Physicsformulas sheet, Study notes of Physics

Download Physicsformulas sheet and more Study notes Physics in PDF only on Docsity! Please Do Not Write on This Sheet Physics Formula Sheet Chapter 1: Introduction: The Nature of Science and Physics 𝑥 = −𝑏 ± √𝑏2 − 4𝑎𝑐 2𝑎 𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 6.38 × 106 𝑚 𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 5.98 × 1024 𝑘𝑔 𝑐 = 3.00 × 108 𝑚/𝑠 𝐺 = 6.673 × 10−11 𝑁𝑚2 𝑘𝑔2 𝑁𝐴 = 6.02 × 10 23 𝑘 = 1.38 × 10−23𝐽/𝐾 𝑅 = 8.31 𝐽 𝑚𝑜𝑙 ⋅ 𝐾⁄ 𝜎 = 5.67 × 10−8𝑊/(𝑚2 ⋅ 𝐾) 𝑘 = 8.99 × 109 𝑁 ⋅ 𝑚2/𝐶2 𝑞𝑒 = −1.60 × 10 −19 𝐶 𝜖0 = 8.85 × 10 −12𝐶2/(𝑁 ⋅ 𝑚2) 𝜇0 = 4π × 10 −7 𝑇 ⋅ 𝑚/𝐴 ℎ = 6.63 × 10−34 𝐽 ⋅ 𝑠 𝑚𝑒 = 9.11 × 10 −31 𝑘𝑔 𝑚𝑝 = 1.6726 × 10 −27 𝑘𝑔 𝑚𝑛 = 1.6749 × 10 −27 𝑘𝑔 𝑎𝑚𝑢 = 1.6605 × 10−27 𝑘𝑔 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 = 1000 𝑘𝑔 𝑚3 Chapter 2: Kinematics 𝛥𝑥 = 𝑥𝑓 − 𝑥0 𝛥𝑡 = 𝑡𝑓 − 𝑡0 𝑣 = 𝛥𝑥 𝛥𝑡 = 𝑥𝑓 − 𝑥0 𝑡𝑓 − 𝑡0 𝑎 = 𝛥𝑣 𝛥𝑡 = 𝑣𝑓 − 𝑣0 𝑡𝑓 − 𝑡0 𝑥 = 𝑥0 + 𝑣𝑡 𝑣 = 𝑣0 + 𝑣 2 𝑣 = 𝑣0 + 𝑎𝑡 𝑥 = 𝑥0 + 𝑣0𝑡 + 1 2 𝑎𝑡2 𝑣2 = 𝑣0 2 + 2𝑎(𝑥 − 𝑥0) 𝑔 = 9.80 𝑚 𝑠2 Chapter 3: Two-Dimensional Kinematics 𝐴𝑥 = 𝐴 𝑐𝑜𝑠 𝜃 𝐴𝑦 = 𝐴 𝑠𝑖𝑛 𝜃 𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦 𝑅 = √𝑅𝑥 2 + 𝑅𝑦 2 𝜃 = 𝑡𝑎𝑛−1 𝑅𝑦 𝑅𝑥 ℎ = 𝑣0𝑦 2 2𝑔 𝑅 = 𝑣0 2 𝑠𝑖𝑛 2𝜃0 𝑔 𝑣𝑥 = 𝑣 𝑐𝑜𝑠 𝜃 𝑣𝑦 = 𝑣 𝑠𝑖𝑛 𝜃 𝑣 = √𝑣𝑥 2 + 𝑣𝑦 2 𝜃 = 𝑡𝑎𝑛−1 𝑣𝑦 𝑣𝑥 Chapter 4: Dynamics: Forces and Newton’s Laws of Motion 𝐹𝑛𝑒𝑡 = 𝑚𝑎 𝑤 = 𝑚𝑔 Chapter 5: Further Applications of Newton’s Laws: Friction, Drag, and Elasticity 𝑓𝑠 ≤ 𝜇𝑠𝑁 𝑓𝑘 = 𝜇𝑘𝑁 𝐹𝐷 = 1 2 𝐶𝜌𝐴𝑣2 𝐹𝑠 = 