Harold’s AP Physics “Cheat Sheet” 24 March 2017
Mechanics: Fluid Atomic and Mechanics: Angular / Electricity / Mechanics / Nuclear / Linear Rotational Magnetism Thermo- Waves and Translation Motion dynamics Optics Kinematics 10−24 = 푦표푐푡표 10−21 = 푧푒푝푡표 Horizontal: 10−18 = 푎푡푡표 1 −15 Waves and Optics: 풙 = 푥 + 푣 푡 + 풂푡2 10 = 푓푒푚푡표 Fluid Mechanics: 0 푥0 −12 1 1 1 1 2 10 = 푝𝑖푐표 2 + = 푃1 + 휌푔푦1 + 휌푣1 10−9 = 푛푎푛표 2 푠푖 푠표 푓 Vertical: 1 1 휃 = 휃 + 휔 푡 + 휶푡2 10−6 = 푚𝑖푐푟표 2 1 0 0 = 푃2 + 휌푔푦2 + 휌푣2 ∆퐿 = 푚휆 Position 풚 = 푦 + 푣 푡 − 품푡2 2 10−3 = 푚𝑖푙푙𝑖 2 0 푦0 (Conservation of (m) 2 100 = 1 푥 = 퐴 cos(휔푡) Mass) 푑 sin 휃 = 푚휆 103 = 푘𝑖푙표 (rad) 풙 = 푥 + 풗푡 0 106 = 푚푒푔푎 푥 = 퐴 cos(2휋푓푡) 푚 Relativity: 109 = 푔𝑖푔푎 휌 = 푠 = 푟휃 12 푉 10 = 푡푒푟푎 푣2 15 퐿 = 퐿 √1 − 10 = 푝푒푡푎 0 2 ∆ℓ = 훼ℓ0∆푇 푐 푥 = ∫ 푣 푑푡 1018 = 푒푥푎 1021 = 푧푒푡푡푎 1024 = 푦표푡푡푎
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 1
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
휃 ∆휃 푑휃 풅 ∆풙 푑풙 휔 = = = 풗 = = = 푡 ∆푡 푑푡 Fluid Mechanics: Waves and Optics: 푡 ∆푡 푑푡 푣 = 푓휆 퐴 푣 = 퐴 푣 흎 = 흎 + 휶푡 1 1 2 2 풗 = 풗 + 풂푡 0 0 푐 Speed of Light: 푛 = 흎2 = 흎2 + 2휶(휃 − 휃 ) 푚 3푅푇 푣 Velocity 풗2 = 푣2 + 2풂(푥 − 푥 ) 0 0 푐 ≈ 3.00 푥 108 푣 = √ 0 0 푟푚푠 (m/s) 푠 푀 흎0 + 흎 푛1 sin 휃1 = 푛2 sin 휃2 (rad/s) 푣0 + 푣 흎̅ = 푚 풗̅ = 2 2 = 299,792,458 2휋 푠 3푘퐵푇 Relativity: 풗 = 푟흎 휔 = = 2휋푓 푣푟푚푠 = √ 푣0 풗 = 흎 × 풓 푇 휇 푣(푡) = 푣2 푘 푔 √1 − 푣 = ∫ 푎 푑푡 휔 = √ = √ 푐2 푚 ℓ
풗 ∆풗 푑풗 풂 = = = Tangential: 푡 ∆푡 푑푡 푎푇 ∆흎 푑흎 휶 = = = ∑ 푭 푭 푟 ∆푡 푑푡 풂 = = 푛푒푡 Acceleratio 푚 푚 ∑ 흉 흉푛푒푡 휶 = = n 퐼 퐼 풂 = 푟휶 NA NA NA (m/풔ퟐ)
(rad/푠2) Centripetal: 푚 2 푔 = 9.80665 2 풗 2 푠 풂풄 = = 흎 푟 푟 푓푡 푔 = 32.1740 풂2 = 풂2 + 풂2 푠2 푐 푇
Jerk (Jolt) 풂 ∆풂 푑풂 휶 ∆휶 푑휶 (m/풔ퟑ) 풋⃗ = = = 훇 = = = NA NA NA 3 푡 ∆푡 푑푡 푡 ∆푡 푑푡 (rad/푠 )
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 2
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
Dynamics 2 Mass 퐼 = ∑ 푚푟 푚푒 = 9.11 (kg) Relativity: ×10−31 푘푔 / m = actual mass 푚0 퐼 = ∫ 푟2 푑푚 NA 푚 = Moment of I = effective mass 푣2 푚푝 ≈ 푚푛 √1 − Inertia 푐2 2 = 1.67 (푘푔 • 푚 ) 퐼 = ∫ 풓 • 푑풎 ×10−27 푘푔 풑 = 푚풗 Atomic and Nuclear: 푳 = 퐼흎 ℎ 휆 = Momentum ∆풑 = 푚∆풗 푝 푳 = 풓 × 풑 Fluid Mechanics: (kg•m/s) NA 2 Conservation of 훻풑 = 휌품 Relativity: (푘푔 • 푚 /푠) Momentum: 푚푣 퐿 = ∫ 풓 × 풗 푑푚 푝 = 풑푖 = 풑푓 푣2 √1 − 푐2
