Please Do Not Write on This Sheet Physics Formula Sheet Chapter 1: Introduction: The 푅푦 = 퐴푦 + 퐵푦 푣 = 푟휔 Nature of Science and Physics 푣2 푅 = √푅2 + 푅2 푎 = 푥 푦 퐶 푟 2 −푏 ± √푏 − 4푎푐 푅 푎 = 푟휔2 푥 = −1 푦 퐶 2푎 휃 = 푡푎푛 푅 퐹퐶 = 푚푎퐶 푅푎푑푢푠 표푓 퐸푎푟푡ℎ = 6.38 × 106 푚 푥 푣2 푚푣2 푀푎푠푠 표푓 퐸푎푟푡ℎ = 5.98 × 1024 푘푔 ℎ = 0푦 퐹 = 2푔 퐶 푟 푐 = 3.00 × 108 푚/푠 2 푣2 푠푛 2휃 푣 푁푚2 푅 = 0 0 푡푎푛 휃 = 퐺 = 6.673 × 10−11 푔 푟푔 푘푔2 2 퐹퐶 = 푚푟휔 23 푣푥 = 푣 푐표푠 휃 푁퐴 = 6.02 × 10 푚푀 −23 푣푦 = 푣 푠푛 휃 퐹 = 퐺 푘 = 1.38 × 10 퐽/퐾 푟2 퐽 푣 = 푣2 + 푣2 퐺푀 푅 = 8.31 ⁄ √ 푥 푦 푚표푙 ⋅ 퐾 푔 = 2 −8 2 푟 휎 = 5.67 × 10 푊/(푚 ⋅ 퐾) −1 푣푦 2 3 휃 = 푡푎푛 푇1 푟1 9 2 2 푘 = 8.99 × 10 푁 ⋅ 푚 /퐶 푣푥 2 = 3 푇2 푟2 푞 = −1.60 × 10−19 퐶 푒 4휋2 휖 = 8.85 × 10−12퐶2/(푁 ⋅ 푚2) Chapter 4: Dynamics: Forces 푇2 = 푟3 0 퐺푀 −7 and Newton’s Laws of Motion 휇0 = 4π × 10 푇 ⋅ 푚/퐴 푟3 퐺 −34 ℎ = 6.63 × 10 퐽 ⋅ 푠 2 = 2 푀 퐹푛푒푡 = 푚푎 푇 4휋 −31 푚푒 = 9.11 × 10 푘푔 푤 = 푚푔 −27 푚푝 = 1.6726 × 10 푘푔 Chapter 7: Work, Energy, and −27 푚푛 = 1.6749 × 10 푘푔 Chapter 5: Further Applications Energy Resources 푎푚푢 = 1.6605 × 10−27 푘푔 of Newton’s Laws: Friction, 푊 = 푓푑 푐표푠 휃 푘푔 퐷푒푛푠푡푦 표푓 푤푎푡푒푟 = 1000 Drag, and Elasticity 1 푚3 퐾퐸 = 푚푣2 2 푓푠 ≤ 휇푠푁 1 2 1 2 Chapter 2: Kinematics 푓푘 = 휇푘푁 푊푛푒푡 = 푚푣푓 − 푚푣0 1 2 2 퐹 = 퐶휌퐴푣2 푃퐸 = 푚푔ℎ 훥푥 = 푥푓 − 푥0 퐷 2 푔 1 훥푡 = 푡푓 − 푡0 퐹푠 = 6휋휂푟푣 푃퐸 = 푘푥2 푠 2 훥푥 푥푓 − 푥0 퐹 = 푘훥푥 푣 = = 퐾퐸0 + 푃퐸0 = 퐾퐸푓 + 푃퐸푓 훥푡 푡푓 − 푡0 1퐹 훥퐿 = 퐿0 퐾퐸0 + 푃퐸0 + 푊푛푐 = 퐾퐸푓 + 푃퐸푓 훥푣 푣푓 − 푣0 푌퐴 푎 = = 퐹 푊표푢푡 훥푡 푡푓 − 