Summary PHYS 20400 Formula Sheet

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Phy s ics Fo rm ula She et
𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦 𝑣 = 𝑟𝜔
𝑣2
Chapter 1: Introduction: The
𝑅 = √𝑅2𝑥 + 𝑅𝑦2 𝑎𝐶 =
𝑟
Nature of Science and Physics
−𝑏 ± √𝑏 2 − 4𝑎𝑐 𝑅𝑦 𝑎𝐶 = 𝑟𝜔2
𝑥= 𝜃 = 𝑡𝑎𝑛−1
2𝑎 𝐹𝐶 = 𝑚𝑎𝐶
𝑅𝑥
𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 6.38 × 106 𝑚
𝑣0𝑦
2 𝑚𝑣 2
𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 5.98 × 1024 𝑘𝑔 ℎ= 𝐹𝐶 =
2𝑔 𝑟
𝑐 = 3.00 × 108 𝑚/𝑠 𝑣2
𝑣02 𝑠𝑖𝑛 2𝜃0 𝑡𝑎𝑛 𝜃 =
𝑁𝑚2 𝑅= 𝑟𝑔
𝐺 = 6.673 × 10−11 𝑔
𝑘𝑔2 𝐹𝐶 = 𝑚𝑟𝜔2
𝑣𝑥 = 𝑣 𝑐𝑜𝑠 𝜃
𝑁𝐴 = 6.02 × 1023 𝑚𝑀
𝑣𝑦 = 𝑣 𝑠𝑖𝑛 𝜃 𝐹=𝐺 2
𝑘 = 1.38 × 10−23 𝐽/𝐾 𝑟
𝐽 𝑣 = √𝑣𝑥2 + 𝑣𝑦2 𝐺𝑀
𝑅 = 8.31 ⁄𝑚𝑜𝑙 ⋅ 𝐾 𝑔= 2
𝑣𝑦 𝑟
𝜎 = 5.67 × 10−8𝑊/(𝑚2 ⋅ 𝐾)
𝜃 = 𝑡𝑎𝑛−1 𝑇12 𝑟13
𝑘 = 8.99 × 109 𝑁 ⋅ 𝑚2 /𝐶 2 𝑣𝑥 2 = 3
𝑇2 𝑟2
𝑞𝑒 = −1.60 × 10−19 𝐶
4𝜋 2 3
𝜖0 = 8.85 × 10−12 𝐶 2 /(𝑁 ⋅ 𝑚2 ) 𝑇2 = 𝑟
𝐺𝑀
Chapter 4: Dynamics: Forces
𝜇0 = 4π × 10−7 𝑇 ⋅ 𝑚/𝐴 𝑟3 𝐺
= 𝑀
and Newton’s Laws of Motion
ℎ = 6.63 × 10−34 𝐽 ⋅ 𝑠 𝐹𝑛𝑒𝑡 = 𝑚𝑎 𝑇 2 4𝜋 2
𝑚𝑒 = 9.11 × 10−31 𝑘𝑔 𝑤 = 𝑚𝑔
𝑚𝑝 = 1.6726 × 10−27 𝑘𝑔
𝑚𝑛 = 1.6749 × 10−27 𝑘𝑔
Chapter 7: Work, Energy, and

𝑎𝑚𝑢 = 1.6605 × 10 𝑘𝑔
Chapter 5: Further Applications Energy Resources
−27
𝑊 = 𝑓𝑑 𝑐𝑜𝑠 𝜃
𝑘𝑔
of Newton’s Laws: Friction,
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 = 1000 1
𝑚3 𝐾𝐸 = 𝑚𝑣2
2
Drag, and Elasticity
𝑓𝑠 ≤ 𝜇𝑠 𝑁
1 1
𝑓𝑘 = 𝜇𝑘 𝑁 𝑊𝑛𝑒𝑡 = 𝑚𝑣𝑓2 − 𝑚𝑣02
Chapter 2: Kinematics
1 2 2
𝛥𝑥 = 𝑥𝑓 − 𝑥0 𝐹𝐷 = 𝐶𝜌𝐴𝑣 2 𝑃𝐸𝑔 = 𝑚𝑔ℎ
2
𝛥𝑡 = 𝑡𝑓 − 𝑡0 𝐹𝑠 = 6𝜋𝜂𝑟𝑣 1 2
𝑃𝐸𝑠 = 𝑘𝑥
𝛥𝑥 𝑥𝑓 − 𝑥0 𝐹 = 𝑘𝛥𝑥 2
𝑣= = 𝐾𝐸0 + 𝑃𝐸0 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓
𝛥𝑡 𝑡𝑓 − 𝑡0 1𝐹
𝛥𝐿 = 𝐿 𝐾𝐸0 + 𝑃𝐸0 + 𝑊𝑛𝑐 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓
𝛥𝑣 𝑣𝑓 − 𝑣0 𝑌𝐴 0
𝑎= = 𝐹 𝑊𝑜𝑢𝑡
𝛥𝑡 𝑡𝑓 − 𝑡0 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝐸𝑓𝑓 =
𝐴 𝐸𝑖𝑛
𝑥 = 𝑥0 + 𝑣𝑡
𝛥𝐿 𝑊
𝑣0 + 𝑣 𝑠𝑡𝑟𝑎𝑖𝑛 = 𝑃=
𝑣= 𝐿0 𝑡
2
𝑣 = 𝑣0 + 𝑎𝑡 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑌 × 𝑠𝑡𝑟𝑎𝑖𝑛
1 1𝐹
𝑥 = 𝑥0 + 𝑣0 𝑡 + 𝑎𝑡 2 𝛥𝑥 = 𝐿
𝑆𝐴 0
Chapter 8: Linear Momentum
2
1𝐹
and Collisions
𝑣 = 𝑣02 + 2𝑎 (𝑥 − 𝑥0 )
2
𝛥𝑉 = 𝑉 𝑝 = 𝑚𝑣
𝑚 𝐵𝐴 0
𝑔 = 9.80 2 𝛥𝑝 = 𝐹𝑛𝑒𝑡 𝛥𝑡
𝑠
𝑝0 = 𝑝𝑓
𝑚1 𝑣01 + 𝑚2 𝑣02 = 𝑚1 𝑣𝑓1 + 𝑚2 𝑣𝑓2
Chapter 6: Uniform Circular
Motion and Gravitation
𝛥𝑠
Chapter 3: Two-Dimensional

𝛥𝜃 =
Kinematics
𝐴𝑥 = 𝐴 𝑐𝑜𝑠 𝜃 𝑟
2𝜋 𝑟𝑎𝑑 = 360° = 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛
𝐴𝑦 = 𝐴 𝑠𝑖𝑛 𝜃
𝛥𝜃
𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 𝜔=
𝛥𝑡