Physics 101 Formulas, Summaries of Physics

Download Physics 101 Formulas and more Summaries Physics in PDF only on Docsity! Physics 101 Formulas 12/7/2017 1 Kinematics 𝒗𝒗𝑎𝑎𝑎𝑎𝑎𝑎 = 𝛥𝛥𝒙𝒙 𝛥𝛥𝛥𝛥 𝒂𝒂𝑎𝑎𝑎𝑎𝑎𝑎 = 𝛥𝛥𝒗𝒗 𝛥𝛥𝛥𝛥 𝑣𝑣 = 𝑣𝑣0 + 𝑎𝑎𝑎𝑎 𝑥𝑥 = 𝑥𝑥0 + 𝑣𝑣0𝑎𝑎 + 1 2 𝑎𝑎𝑎𝑎2 𝑣𝑣2 = 𝑣𝑣02 + 2𝑎𝑎𝑎𝑎𝑥𝑥 𝑔𝑔 = 9.8 m/s2 = 32.2 ft/s2 (near Earth’s surface) Dynamics 𝛴𝛴𝑭𝑭 = 𝑚𝑚𝒂𝒂 𝑊𝑊𝑊𝑊𝑊𝑊𝑔𝑔ℎ𝑎𝑎 = 𝑚𝑚𝑔𝑔 (near Earth’s surface) 𝑓𝑓𝑠𝑠,𝑚𝑚𝑎𝑎𝑚𝑚 = 𝜇𝜇𝑠𝑠𝐹𝐹𝑁𝑁 𝑓𝑓𝑘𝑘 = 𝜇𝜇𝑘𝑘𝐹𝐹𝑁𝑁 𝑎𝑎𝑐𝑐 = 𝑎𝑎2 𝑅𝑅 = 𝜔𝜔2𝑅𝑅 Universal Gravitation Universal Gravitational Constant 𝐺𝐺 = 6.7 × 10–11 N ∙ m 2 kg2 𝐹𝐹𝑔𝑔 = 𝐺𝐺𝑚𝑚1𝑚𝑚2 𝑅𝑅2 𝑈𝑈𝑔𝑔 = −𝐺𝐺𝑚𝑚1𝑚𝑚2 𝑅𝑅 Work & Energy 𝑊𝑊𝐹𝐹 = 𝐹𝐹𝐹𝐹cos(𝜃𝜃) 𝐾𝐾 = 1 2 𝑚𝑚𝑣𝑣2 = 𝑝𝑝2 2𝑚𝑚 𝑊𝑊𝑁𝑁𝑁𝑁𝑁𝑁 = 𝑎𝑎𝐾𝐾 = 𝐾𝐾𝑓𝑓 – 𝐾𝐾𝑖𝑖 𝐸𝐸 = 𝐾𝐾 + 𝑈𝑈 𝑊𝑊𝑛𝑛𝑐𝑐 = 𝑎𝑎𝐸𝐸 = 𝐸𝐸𝑓𝑓 – 𝐸𝐸𝑖𝑖 = (𝐾𝐾𝑓𝑓 + 𝑈𝑈𝑓𝑓) – (𝐾𝐾𝑖𝑖 + 𝑈𝑈𝑖𝑖) 𝑈𝑈𝑔𝑔𝑔𝑔𝑎𝑎𝑎𝑎 = 𝑚𝑚𝑔𝑔𝑚𝑚 Impulse & Momentum Impulse: 𝑰𝑰 = 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑 = 𝑚𝑚𝒗𝒗𝑓𝑓 – 𝑚𝑚𝒗𝒗𝑖𝑖 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑/𝑎𝑎𝑎𝑎 𝛴𝛴𝑭𝑭𝑎𝑎𝑚𝑚𝛥𝛥𝑎𝑎𝑎𝑎 = 𝑎𝑎𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡 = 𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡,𝑓𝑓𝑖𝑖𝑛𝑛𝑎𝑎𝑡𝑡 – 𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡,𝑖𝑖𝑛𝑛𝑖𝑖𝛥𝛥𝑖𝑖𝑎𝑎𝑡𝑡 (momentum conserved if 𝛴𝛴𝑭𝑭𝑎𝑎𝑚𝑚𝛥𝛥 = 0) 𝒙𝒙𝑐𝑐𝑚𝑚 = 𝑚𝑚1𝒙𝒙1 + 𝑚𝑚2𝒙𝒙2 𝑚𝑚1 + 𝑚𝑚2 Elastic Collisions: Mass 𝒎𝒎𝒊𝒊 moving with 𝒗𝒗𝒊𝒊; Stationary mass 𝑴𝑴 𝑣𝑣𝑚𝑚,𝑓𝑓 = 𝑣𝑣𝑚𝑚,𝑖𝑖 𝑚𝑚−𝑀𝑀 𝑚𝑚+𝑀𝑀 𝑣𝑣𝑀𝑀,𝑓𝑓 = 𝑣𝑣𝑚𝑚,𝑖𝑖 2𝑚𝑚 𝑚𝑚+𝑀𝑀 Rotational