: I_z = I_x + I_y
- Rolling without slipping: v = ωR
- Conservation of angular momentum

📌 Common Moments of Inertia:
- Ring: MR²
- Disk: MR²/2
- Sphere: 2MR²/5
- Rod (center): ML²/12

⚠️ Common Mistakes:
- Wrong moment of inertia values
- Not using parallel axis theorem correctly
- Confusing linear and angular quantities

Gravitation

🎯 Key Formulas:
F = Gm₁m₂/r²
g = GM/r²
v_orbital = √(GM/r)
v_escape = √(2GM/r)

💡 Important Points:
- Gravitational force always attractive
- Potential energy is negative
- Escape velocity independent of mass
- Kepler's laws from Newton's laws

📌 Orbital Mechanics:
- Period: T = 2π√(r³/GM)
- Energy: E = -GMm/(2r)
- Angular momentum: L = m√(GMr)

⚠️ Common Mistakes:
- Wrong sign conventions
- Confusing orbital and escape velocities
- Not using correct distance from center

🔥 Thermodynamics

Heat and Temperature

🎯 Key Formulas:
Q = mcΔT
Q = mL (latent heat)
PV = nRT

💡 Important Points:
- Heat flows from hot to cold
- Temperature measures average KE
- Specific heat varies with substance
- Latent heat during phase change

📌 Gas Laws:
- Boyle's: P₁V₁ = P₂V₂
- Charles's: V₁/T₁ = V₂/T₂
- Ideal gas: PV = nRT

⚠️ Common Mistakes:
- Confusing heat and temperature
- Wrong specific heat values
- Not considering latent heat

Laws of Thermodynamics

🎯 Key Formulas:
ΔU = Q - W (first law)
ΔS ≥ 0 (second law)
W = ∫PdV

💡 Important Points:
- Internal energy depends only on state
- Entropy measures disorder
- Work done by system positive
- Heat into system positive

📌 Processes:
- Isothermal: ΔT = 0, W = nRT ln(V₂/V₁)
- Adiabatic: Q = 0, PV^γ = constant
- Isochoric: W = 0, ΔU = Q
- Isobaric: P = constant, W = PΔV

⚠️ Common Mistakes:
- Wrong sign conventions
- Confusing heat and work
- Not using correct process formulas

⚡ Electromagnetism

Electrostatics

🎯 Key Formulas:
F = kq₁q₂/r²
E = F/q = kQ/r²
V = kQ/r
C = ε₀A/d

💡 Important Points:
- Electric field direction: positive to negative
- Potential energy: U = qV
- Capacitance depends on geometry
- Energy in capacitor: U = ½CV²

📌 Important Concepts:
- Gauss's law: Φ = Q_enc/ε₀
- Electric dipole: p = qd
- Field due to dipole falls as 1/r³
- Equipotential surfaces perpendicular to field

⚠️ Common Mistakes:
- Wrong direction of electric field
- Forgetting dielectric constant
- Not considering superposition

Current Electricity

🎯 Key Formulas:
V = IR
P = I²R = V²/R
ρ = RA/L

💡 Important Points:
- Current direction: conventional vs electron
- Resistance depends on temperature
- Power dissipation in resistor
- Kirchhoff's laws for circuits

📌 Circuit Analysis:
- Series: same current, R_total = R₁ + R₂
- Parallel: same voltage, 1/R_total = 1/R₁ + 1/R₂
- Wheatstone bridge: R₁/R₂ = R₃/R₄ for balance

⚠️ Common Mistakes:
- Wrong current direction
- Not using equivalent resistance
- Forgetting internal resistance

Magnetism

🎯 Key Formulas:
F = qvB (Lorentz force)
τ = NIAB (torque on coil)
B = μ₀I/(2πr) (long straight wire)

💡 Important Points:
- Magnetic field direction: right-hand rule
- Force on moving charge perpendicular to both v and B
- Torque on current loop in magnetic field
- Magnetic materials: diamagnetic, paramagnetic, ferromagnetic

📌 Important Laws:
- Biot-Savart law: dB = (μ₀/4π)(Idlsinθ/r²)
- Ampere's law: ∮B·dl = μ₀I_enc
- Force on conductor: F = ILB sin θ

⚠️ Common Mistakes:
- Wrong direction using right-hand rule
- Not considering angle between v and B
- Confusing magnetic field and force

Electromagnetic Induction

🎯 Key Formulas:
ε = -dΦ/dt (Faraday's law)
ε = -L(dI/dt) (self-induction)
Φ = BA cos θ

💡 Important Points:
- Changing flux induces emf
- Lenz's law: induced current opposes change
- Self-inductance depends on geometry
- Transformers work on AC only

📌 Applications:
- Generator: mechanical to electrical
- Motor: electrical to mechanical
- Transformer: voltage step-up/down
- Induction coil: high voltage generation

⚠️ Common Mistakes:
- Wrong sign in Faraday's law
- Not considering flux change
- Confusing self and mutual induction