푡0 푠푡푟푒푠푠 = 퐸푓푓 = 퐸 푥 = 푥 + 푣푡 퐴 푖푛 0 훥퐿 푊 푣0 + 푣 푠푡푟푎푛 = 푃 = 푣 = 퐿 푡 2 0 푠푡푟푒푠푠 = 푌 × 푠푡푟푎푛 푣 = 푣0 + 푎푡 1 1퐹 Chapter 8: Linear Momentum 푥 = 푥 + 푣 푡 + 푎푡2 훥푥 = 퐿0 0 0 2 푆퐴 and Collisions 1퐹 푣2 = 푣2 + 2푎(푥 − 푥 ) 0 0 훥푉 = 푉0 푝 = 푚푣 푚 퐵퐴 푔 = 9.80 훥푝 = 퐹푛푒푡훥푡 푠2 Chapter 6: Uniform Circular 푝0 = 푝푓 Chapter 3: Two-Dimensional Motion and Gravitation 푚1푣01 + 푚2푣02 = 푚1푣푓1 + 푚2푣푓2 Kinematics 훥푠 훥휃 = 푟 퐴푥 = 퐴 푐표푠 휃 2휋 푟푎푑 = 360° = 1 푟푒푣표푙푢푡표푛 퐴 = 퐴 푠푛 휃 푦 훥휃 푅 = 퐴 + 퐵 휔 = 푥 푥 푥 훥푡 Please Do Not Write on This Sheet 1 2 1 2 Thin rod about axis through center 1 2 푚1푣01 + 푚2푣02 푃1 + 휌푣1 + 휌푔ℎ1 2 2 푀ℓ2 2 ⊥ to length: 퐼 = 1 12 1 = 푚 푣2 = 푃 + 휌푣2 2 1 푓1 Thin rod about axis through one end 2 2 2 1 푀ℓ2 + 휌푔ℎ + 푚 푣2 ⊥ to length: 퐼 = 2 2 2 푓2 3 1 2푀푅2 2 푚 푣 = 푚 푣′ 푐표푠 휃 + 푚 푣′ 푐표푠 휃 Solid sphere: 퐼 = (Δ푃 + Δ 휌푣 + Δ휌푔ℎ) 푄 = 푝표푤푒푟 1 1 1 1 1 2 2 2 5 2 ′ ′ 0 = 푚 푣 푠푛 휃 + 푚 푣 푠푛 휃 2푀푅2 1 1 1 2 2 2 Thin spherical shell: 퐼 = 푣1 = √2푔ℎ 3 1 2 1 ′2 1 ′2 퐹퐿 푚푣1 = 푚푣1 + 푚푣2 Slab about ⊥ axis through center: 휂 = 2 2 2 푣퐴 ′ ′ 푀(푎2+푏2) + 푚푣1푣2 푐표푠(휃1 퐼 = 푃2 − 푃1 12 − 휃 ) 푄 = 2 푛푒푡 푊 = (푛푒푡 휏)휃 푅 푣 훥푚 8휂푙 푒 1 푎 = − 푔 2 푅 = 4 푚 훥푡 퐾퐸푟표푡 = 퐼휔 휋푟 2 4 푣1푚1 + 푣2푚2 (푃 − 푃 )휋푟 푣 = 퐿 = 퐼휔 2 1 푐푚 푚 + 푚 푄 = 1 2 훥퐿 8휂푙 푛푒푡 휏 = 2휌푣푟 훥푡 푁 = Chapter 9: Statics and Torque 푅 휂 휌푣퐿 휏 = 푟퐹 푠푛 휃 Chapter 11: Fluid Statics 푁′ = 푅 휂 푟⊥ = 푟 푠푛 휃 푚 휌 = 푥 = √2퐷푡 퐹표 푙푖 푉 푟푚푠 푀퐴 = = 퐹푖 푙표 퐹 푃 = Chapter 13: Temperature, 푙푖퐹푖 = 