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 3
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
푭 = 푚풂 Electricity:
Coulomb’s Law: 휏 = 푟퐹 sin 휃 푭 = 푚품 푞1푞2 푔 퐹 = 푘 풓2 Fluid Mechanics: ∑ 흉 = 흉푛푒푡 = 퐼휶 퐹 = 푃퐴 ∑ 푭 = 푭푛푒푡 = 푚풂 1 푞 푞 퐹 = 1 2 2 퐹 휏 = 푟퐹 = 퐼휶 4휋휖0 풓 풑 ∆푝 푑풑 푃 = = 휌ℎ푔 Force 퐴 푭 = = = 푭 = 푬푞 (N = 푡 ∆푡 푑푡 흉 = 풓 × 푭 퐹 = 휌푉푔 kg•m/풔ퟐ) 푏푢표푦 푭 ≤ 휇푁 Magnetism: NA / 푓푟푖푐 푑퐿 흉 = 퐹퐵 = 푞푣퐵 sin 휃 푃푉 = 푛푅푇 = 푁푘 푇 Torque 푑푡 퐵 Hooke’s Law: (J = N•m) 푭 = −푘풙 퐹퐵 = 퐵퐼ℓ sin 휃 퐽 푠 푭 = 푚풂풄 푅 = 8.31 (푚표푙 • 퐾) 퐺푚1푚2 푚풗2 푭퐵 = 푞풗 × 푩 퐹퐺 = − 2 푟 푭 = −23 퐽 푟 푘퐵 = 1.38 ×10 푭퐵 = 퐼ℓ × 푩 퐾 퐺푚 푚 1 2 푭 = 푚푟흎2 푭퐺 = − 2 풓̂ 푟 푭 = ∫ 퐼 푑ℓ × 푩
Impulse 푱 = 푭 ∆푡 = ∆풑 = 풎 ∆풗 푯 = 흉 ∆푡 = ∆푳 = 푰 ∆휔 (N•s) NA NA NA (N•m•s) 푱 = ∫ 푭 푑푡 = ∆풑 푯 = ∫ 흉 푑푡 = ∆푳
Yank 풀 = 푚 푱 푷 = 풓 × 풀 (N/풔ퟐ) NA NA NA Rotatum 푭 ∆퐹 푑푭 흉 ∆휏 푑흉 풀 = = = 푷 = = = (J/s) 푡 ∆푡 푑푡 푡 ∆푡 푑푡
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 4
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
Energy Thermodynamics: 푊 = 퐹푑 푊 = 휏 ∆휃 푊 = −푃 ∆푉
Work 푊 = 퐹 ∆푥 cos 휃 푊 = 휏 (휃 − 휃 ) 푊 0 푾 = 푸푉 푒 = | | NA (J = N•m) 푄퐻
푊 = ∫ 푭 • 푑풓 푊 = ∫ 흉 • 푑휽 푇퐻 − 푇퐶 푒푐 = 푇퐻 Fluid Mechanics: Atomic and Nuclear: 1 퐾푚푎푥 = ℎ푓 − 휙 푃 + 휌푔푦 + 휌푣2 2 Kinetic = 푐표푛푠푡푎푛푡 Relativity: 1 1 1 푒푉 Energy 퐾 = 푚풗2 퐾 = 퐼휔2 퐾 = = 1.60 ×10−19 퐽 (J) 2 2 Thermodynamics: 2 1 푚0푐 − 1 3 푣2 퐾푎푣푔 = 푘퐵푇 √1 − 2 ( 푐2 ) 푈퐸 = 푞푉 Atomic and Nuclear: 1 푞1푞2 퐸 = ℎ푓 = 푝푐 푈퐸 = 4휋휖0 푟 ∆푈 = 푚푔ℎ 퐸 = 푚푐2 푔 Fluid Mechanics: 1 ∆퐸 = (∆푚)푐2 Potential Coiled spring: 푃 = 푃 + 휌푔ℎ 퐺푚 푚 푈푐 = 푄푉 0 Energy 푈 = − 1 2 1 2 퐺 푟 푈 = − 푘푥2 Relativity: (J) 푠 2 Thermodynamics: 1 2 −11 푈푐 = 퐶푉 ∆푈 = 푄 + 푊 1 퐺 = 6.67 ×10 2 퐸 = 푚푐2 푣2 1 √1 − 2 푈 = 퐿퐼2 ( 푐 ) 퐿 2
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 5
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
Thermodynamics: 푘퐴∆푇 퐻 = 퐿
푄 = 푚퐻푓 Conservation of Energy: 푄 = 푚퐻푣 푬푖 = 푬푓 Heat ∆퐸 = 푄 = 푚퐶∆푇 Energy 퐸 NA NA 푚퐶∆푇 = 푚퐶(푇 − 푇 ) NA = 푊 + 푄 + 퐾 + ∆푈 푓 푖 (J) 푔 + 푈퐺 + 푈푠 + 푈퐸 + 푈푐 퐶 = 4180 퐽/Kg °K + 푈 + ⋯ = 푐표푛푠푡푎푛푡 퐻2푂 퐿 푇푓 푚 퐶 ∆푇 + 푚 퐶 ∆푇 = 1 1 1푖 2 2 2푖 푚1퐶1 + 푚2퐶2