6𝜋𝜂𝑟𝑣 𝐹 = 𝑘𝛥𝑥 𝛥𝐿 = 1𝐹 𝑌𝐴 𝐿0 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝐹 𝐴 𝑠𝑡𝑟𝑎𝑖𝑛 = 𝛥𝐿 𝐿0 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑌 × 𝑠𝑡𝑟𝑎𝑖𝑛 𝛥𝑥 = 1𝐹 𝑆𝐴 𝐿0 𝛥𝑉 = 1𝐹 𝐵𝐴 𝑉0 Chapter 6: Uniform Circular Motion and Gravitation 𝛥𝜃 = 𝛥𝑠 𝑟 2𝜋 𝑟𝑎𝑑 = 360° = 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝜔 = 𝛥𝜃 𝛥𝑡 𝑣 = 𝑟𝜔 𝑎𝐶 = 𝑣2 𝑟 𝑎𝐶 = 𝑟𝜔 2 𝐹𝐶 = 𝑚𝑎𝐶 𝐹𝐶 = 𝑚𝑣2 𝑟 𝑡𝑎𝑛 𝜃 = 𝑣2 𝑟𝑔 𝐹𝐶 = 𝑚𝑟𝜔 2 𝐹 = 𝐺 𝑚𝑀 𝑟2 𝑔 = 𝐺𝑀 𝑟2 𝑇1 2 𝑇2 2 = 𝑟1 3 𝑟2 3 𝑇2 = 4𝜋2 𝐺𝑀 𝑟3 𝑟3 𝑇2 = 𝐺 4𝜋2 𝑀 Chapter 7: Work, Energy, and Energy Resources 𝑊 = 𝑓𝑑 𝑐𝑜𝑠 𝜃 𝐾𝐸 = 1 2 𝑚𝑣2 𝑊𝑛𝑒𝑡 = 1 2 𝑚𝑣𝑓 2 − 1 2 𝑚𝑣0 2 𝑃𝐸𝑔 = 𝑚𝑔ℎ 𝑃𝐸𝑠 = 1 2 𝑘𝑥2 𝐾𝐸0 + 𝑃𝐸0 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 𝐾𝐸0 + 𝑃𝐸0 + 𝑊𝑛𝑐 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 𝐸𝑓𝑓 = 𝑊𝑜𝑢𝑡 𝐸𝑖𝑛 𝑃 = 𝑊 𝑡 Chapter 8: Linear Momentum and Collisions 𝑝 = 𝑚𝑣 𝛥𝑝 = 𝐹𝑛𝑒𝑡𝛥𝑡 𝑝0 = 𝑝𝑓 𝑚1𝑣01 + 𝑚2𝑣02 = 𝑚1𝑣𝑓1 + 𝑚2𝑣𝑓2 Please Do Not Write on This Sheet 1 2 𝑚1𝑣01 2 + 1 2 𝑚2𝑣02 2 = 1 2 𝑚1𝑣𝑓1 2 + 1 2 𝑚2𝑣𝑓2 2 𝑚1𝑣1 = 𝑚1𝑣1 ′ 𝑐𝑜𝑠 𝜃1 + 𝑚2𝑣2 ′ 𝑐𝑜𝑠 𝜃2 0 = 𝑚1𝑣1 ′ 𝑠𝑖𝑛 𝜃1 + 𝑚2𝑣2 ′ 𝑠𝑖𝑛 𝜃2 1 2 𝑚𝑣1 2 = 1 2 𝑚𝑣1 ′2 + 1 2 𝑚𝑣2 ′2 + 𝑚𝑣1 ′ 𝑣2 ′ 𝑐𝑜𝑠(𝜃1 − 𝜃2) 𝑎 = 𝑣𝑒 𝑚 𝛥𝑚 𝛥𝑡 − 𝑔 𝑣𝑐𝑚 = 𝑣1𝑚1 + 𝑣2𝑚2 𝑚1 + 𝑚2 Chapter 9: Statics and Torque 𝜏 = 𝑟𝐹 𝑠𝑖𝑛 𝜃 𝑟⊥ = 𝑟 𝑠𝑖𝑛 𝜃 𝑀𝐴 = 𝐹𝑜 𝐹𝑖 = 𝑙𝑖 𝑙𝑜 𝑙𝑖𝐹𝑖 = 𝑙𝑜𝐹𝑜 Chapter 10: Rotational Motion and Angular Momentum 𝜔 = 𝛥𝜃 𝛥𝑡 𝑣 = 𝑟𝜔 𝛼 = 𝛥𝜔 𝛥𝑡 𝑎𝑡 = 𝛥𝑣 𝛥𝑡 𝑎𝑡 = 𝑟𝛼 𝜃 = 𝜔𝑡 𝜔 = 𝜔0 + 𝛼𝑡 𝜃 = 𝜔0𝑡 + 1 2 𝛼𝑡2 𝜔2 = 𝜔0 2 + 2𝛼𝜃 𝜔 = 𝜔0 + 𝜔 2 𝑛𝑒𝑡 𝜏 = 𝐼𝛼 Hoop about cylinder axis: 𝐼 = 𝑀𝑅2 Hoop about any diameter: 𝐼 = 𝑀𝑅2 