EQUATIONS AND CONSTANTS FOR GRADE 12 PHYSICS These equations make doing homework and exams a bit easier, but they are not an excuse for not learning the course material. If you don’t know what these equations mean and how to use them, they will not help you at all. KINEMATIC EQUATIONS: π£®avg = Δπ® Δπ‘ π®avg = Δ®π£ Δπ‘ 1 Δπ® = π£®1 Δπ‘ + πΔπ‘ ® 2 2 1 Δπ® = π£®2 Δπ‘ − πΔπ‘ ® 2 2 π£®1 + π£®2 Δπ® = Δπ‘ 2 π£ 22 = π£ 21 + 2πΔπ π£®2 = π£®1 + πΔπ‘ ® SYMMETRIC PROJECTILES: 2π£ π sin π Total time: π = π 2 π£ sin(2π) Range: π = π π 2 π£ sin2 π Max height: π» = π 2π LAWS OF MOTION: First law: πΉ®net = 0® → π® = 0® Δ π® Second law: πΉ®net = π π® = Δπ‘ Third law: πΉ®AB = −πΉ®BA MOMENTUM & IMPULSE π® = π®π£ π½® = πΉΔπ‘ π½®net = Δ π® COLLISIONS: ∑οΈ ∑οΈ π®π = π®π′ (all collisions) π ∑οΈ πΎπ = π π ∑οΈ πΎπ′ (elastic only) CONSERVATION OF ENERGY: ∑οΈ πΈ mech = πΎ + ππ π πΈ sys = πΈ mech + πΈ int ΔπΈ sys = πext πΊπ 1 π 2 π2 πΊπ π π= 2 π ππ = − πΉπ = πΊπ 1 π 2 π πΉ®π = π π® π 1D ELASTIC COLLISION: π£ 1 (π 1 − π 2 ) + 2π 2 π£ 2 π£ 1′ = π1 + π2 π£ (π − π 1 ) + 2π 1 π£ 1 2 2 π£ 2′ = π1 + π2 ELECTROSTATICS: ππ 1 π 2 π2 ππ π πΈ= 2 π ππ π π= π πΉπ = ππ = ππ 1 π 2 π πΉ®π = π πΈ® Δπ = Δπ π FORCES: parallel plate: Gravity πΉ®π = π π® Static friction: πΉπ ≤ π π πΉπ Kinetic friction: πΉπ = π π πΉπ Hooke’s Law: πΉ®π = −π π₯® 1 Drag: πΉπ· = ππ£ 2∞πΆπ· π΄ref 2 πΈ= π Δπ = π0 π MAGNETISM: πΉπ = ππ£π΅ sin π πΉπ = πΌπ π΅ sin π CIRCULAR MOTION: π®π ⊥ π£® ππ = π£2 π ππ£ 2 πΉπ = ππ π = π 2ππ 1 π= π = π£ π π£2 tan π = ππ WORK & ENERGY: π = πΉΔπ cos π (constant force) 1 πnet = ΔπΎ πΎ = ππ£ 2 2 1 ππ = ππβ ππ = ππ₯ 2 2 π = −Δπ (conservative forces) GRAVITY: ORBITAL MOTION: √οΈ πΊπ π£ orb = π √οΈ 2πΊ π √ π£ esc = = 2π£ orb π πΊ ππ 1 2 πΎorb = = ππ£ orb 2π 2 πΊ ππ πorb = − = −2πΎorb π πΊ ππ πΈ tot = πΎorb + ππ = − = −πΎorb 2π π2 = constant π3 1 TRAVELLING WAVE: π£ = ππ = π π REFRACTION: π1 sin π 1 = π2 sin π 2 π π= π£ ONE-SLIT DIFFRACTION: Bright fringes: 1 π+ π = π sin π 2 1 ππΏ π¦π = π + π = 1, 2, 3 · · · 2 π Dark fringes: ππ = π sin π πππΏ π¦π = π π = 1, 2, 3 · · · TWO-SLIT INTERFERENCE: Bright fringe: ππ = π sin π πππΏ π¦π = π Δπ¦π π≈ π₯ π = 0, 1, 2, 3 · · · 1 eV = 1.602 × 10−19 J πΈ = βπ ( βπ −π πΎmax = 0 π = 0, 1, 2, 3 · · · OPTICAL RESOLUTION: Rectangular: π min Circular: π min π = π 1.22π = π· THIN-FILM INTERFERENCE: One phase shift 1 Constructive: 2ππ‘ = π − π 2 Destructive: 2ππ‘ = ππ Two phase shifts if β π > π otherwise πΈ βπ β = = π π π β π= ππ£ β ππ ππ₯ ≥ 4π 1 km/h = 0.278 m/s 1 m/s = 3.6 km/h 1 ly = 9.461 × 1015 m SPECIAL RELATIVITY: πΆ = 2ππ π΄ = ππ 2 SI UNIT PREFIXES: tera giga mega kilo centi milli micro nano pico femto 1012 109 106 103 10−2 10−3 10−6 10−9 10−12 10−15 T G M k c m π n p f Spheres: π = 4ππ 2 4 π = ππ 3 3 π π Small angles: tan π ≈ sin π ≈ π Density: π = USEFUL CONSTANTS: Universal gravitational constant: πΊ = 6.674 × 10−11 N · m2 /kg2 Coulomb’s constant: π = 8.988 × 109 N · m2 /C2 Electron rest mass: π π = 9.110 × 10−31 kg Proton rest mass: π π = 1.673 × 10−27 kg Elementary charge: π = 1.602 × 10−19 C 1 1− MATHEMATICAL FORMULAS: Circles: Acceleration to to gravity: π = 9.81 m/s2 (near surface of Earth) Constructive: 2ππ‘ = ππ 1 Destructive: 2ππ‘ = π − π 2 Speed of light in vacuum: π = 2.998 × 108 m/s π£ 2 Planck’s constant: β = 6.626 × 10−34 J · s π = 4.136 × 10−15 eV · s π‘ ′ = πΎπ‘ πΏ πΏ′ = πΎ ′ π = πΎπ π Earth = 5.972 × 1024 kg π Earth = 6.371 × 106 m π Sun = 1.989 × 1030 kg ′ π=ππ£ π Sun = 6.957 × 108 m πΈ 0 = ππ2 ′ 2 1 kW · h = 3.6 × 106 J π= Dark fringes: 1 π+ π = π sin π 2 1 ππΏ π¦π = π + 2 π πΎ = √οΈ UNIT CONVERSIONS: QUANTUM MECHANICS: πΈπ = π π = πΎππ π Moon = 7.348 × 1022 kg 2 π Moon = 1.737 × 106 m πΎ = πΈπ − πΈ 0 = (πΎ − 1)ππ2 πEarth-to-moon = 3.844 × 108 m 2