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Comprehensive Physics Formulas Summary
Complete Equation Sheets Handout for Revision & Exam Preparation
1. Mechanics & Dynamics
Kinematics & Projectile Motion
Equations of Motion (Constant Acceleration): v = u + at | s = ut + ½at² | v² = u² + 2as Relative Velocity: V{A/B} = V_A - V_B_ Projectile Motion: Horizontal and Vertical Component of Initial Velocity: u_x = u cos θ , u_y = u sin θ Total Time of Flight: T = 2u sin θ / g Maximum Height Reached: H = u² sin² θ / 2g Maximum Horizontal Range: R = u² sin 2θ / g Trajectory Equation: y = x tan θ - gx² / (2u² cos² θ)
Laws of Motion & Friction
Newton's Second Law: F = dp/dt = ma where p = mv (Momentum) Friction Forces (Static and Kinetic): f{static, max} = μs N , _f_k = μk N Banking of Roads: Without friction: v² / rg = tan θ With friction (Maximum safe speed): v² / rg = (μ + tan θ) / (1 - μ tan θ)
Work, Power, Energy & Collisions
Work Done by a Force: W = F · S = Fs cos θ = ∫ F · ds Mechanical Power: P = dW/dt = F · v Kinetic and Potential Energy: KE = ½mv² | Spring Potential Energy: U = ½kx² Conservative Force & Potential Energy relation: F = -dU/dx Coefficient of Restitution (Collisions): e = (v₂ - v₁) / (u₁ - u₂)
2. Rigid Body Dynamics
Rotational Motion Variables: ω = dθ/dt | α = dω/dt | a = α × r Torque & Angular Momentum: τ = r × F = Iα | L = r × p = Iω
Moment of Inertia: I = ∑ m_i r_i² = ∫ r² dm Parallel Axis Theorem: I = I{cm} + md²_
Geometric Object & Rotational Axis Moment of Inertia ( I ) Thin Rod of length L (Axis through center, perpendicular to length) I = 1/12 mL² Thin Rod of length L (Axis through one end, perpendicular to length) I = 1/3 mL² Thin Ring of radius R (Axis through central symmetry axis) I = mR² Solid Disk or Cylinder of radius R (Axis through symmetry center) I = ½ mR² Hollow Thin-Walled Sphere of radius R (Axis through center diameter) (^) I = ⅔ mR² Solid Uniform Sphere of radius R (Axis through center diameter) I = 2/5 mR²
3. Simple Harmonic Motion (SHM) & Gravitation
Simple Harmonic Motion (SHM)
Displacement & Acceleration Equations: x = A sin(ωt + φ) | a = -ω²x = -k/m x Velocity & Total Energy: v = Aω cos(ωt + φ) | E = ½kA² = ½mω²A² Time Period of Simple Pendulum & Spring-Mass: T = 2π √(L/g) | T = 2π √(m/k) Superposition of two SHMs: Resultant Amplitude A = √(A₁² + A₂² + 2A₁A₂ cos φ)
Gravitation
Gravitational Force & Potential Energy: F = G M m / R² | U = -G M m / R Variation of Acceleration due to Gravity (g): With height h above the surface: g' ≈ g(1 - 2h/R) (for h << R) With depth d below the surface: g' = g(1 - d/R) Orbital and Escape Velocity: V{orbit} = √(GM/R)_ | V{escape} = √(2GM/R)_
4. Fluid Mechanics & Elasticity
Elastic Moduli: Young's Modulus Y = (F/A) / (ΔL/L) | Bulk Modulus B = -V ΔP / ΔV Hydrostatic Pressure & Buoyant Force (Archimedes): P = ρgh | F{buoyant} = ρ g V_{displaced}_ Fluid Dynamics: Equation of Continuity: A₁ v₁ = A₂ v₂ Bernoulli's Equation (Energy Conservation): P + ρgh + ½ρv² = constant
7. Electrostatics & Current Electricity
Coulomb's Law & Electric Field: F = 1/(4πε₀) · q₁q₂/r² | Electric Potential: V = 1/(4πε₀) · q/r Gauss's Law for Electric Flux: Φ = ∮ E · ds = q{in} / ε₀_ Electric Field for Continuous Charge Distributions: Infinitely Long Uniformly Charged Wire: E = λ / (2πε₀ r) Infinite Uniformly Charged Flat Sheet: E = σ / 2ε₀ Capacitors: Parallel Plate Capacitor with Dielectric material K: C = K ε₀ A / d Energy Stored in Capacitor Field: U = ½CV² = Q² / 2C Direct Current (DC) Circuits: Ohm's Law & Resistance: V = iR | R = ρ L / A Kirchhoff's Rules: Junction Rule ∑ i{in} = 0_ | Loop Rule ∑ ΔV = 0
8. Electromagnetism & Modern Physics
Lorentz Force & Magnetic Circular Path: F = q(v × B + E) | Radius of Path: r = mv / qB Biot-Savart Law & Ampere's Law: dB = (μ₀/4π) · (i dl × r) / r³ | ∮ B · dl = μ₀ I{in}_ Faraday's Law of Electromagnetic Induction: e = -dΦ/dt Resonant Frequency in AC LCR Circuits: ν{res} = 1 / (2π√(LC))_ Modern & Quantum Physics: Einstein's Photoelectric Effect: K{max} = hν - φ_ De Broglie Matter Wavelength: λ = h / p = h / mv Bohr Hydrogen Atom Energy Levels: E_n = -13.6 Z² / n² (eV) Radioactive Decay Law: N = N₀ e^{-λt} | Half-Life t{1/2} = ln 2 / λ ≈ 0.693 / λ_
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