2 Ring: 𝐼 = 𝑀 2 (𝑅1 2 + 𝑅2 2) Solid cylinder (or disk) about cylinder axis: 𝐼 = 𝑀𝑅2 2 Solid cylinder (or disk) about central diameter: 𝐼 = 𝑀𝑅2 4 + 𝑀ℓ2 12 Thin rod about axis through center ⊥ to length: 𝐼 = 𝑀ℓ2 12 Thin rod about axis through one end ⊥ to length: 𝐼 = 𝑀ℓ2 3 Solid sphere: 𝐼 = 2𝑀𝑅2 5 Thin spherical shell: 𝐼 = 2𝑀𝑅2 3 Slab about ⊥ axis through center: 𝐼 = 𝑀(𝑎2+𝑏2) 12 𝑛𝑒𝑡 𝑊 = (𝑛𝑒𝑡 𝜏)𝜃 𝐾𝐸𝑟𝑜𝑡 = 1 2 𝐼𝜔2 𝐿 = 𝐼𝜔 𝑛𝑒𝑡 𝜏 = 𝛥𝐿 𝛥𝑡 Chapter 11: Fluid Statics 𝜌 = 𝑚 𝑉 𝑃 = 𝐹 𝐴 𝑃𝑎𝑡𝑚 = 1.01 × 10 5 𝑃𝑎 𝑃 = 𝜌𝑔ℎ 𝑃2 = 𝑃1 + 𝜌𝑔ℎ 𝐹1 𝐴1 = 𝐹2 𝐴2 𝐹𝐵 = 𝑤𝑓𝑙 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 = 𝜌𝑜𝑏𝑗 𝜌𝑓𝑙 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝜌 𝜌𝑤 𝛾 = 𝐹 𝐿 𝑃 = 4𝛾 𝑟 ℎ = 2𝛾 𝑐𝑜𝑠 𝜃 𝜌𝑔𝑟 Chapter 12: Fluid Dynamics and Its Biological Medical Applications 𝑄 = 𝑉 𝑡 𝑄 = 𝐴𝑣 𝐴1𝑣1 = 𝐴2𝑣2 𝑛1𝐴1𝑣1 = 𝑛2𝐴2𝑣2 𝑃1 + 1 2 𝜌𝑣1 2 + 𝜌𝑔ℎ1 = 𝑃2 + 1 2 𝜌𝑣2 2 + 𝜌𝑔ℎ2 (Δ𝑃 + Δ 1 2 𝜌𝑣2 + Δ𝜌𝑔ℎ) 𝑄 = 𝑝𝑜𝑤𝑒𝑟 𝑣1 = √2𝑔ℎ 𝜂 = 𝐹𝐿 𝑣𝐴 𝑄 = 𝑃2 − 𝑃1 𝑅 𝑅 = 8𝜂𝑙 𝜋𝑟4 𝑄 = (𝑃2 − 𝑃1)𝜋𝑟 4 8𝜂𝑙 𝑁𝑅 = 2𝜌𝑣𝑟 𝜂 𝑁𝑅 ′ = 𝜌𝑣𝐿 𝜂 𝑥𝑟𝑚𝑠 = √2𝐷𝑡 Chapter 13: Temperature, Kinetic Theory, and the Gas Laws 𝑇(°𝐹) = 9 5 𝑇(°𝐶) + 32 𝑇(𝐾) = 𝑇(°𝐶) + 273.15 𝛥𝐿 = 𝛼𝐿𝛥𝑇 𝛥𝐴 = 2𝛼𝐴𝛥𝑇 𝛥𝑉 = 𝛽𝑉𝛥𝑇 𝛽 ≈ 3𝛼 𝑃𝑉 = 𝑁𝑘𝑇 𝑘 = 1.38 × 10−23 𝐽/𝐾 𝑁𝐴 = 6.02 × 10 23 𝑚𝑜𝑙−1 𝑃𝑉 = 𝑛𝑅𝑇 𝑅 = 8.31 𝐽 𝑚𝑜𝑙 ⋅ 𝐾 𝑃𝑉 = 1 3 𝑁𝑚𝑣 2 𝐾𝐸 = 1 2 𝑚𝑣 2 = 3 2 𝑘𝑇 𝑣𝑟𝑚𝑠 = √ 3𝑘𝑇 𝑚 % 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 ℎ𝑢𝑚𝑖𝑑𝑖𝑡𝑦 = 𝑣𝑎𝑝𝑜𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑑𝑒𝑛𝑎𝑠𝑖𝑡𝑦 × 100% Chapter 14: Heat and Heat Transfer Methods