University:
University of Houston
Course:
PHYS 1301 | University Physics I
Academic year:

2021
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495

Pages:

2
Author:

klopkar0qn

Vectors 𝐴⃗ = 𝐴𝑥 𝑥̂ + 𝐴𝑦 𝑦̂ Work, Energy, and Power Equations 𝐴 = √𝐴𝑥 2 + 𝐴𝑦 2 𝑜𝑝𝑝 𝑎𝑑𝑗 𝑜𝑝𝑝 , cos 𝜃 = , tan 𝜃 = ℎ𝑦𝑝 ℎ𝑦𝑝 𝑎𝑑𝑗 sin 𝜃 = Vector Addition 𝑊 = 𝐹 𝑑 𝑐𝑜𝑠𝜃 𝐾𝐸 = (for constant force) 1 𝑚v 2 2 (for linear motion) 𝑊𝑡𝑜𝑡 = ∑ 𝑊 , 𝑊𝑡𝑜𝑡 = ∆𝐾, (for constant g-acceleration) ⃗⃗⃗ + 𝑩 ⃗⃗⃗ = (𝐴𝑥 + 𝐵𝑥 )𝒙 ̂ + (𝐴𝑦 +𝐵𝑦 )𝒚 ̂ 𝑨 𝑃𝐸𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝑚𝑔𝑦 𝑣⃗𝐴𝐶 = 𝑣⃗𝐴𝐵 + 𝑣⃗𝐵𝐶 (Relative Motion) 𝑃𝐸𝑠𝑝𝑟𝑖𝑛𝑔 = 2 𝑘𝑠𝑝𝑟𝑖𝑛𝑔 𝑥 2 General Definitions for Linear Motion Ave. speed = v𝑥,𝑎𝑣𝑔 = 𝑎𝑥,𝑎𝑣𝑔 = ∆𝑥 distance time (motion along x-direction) ∆𝑡 ∆v𝑥 (motion along x-direction) ∆𝑡 ⃗⃗ ∆𝒓 , ∆𝑡→0 ∆𝑡 ∆𝐯⃗⃗ ∆𝑡→0 ∆𝑡 ⃗⃗ = lim 𝒂 𝐯⃗⃗ = lim 𝑔 = 9.8𝑚/𝑠 2 (on Earth’s surface) 1 (for ideal spring along x-axis) 𝐸𝑚𝑒𝑐ℎ = 𝑃𝐸 + 𝐾𝐸, 𝑊 𝑃𝑎𝑣𝑔 = ∆𝑡 , 𝑊𝑐𝑜𝑛𝑠 = −∆𝑈 𝑊𝑛𝑜𝑛 𝑐𝑜𝑛𝑠 = ∆𝐸𝑚𝑒𝑐ℎ 𝑃 = 𝐹 v 𝑐𝑜𝑠𝜙 (for constant force) Universal Gravitation 𝐹=𝐺 𝑚1 𝑚2 , 𝑟2 𝑔=𝐺 𝑀 𝑟2 𝐺 = 6.67 × 10−11 𝑁 ∙ 𝑚2 /𝑘𝑔 2 𝑀𝐸𝑎𝑟𝑡ℎ = 5.97 × 1024 𝑘𝑔, 𝑅𝐸𝑎𝑟𝑡ℎ = 6.38 × 103 𝑘𝑚 Linear Motion at Constant Acceleration 𝑀𝑆𝑢𝑛 = 1.99 × 1030 𝑘𝑔 v𝑥 = v𝑜𝑥 + 𝑎𝑥 𝑡 Uniform Rotational Motion v𝑥 2 = v𝑜𝑥 2 + 2𝑎𝑥 (𝑥 − x𝑜 ) 1 𝑥 = x𝑜 + v𝑜𝑥 𝑡 + 𝑎𝑥 𝑡 2 2 1 𝑥 = x𝑜 + (v𝑥 + v𝑜𝑥 )𝑡 2 Quadratic Equation Solver 𝑥= −𝐵±√𝐵2−4𝐴𝐶 (A,B,C coefficients) 2𝐴 Equations Associated with Newton’s Laws ∑ 𝐹⃗ = 𝑚𝑎⃗, w = 𝑚𝑔, 0 ≤ 𝑓𝑠 ≤ 𝜇𝑠 𝑁 , 𝑓𝑘 = 𝜇𝑘 𝑁 1 𝑓𝑑𝑟𝑎𝑔 = 2𝐶𝜌𝐴𝑣 2 ∆𝜃 , ∆𝑡 ω = lim 𝑠 = 𝑟𝜃, 𝑣 = 𝑟ω ω𝑎𝑣𝑔 = 𝑎𝑐𝑝 = 𝑣2 , 𝑟 ∆𝑡→0 𝑇= ∆𝜃 ∆𝑡 2𝜋 𝜔 Equations Associated with Linear Momentum ⃗⃗ = 𝑚𝐯⃗⃗, 𝒑 Impulse: ⃗⃗𝒔𝒚𝒔𝒕𝒆𝒎 = ∑ 𝒑 ⃗⃗ 𝒑 ⃗⃗𝒂𝒗𝒈 ∙ ∆𝑡 ⃗⃗ = 𝑭 𝑰⃗ = ∆𝒑 Rotational Motion and Torque 𝜏 = 𝑟 𝐹𝑡𝑎𝑛 = 𝑟⊥ 𝐹 = 𝑟 F 𝑠𝑖𝑛𝜃 ∑ 𝜏⃗ = 𝐼𝛼⃗, 𝐼 = ∑ 𝑚𝑖 𝑟𝑖2 𝑖 𝐹𝑠𝑝𝑟𝑖𝑛𝑔 = −𝑘𝑠𝑝𝑟𝑖𝑛𝑔 𝑥 (deformation along x-direction) 1 PHYS 1301 Equation Sheet Rotational Motion at Constant Acceleration 𝛼𝑎𝑣𝑔 = ∆ω , ∆𝑡 Simple Harmonic Oscillations ∆ω ∆𝑡→0 ∆𝑡 𝑓= α = lim 1 , 𝑇 𝜔 = 2𝜋𝑓 = 2𝜋 𝑇 𝜔 = ω𝑜 + 𝛼𝑡 𝑥 = 𝐴𝑐𝑜𝑠(𝜔𝑡 + 𝜑), v = − 𝐴𝜔𝑠𝑖𝑛(𝜔𝑡 + 𝜑) 𝜔2 = 𝜔𝑜 2 + 2𝛼(𝜃 − 𝜃𝑜 ) 𝑎 = −𝐴𝜔2 𝑐𝑜𝑠(𝜔𝑡 + 𝜑) 1 𝜃 = 𝜃𝑜 + 𝜔0 𝑡 + 𝛼𝑡 2 2 1 𝜃 = 𝜃𝑜 + (𝜔 + ω𝑜 )𝑡 2 𝜔=√ 𝑘𝑠𝑝𝑟𝑖𝑛𝑔 𝑚 (ideal spring) 𝑠𝑝𝑟𝑖𝑛𝑔 𝑙 𝑇 = 2𝜋√𝑔 𝑎 = √𝑎𝑐𝑝 2 + 𝑎𝑡𝑎𝑛 2 𝑎𝑡𝑎𝑛 = 𝑟𝛼, 𝑚 , 𝑇 = 2𝜋 √𝑘 (simple pendulum) 𝐸𝑆𝐻𝑂 = 1 𝑘 𝐴2 2 𝑠𝑝𝑟𝑖𝑛𝑔 Angular Momentum and Energy 𝐿 = 𝑟 𝑚 𝑣𝑡𝑎𝑛 ⃗⃗ = 𝜏 ⃗⃗𝑛𝑒𝑡 ∆𝑡 ∆𝐿 ⃗⃗ = 𝐼𝜔 𝐿 ⃗⃗, 𝐼𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 = 𝑚𝑅2 , 𝐼𝑠𝑝ℎ𝑒𝑟𝑒 = Traveling Waves and Sound 2 𝑚𝑅2 , 5 1 𝐾𝐸 = 2 𝐼ω2 𝐼ℎ𝑜𝑜𝑝 = 𝑚𝑅2 𝐼𝑑𝑖𝑠𝑘 = 𝑣=𝜆𝑓 v𝑠𝑜𝑢𝑛𝑑 = 343 𝑚/𝑠 1 𝑚𝑅2 2 𝑣𝑠𝑜𝑢𝑛𝑑 = (331 𝑚/𝑠)√ 𝑓𝑝𝑒𝑟𝑐𝑒𝑖𝑣𝑒𝑑 = 𝑓 (for rotational motion) 𝐾𝐸𝑡𝑜𝑡𝑎𝑙 = 1 1 𝑚v 2 + 𝐼ω2 2 2 𝐹 𝐹 𝑝 = 𝑝𝑡𝑜𝑝 + 𝜌𝑔ℎ 𝑝𝑎𝑡𝑚 = 1.01 × 105 𝑃𝑎, 𝑚 𝑙 (taut string) Wave Intensity (uniformly distributed perpendicular force) 𝜌𝑎𝑖𝑟 = 1.29 𝑘𝑔/𝑚3 , 𝑇 273 𝐾 v ± v𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 v ∓ v𝑠𝑜𝑢𝑟𝑐𝑒 v𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑒 = √𝜇 , 𝜇 = Fluids 𝑝=𝐴 (in calm air at 20C) 𝜌𝑤𝑎𝑡𝑒𝑟 = 1000𝑘𝑔/𝑚3 𝐼= 𝑃 𝐼 = 4𝜋𝑟 2 𝑃 ∆𝐴 (at distance r from a point source) 𝐼 𝛽(𝑑𝐵) = (10 𝑑𝐵) log ( ) 𝐼0 𝑝𝑔𝑎𝑢𝑔𝑒 = 𝑝 − 𝑝𝑎𝑡𝑚 𝐹𝐵 = 𝜌𝑓𝑙𝑢𝑖𝑑 𝑉𝑏𝑜𝑑𝑦 𝑔 Standing Waves String: 𝑓𝑛 = 𝑛 2𝑙 𝐹 √𝜇 , n=1,2,3,… Open pipe: 𝑓𝑛 = 𝑛v 2𝑙 , n=1,2,3,… Closed pipe: 𝑓𝑛 = 𝑛v 4𝑙 , n=1,3,5,… 2

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