🔬 Optics

Ray Optics

🎯 Key Formulas:
1/f = 1/v + 1/u (lens/mirror)
m = -v/u = h_i/h_o (magnification)
n₁sin i = n₂sin r (Snell's law)

💡 Important Points:
- Real images: inverted, can be projected
- Virtual images: upright, cannot be projected
- Lens formula sign convention
- Total internal reflection when i > critical angle

📌 Important Concepts:
- Power of lens: P = 1/f (diopters)
- Critical angle: sin θ_c = n₂/n₁
- Dispersion: different λ, different refractive index
- Optical instruments: microscope, telescope

⚠️ Common Mistakes:
- Wrong sign conventions
- Confusing real and virtual images
- Not applying Snell's law correctly

Wave Optics

🎯 Key Formulas:
d sin θ = nλ (diffraction grating)
β = λD/d (fringe width)
I = I₀cos²θ (Malus's law)

💡 Important Points:
- Interference requires coherent sources
- Diffraction grating produces sharp lines
- Polarization: transverse waves only
- Huygens' principle explains wave propagation

📌 Important Concepts:
- Young's double slit: constructive when path difference = nλ
- Single slit diffraction: central maximum brightest
- Polarization by reflection: Brewster's angle
- Coherent sources: constant phase difference

⚠️ Common Mistakes:
- Confusing interference and diffraction
- Wrong grating formula usage
- Not considering wavelength dependence

⚛️ Modern Physics

Atomic Structure

🎯 Key Formulas:
E_n = -13.6/n² eV (hydrogen)
1/λ = R∞(1/n₁² - 1/n₂²)
λ = h/p (de Broglie)

💡 Important Points:
- Bohr model: circular orbits, quantized energy
- Energy levels negative (bound states)
- Spectral lines: photon emission/absorption
- Wave-particle duality

📌 Important Series:
- Lyman: n_f = 1 (UV)
- Balmer: n_f = 2 (visible)
- Paschen: n_f = 3 (IR)

⚠️ Common Mistakes:
- Wrong energy level calculations
- Confusing different series
- Not using correct Rydberg formula

Nuclear Physics

🎯 Key Formulas:
N = N₀e^(-λt) (radioactive decay)
T½ = 0.693/λ (half-life)
E = mc² (mass-energy)

💡 Important Points:
- Radioactivity: α, β, γ decay
- Half-life: time for half nuclei to decay
- Binding energy: energy to separate nucleus
- Nuclear fusion vs fission

📌 Important Reactions:
- α decay: ᵐXₙ → ᵐ⁻⁴Yₙ₋₂ + ⁴He₂
- β decay: ᵐXₙ → ᵐYₙ₊₁ + β⁻ + ν̄
- Nuclear fission: heavy nucleus splits
- Nuclear fusion: light nuclei combine

⚠️ Common Mistakes:
- Wrong decay equations
- Not conserving nucleon number
- Confusing binding energy and mass defect

Semiconductors

🎯 Key Formulas:
I = I₀(e^(qV/kT) - 1) (diode equation)
β = I_c/I_b (transistor gain)

💡 Important Points:
- Intrinsic: pure semiconductor
- Extrinsic: doped semiconductor
- p-type: acceptor dopants
- n-type: donor dopants

📌 Important Devices:
- Diode: rectifier
- Transistor: amplifier/switch
- LED: light emission
- Solar cell: light to electricity

⚠️ Common Mistakes:
- Confusing p-type and n-type
- Wrong diode equation usage
- Not considering temperature effects

🔬 Experimental Physics

Measurements and Errors

🎯 Key Concepts:
- Significant figures: all certain + first uncertain digit
- Absolute error: |measured - true|
- Relative error: absolute error/true value
- Percentage error: relative error × 100%

💡 Important Points:
- Error propagation: different rules for different operations
- Systematic errors: consistent bias
- Random errors: unpredictable variations
- Accuracy vs precision

📌 Instruments:
- Vernier calipers: LC = 1 MSD - 1 VSD
- Screw gauge: LC = pitch/total divisions
- Error analysis: combine errors properly

⚠️ Common Mistakes:
- Wrong significant figures
- Incorrect error propagation
- Not using correct least count

🎯 Exam Tips

Problem-Solving Strategy

1. Read question carefully
2. Identify the concept
3. Draw diagram (if applicable)
4. Write given quantities
5. Choose appropriate formula
6. Substitute with units
7. Solve step-by-step
8. Check answer dimensionally

Common Topics in Exams

High Weightage:
- Mechanics (30-35%)
- Electromagnetism (25-30%)
- Modern Physics (15-20%)
- Optics (10-15%)
- Thermodynamics (10-15%)

Must-Know Formulas:
- All kinematics equations
- Newton's laws applications
- Work-energy theorem
- Ohm's law and Kirchhoff's laws
- Electrostatics formulas
- Ray optics formulas
- Modern physics energy levels

Use these quick notes for rapid revision and last-minute preparation! Focus on understanding concepts and practicing problems regularly. 🎯