푊 푊 푃 = = 퐹푣 푃 = = 휏휔 ∆푡 ∆푡 푃 = 퐼푉
∆퐸 푑퐸 ∆푊 푑푊 Power 푃 = = 푃 = = 푃 = 퐼2푅 NA NA ∆푡 푑푡 ∆푡 푑푡 (W) 푉2 푃 = 퐹푣 cos 휃 푃 = 휏휔 cos 휃 푃 = 푅 푃 = 푭 • 풗 푃 = 흉 • 흎
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 6
Fluid Atomic and Mechanics: Mechanics: Electricity / Mechanics / Nuclear / Linear Angular Magnetism Thermo- Waves and dynamics Optics
Engineering Application Waves and Optics:
휆 1 2휋 푓 = 푇 = = 푣 푓 휔 2휋 1 푇 = 푇 = 푏 Doppler Effect: Period / 푓 푚 풗 ± 풗풓 푇푠 = 2휋√ NA 풇 = 풇 ( ) Frequency 푘 For: 풓 풔 풗 ∓ 풗 (Hz) 1 풔 푓 = 푦 = 푠𝑖푛(푏휃) 푇 ℓ 푦 = 푐표푠(푏휃) Relativity: 푇푝 = 2휋√ 푡 푔 푡 = 0 푣2 √1 − 푐2 푚1푥1 + 푚2푥2 푥퐶푀 = 푚1 + 푚2
∑ 푚푖푥푖 푥퐶푀 = ∑ 푚푖 Waves and Optics: Center ∑ 푚풓 ℎ푖 푠푖 of Mass 푀 풓 = NA NA |푀| = | | = | | 1 퐶푀 ∑ 푚 ℎ 푠 (m) 푥̅ = ∫ 푥 푑푚 표 표 푀 0 (magnification)
푀 where 푀 = ∫0 푑푚 and 푑푚 = 휌 푑푧 푑푦 푑푥
∑ 퐹 = ∑ 푚푔 = 0 ∑ 휏 = ∑ 퐹 푥 = 0 Rigid 푦 푦 퐶푀 Conservation of Conservation of Conservation of Mass Bodies Charge Energy (Down = ‘−‘) (CW = ‘−‘)
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 7
Electricity Electricity
푭 푄 푬 = 퐶 = 푞 푉
휖 퐴 푉 퐶 = 0 퐸 = − 푑 푎푣푔 푑 Electric 휅휖 퐴 Field ∆푉 푑푉 Capacitance 퐶 = 0 퐸 = − = − 푑 (V/m) ∆푟 푑푟 (F) (N/C) Gauss’s Law: 퐶푝 = ∑ 퐶푖 푄 푖 ∮ 푬 • 푑푨 = 휖0 1 1 = ∑ 퐶푠 푖 퐶푖 푬 = 휌푱
푉 푉 = 퐼푅 푅 = 퐼
푄 푉 = 휌ℓ 퐶 푅 = 퐴
Potential 푞푖 Resistance (V) 푉 = 푘 ∑ (Ω) 푖 푟푖 푅푠 = ∑ 푅푖 푖
1 푞푖 1 1 푉 = ∑ = ∑ 4휋휖0 푖 푟푖 푅 푅 푝 푖 푖
∆푄 퐼 = 푎푣푔 ∆푡
푑푄 퐼 = Faraday’s Law of Induction: 푑푡 ∆휙 ∮ 푬 • 푑퓵 = − 퐵 Current 푉 EMF ∆푡 (A) 퐼 = (V) 푅 푑퐼 휀 = −퐿 푑푡 퐼 = 푁푒푣푑퐴
푒 = 1.60 ×10−19 퐶
Copyright © 2011-2017 by Harold Toomey, WyzAnt Tutor 8
Magnetism Magnetism 휇 퐼 퐵 = 0 2휋 푟
푆표푙푒푛표𝑖푑: 퐵푠 = 휇0푛퐼
푁 푤ℎ푒푟푒 푛 = 푡푢푟푛푠 푝푒푟 푚푒푡푒푟 퓵
휇 푞풗⃗⃗⃗ × 풓⃗⃗ 푩 = 0 4휋 푟3 Magnetic Field 휇 푞풗⃗⃗⃗ × 풓̂ 푩 = 0 (T) 4휋 푟2
(푇 • 푚) 휇 = 4휋 ×10−7 0 퐴
Ampere’s Circuit Law:
∮ 푩 • 푑퓵 = 휇표퐼
휇 퐼 푑퓵 × 풓⃗⃗ 푑퐵 = 0 4휋 푟3
휙푩 = 퐵퐴 cos 휃
Magnetic 휙퐵 = 푩 • 푨
Flux Gauss’s Law for Magnetism: (Wb) 휙퐵 = ∫ 푩 • 푑푨
∆휙 휀 = − 퐵 EMF 푎푣푔 ∆푡 (V) 휺 = 푩푙푣
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