푙표퐹표 퐴 5 푃푎푡푚 = 1.01 × 10 푃푎 Kinetic Theory, and the Gas Chapter 10: Rotational Motion 푃 = 휌푔ℎ Laws and Angular Momentum 푃2 = 푃1 + 휌푔ℎ 9 퐹1 퐹2 푇(°퐹) = 푇(°퐶) + 32 훥휃 = 5 휔 = 퐴1 퐴2 푇(퐾) = 푇(°퐶) + 273.15 훥푡 퐹퐵 = 푤푓푙 훥퐿 = 훼퐿훥푇 푣 = 푟휔 휌 훥휔 퐹푟푎푐푡표푛 푠푢푏푚푒푟푔푒푑 = 표푏푗 훥퐴 = 2훼퐴훥푇 훼 = 휌 훥푡 푓푙 훥푉 = 훽푉훥푇 휌 훥푣 푠푝푒푐푓푐 푔푟푎푣푡푦 = 훽 ≈ 3훼 푎푡 = 훥푡 휌푤 푃푉 = 푁푘푇 푎 = 푟훼 퐹 −23 푡 훾 = 푘 = 1.38 × 10 퐽/퐾 휃 = 휔푡 퐿 23 −1 4훾 푁퐴 = 6.02 × 10 푚표푙 휔 = 휔0 + 훼푡 푃 = 푃푉 = 푛푅푇 1 푟 휃 = 휔 푡 + 훼푡2 2훾 푐표푠 휃 퐽 0 2 ℎ = 푅 = 8.31 휌푔푟 푚표푙 ⋅ 퐾 휔2 = 휔2 + 2훼휃 0 1 2 휔 + 휔 푃푉 = 푁푚푣 휔 = 0 3 2 Chapter 12: Fluid Dynamics 1 3 퐾퐸 = 푚푣2 = 푘푇 푛푒푡 휏 = 퐼훼 and Its Biological Medical 2 2 Hoop about cylinder axis: 퐼 = 푀푅2 Applications 3푘푇 푀푅2 √ Hoop about any diameter: 퐼 = 푉 푣푟푚푠 = 2 푄 = 푚 푀 푡 Ring: 퐼 = (푅2 + 푅2) 2 1 2 푄 = 퐴푣 % 푟푒푙푎푡푣푒 ℎ푢푚푑푡푦 Solid cylinder (or disk) about 푣푎푝표푟 푑푒푛푠푡푦 퐴1푣1 = 퐴2푣2 = 푀푅2 푠푎푡푢푟푎푡표푛 푣푎푝표푟 푑푒푛푎푠푡푦 cylinder axis: 퐼 = 푛1퐴1푣1 = 푛2퐴2푣2 2 × 100% Solid cylinder (or disk) about 푀푅2 푀ℓ2 central diameter: 퐼 = + 4 12 Chapter 14: Heat and Heat Transfer Methods Please Do Not Write on This Sheet 1.000 푘푐푎푙 = 4186 퐽 1 푃퐸 푃퐸 = 푘푥2 푉 = 푄 = 푚푐훥푇 푒푙 2 푞 푚 훥푃퐸 = 푞훥푉 푄 = 푚퐿푓 푇 = 2휋√ 푘 푊 = 푞푉 푄 = 푚퐿푣 퐴퐵 푉 푄 푘퐴(푇2 − 푇1) 1 푘 퐴퐵 = 푓 = √ 퐸 = 푡 푑 2휋 푚 푑 푄 훥푉 = 휎푒퐴푇4 2휋푡 퐸 = − 푡 푥(푡) = 푋 푐표푠 ( ) 훥푠 퐽 푇 푘푄 −8 2휋푡 푉 = 휎 = 5.67 × 10 2 4 푟 푠 ⋅ 푚 ⋅ 퐾 푣(푡) = −푣푚푎푥 푠푛 ( ) 푄 푇 푄 푛푒푡 = 휎푒퐴(푇4 − 푇4) 퐶 = 푡 2 1 2휋푋 푘 푉 푣푚푎푥 = = 푋√ 퐴 푇 푚 퐶 = 휖0 Chapter 15: Thermodynamics 푑 푘푋 2휋푡 퐹 푎(푡) = − 푐표푠 ( ) 휖 = 8.85 × 10−12 3 푚 푇 0 푈 = 푁푘푇 푚 퐴 2 퐹 퐶 = 휅휖0 훥푈 = 푄 − 푊 푣푠푡푟푖푛푔 = √ 푑 푚/퐿 푊 = 푃훥푉 (푠표푏푎푟푐 푝푟표푐푒푠푠) 푄푉 퐶푉2 푄2 퐸푐푎푝 = = = Δ푈 = 푄 − 푃Δ푉 푚 푇 2 2 2퐶 푣 = (331 ) √ 푊 = 0 (푠표푐ℎ표푟푐 푝푟표푐푒푠푠) 푤 푠 273 퐾 Chapter 20: Electric Current, Δ푈 = 푄 푃 푄 = 푊 (푠표푡ℎ푒푟푚푎푙 푝푟표푐푒푠푠) 퐼 = Resistance, and Ohm’s Law 퐴 Δ푈 = 0 퐴 = 4휋푟2 훥푄 푠푝ℎ푒푟푒 퐼 = 푄 = 0 (푎푑푎푏푎푡푐 푝푟표푐푒푠푠) (훥푝)2 훥푡 퐼 = Δ푈 = −푊 퐼 = 푛푞퐴푣푑 2휌푣푤 푊 푉 = 퐼푅 퐸푓푓 = 푄 휌퐿 ℎ Chapter 17: Physics of Hearing 푅 = 푄 퐴 퐸푓푓 = 1 − 푐 (푐푦푐푙푐푎푙 푝푟표푐푒푠푠) 퐼 휌 = 휌 (1 + 훼훥푇) 푄ℎ 훽 = (10 푑퐵) 푙표푔 ( ) 0 푇 퐼0 푅 = 푅 (1 + 훼훥푇) 퐸푓푓 = 1 − 푐 0 퐶 푇 푣푤 ± 푣표 푉2 ℎ 푓 = 푓 ( ) 2 표 푠 푣 ∓ 푣 푃 = 퐼푉 = = 퐼 푅 푄ℎ 푤 푠 푅 퐶푂푃ℎ푝 = 푊 푓퐵 = |푓1 − 푓2| 1 푃 = 퐼 푉 푄 푣푤 푎푣푒 0 0 푐 푓 = 푛 ( ) 2 퐶푂푃푟푒푓 = 퐶푂푃ℎ푝 − 1 = 푛 푊 2퐿 퐼0 푣푤 퐼푟푚푠 = 푄푐⁄푡1 푓 = 푛 ( ) √2 퐸퐸푅 = 푛 4퐿 푄ℎ⁄푡2 푉0 푍 = 휌푣 푉푟푚푠 = 푄 √2 훥푆 = (푍 − 푍 )2 푇 푎 = 2 1 (푍 + 푍 )2 푄ℎ 푄푐 1 2 Chapter 21: Circuits, 훥푆푡표푡 = + = 0 푇ℎ 푇푐 Bioelectricity, and DC Chapter 18: Electric Charge 푊푢푛푎푣푎푖푙 = 훥푆 ⋅ 푇0 Instruments 푆 = 푘 푙푛 푊 and Electric Field −23 푅 = 푅 + 푅 + 푅 + ⋯ 푘 = 1.38 × 10 퐽/퐾 |푞 | = 1.60 × 10−19 퐶 푆 1 2 3 푒 1 1 1 1 |푞 푞 | = + + + ⋯ 퐹 = 푘 1 2 푅 푅 푅 푅 Chapter 16: Oscillatory Motion 푟2 푃 1 2 3 푉 = 푒푚푓 − 퐼푟 and Waves 퐸 = 퐹/푞 푡 − |푄| 푉 = 푒푚푓 (1 − 푒 푅퐶) 1 퐸 = 푘 푓 = 2 푇 푟 휏 = 푅퐶 푡 휆 − 푣 = = 푓휆 푉 = 푉 푒 푟퐶 푇 Chapter 19: Electric Potential 0 퐹 = −푘푥 and Electric Energy Please Do Not Write on This Sheet 푅 1 휆 Chapter 22: Magnetism 푐표푠 휙 = 푠푛 휃 = (푚 + ) 푍 2 푑 퐹 = 푞푣퐵 푠푛 휃 푃 = 퐼 푉 푐표푠 휙 휆 푚푣 푎푣푒 푟푚푠 푟푚푠 푠푛 휃 = 푚 푟 = 푊 푞퐵 Chapter 24: Electromagnetic 휆 휖 = 퐵푙푣 휃 = 1.22 Waves 퐷 퐹 = 퐼퐿퐵 푠푛 휃 휆푛 1 2푡 = 휏 = 푁퐼퐴퐵 푠푛 휃 푐 = 2 휇 퐼 √휇 휖 2푡 = 휆푛 퐵 = 0 0 0 2휋푟 퐸 I = ½ I0 휇 퐼 = 푐 2 퐵 = 0 퐵 퐼 = 퐼0 푐표푠 휃 2푅 푐 = 푓휆 푛2 푡푎푛 휃 = 퐵 = 휇 푛퐼 2 푏 0 푐휖0퐸0 푛1 퐹 휇 퐼 퐼 퐼푎푣푒 = = 0 1 2 2 푙 2휋푟 2 푐퐵0 Chapter 28: Special Relativity 퐼푎푣푒 = 2휇0 Chapter 23: Electromagnetic 훥푡0 퐸0퐵0 훥푡 = 퐼 = 푣2 Induction, AC Circuits, and 푎푏푒 2휇 √1 − 0 푐2 Electrical Technologies 1 Chapter 25: Geometric Optics 훾 = 훷 = 퐵퐴 푐표푠 휃 푣2 √1 − 훥훷 푐2 푒푚푓 = −푁 휃푖 = 휃푟 훥푡 푐 푛 = 푣2 푒푚푓 = 푣퐵퐿 푣 퐿 = 퐿 √1 − 0 푐2 푒푚푓 = 푁퐴퐵휔 푠푛 휔푡 푛1 푠푛 휃1 = 푛2 푠푛 휃2 푣 + 푣 푉푆 푁푆 퐼푃 −1 푛2 퐿푇 푇퐺 = = 휃푐 = 푠푛 푣퐿퐺 = 푣 푣 푉 푁 퐼 푛 1 + 퐿푇 푇퐺 푃 푃 푆 1 푐2 훥퐼2 1 푒푚푓 = −푀 푃 = 푢 1 푓 1 + 훥푡 푐 훥퐼 1 1 1 휆표푏푠 = 휆푠√ 푢 푒푚푓 = −퐿 1 − = + 푐 훥푡 푓 푑표 푑푖 훥훷 퐿 = 푁 ℎ푖 푑푖 푢 훥퐼 푚 = = − 1 − ℎ표 푑표 푐 μ 푁2퐴 푓표푏푠 = 푓푠√ 푢 0 푅 1 + 퐿 = 푓 = 푐 ℓ 2 푚푣 1 2 퐸푖푛푑 = 퐿퐼 푝 = 2 푣2 푡 Chapter 26: Vision and Optical √1 − − 푐2 퐼 = 퐼0 (1 − 푒 휏) Instruments 푚푐2 퐿 퐸 = 휏 = 1 1 2 푃 = + √ 푣 푅 푑 푑 1 − 2 푡 표 푖 푐 − 휏 2 퐼 = 퐼0푒 푚 = 푚표푚푒 퐸0 = 푚푐 푉 푁퐴 = 푛 푠푛 훼 푚푐2 퐼 = 2 푋 푓 1 퐾퐸푟푒푙 = − 푚푐 퐿 푣2 푓/# = ≈ √1 − 푋퐿 = 2휋푓퐿 퐷 2푁퐴 푐2 푉 푑 = 푓 2 2 2 2 퐼 = 푖 표 퐸 = (푝푐) + (푚푐 ) 푋 푓표 퐶 푀 = 1 푓 푋 = 푒 퐶 2휋푓퐶 푉0 푉푟푚푠 Chapter 27: Wave Optics 퐼 = 표푟 퐼 = 0 푍 푟푚푠 푍 휆 2 2 푍 = √푅 + (푋 − 푋 ) 휆푛 = 퐿 퐶 푛 1 휆 푓0 = sin 휃 = 푚 2휋√퐿퐶 푑.