Kinematics 𝜔𝜔 = 𝜔𝜔0 + 𝛼𝛼𝑎𝑎 𝜃𝜃 = 𝜃𝜃0 + 𝜔𝜔0𝑎𝑎 + 1 2 𝛼𝛼𝑎𝑎2 𝜔𝜔2 = 𝜔𝜔0 2 + 2𝛼𝛼𝑎𝑎𝜃𝜃 𝑎𝑎𝑥𝑥𝑁𝑁 = 𝑅𝑅𝑎𝑎𝜃𝜃 𝑣𝑣𝑁𝑁 = 𝑅𝑅𝜔𝜔 𝑎𝑎𝑁𝑁 = 𝑅𝑅𝛼𝛼 (rolling without slipping: 𝑎𝑎𝑥𝑥 = 𝑅𝑅𝑎𝑎𝜃𝜃 𝑣𝑣 = 𝑅𝑅𝜔𝜔 𝑎𝑎 = 𝑅𝑅𝛼𝛼 ) 1 revolution = 2π radians Rotational Statics & Dynamics 𝜏𝜏 = 𝐹𝐹𝐹𝐹 sin 𝜃𝜃 𝛴𝛴𝜏𝜏 = 0 and 𝛴𝛴𝐹𝐹 = 0 (static equilibrium) 𝛴𝛴𝜏𝜏 = 𝐼𝐼𝛼𝛼 𝑊𝑊 = 𝜏𝜏𝜃𝜃 𝑳𝑳 = 𝐼𝐼𝝎𝝎 𝛴𝛴𝝉𝝉𝑎𝑎𝑚𝑚𝛥𝛥𝑎𝑎𝑎𝑎 = 𝑎𝑎𝑳𝑳 (angular momentum conserved if 𝑎𝑎𝝉𝝉𝑎𝑎𝑚𝑚𝛥𝛥 = 0) 𝐾𝐾𝑔𝑔𝑡𝑡𝛥𝛥 = 1 2 𝐼𝐼𝜔𝜔2 = 𝐿𝐿2 2𝐼𝐼 𝐾𝐾𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡 = 𝐾𝐾𝛥𝛥𝑔𝑔𝑎𝑎𝑛𝑛𝑠𝑠 + 𝐾𝐾𝑔𝑔𝑡𝑡𝛥𝛥 = 1 2 𝑚𝑚𝑣𝑣2 + 1 2 𝐼𝐼𝜔𝜔2 𝐼𝐼 = 𝐼𝐼𝑐𝑐𝑚𝑚 + 𝑚𝑚𝐹𝐹2 Parallel axis theorem Moments of Inertia (I) 𝐼𝐼 = 𝛴𝛴𝑚𝑚𝐹𝐹2 (for a collection of point particles) 𝐼𝐼 = 1 2 𝑀𝑀𝑅𝑅2 (solid disk or cylinder) 𝐼𝐼 = 2 5 𝑀𝑀𝑅𝑅2 (solid ball) 𝐼𝐼 = 2 3 𝑀𝑀𝑅𝑅2 (hollow sphere) 𝐼𝐼 = 𝑀𝑀𝑅𝑅2 (hoop or hollow cylinder) 𝐼𝐼 = 1 12 𝑀𝑀𝐿𝐿2 (uniform rod about center) 𝐼𝐼 = 1 3 𝑀𝑀𝐿𝐿2 (uniform rod about one end) Last Name: First Name: Lab Section: Exam Day: Exam Time Physics 101 Formulas 12/7/2017 2 Fluids 𝑃𝑃 = 𝐹𝐹 𝐴𝐴 , 𝑃𝑃(𝑑𝑑) = 𝑃𝑃(0) + 𝜌𝜌𝑔𝑔𝑑𝑑 change in pressure with depth 𝑑𝑑 𝜌𝜌 = 𝑀𝑀 𝑉𝑉 (density) Buoyant force 𝐹𝐹𝐵𝐵 = 𝜌𝜌𝑔𝑔𝑉𝑉𝑑𝑑𝑖𝑖𝑠𝑠 = weight of displaced fluid Flow rate 𝑄𝑄 = 𝑣𝑣1𝐴𝐴1 = 𝑣𝑣2 𝐴𝐴2 continuity equation 𝑃𝑃1 + 1 2 𝜌𝜌𝑣𝑣12 + 𝜌𝜌𝑔𝑔𝑚𝑚1 = 𝑃𝑃2 + 1 2 𝜌𝜌𝑣𝑣22 + 𝜌𝜌𝑔𝑔𝑚𝑚2 Bernoulli equation Simple Harmonic Motion Hooke’s Law: 𝐹𝐹𝑠𝑠 = – 𝑘𝑘𝑥𝑥 𝑈𝑈𝑠𝑠𝑝𝑝𝑔𝑔𝑖𝑖𝑛𝑛𝑔𝑔 = 1 2 𝑘𝑘𝑥𝑥2 𝑥𝑥(𝑎𝑎) = 𝐴𝐴 cos(𝜔𝜔𝑎𝑎) or 𝑥𝑥(𝑎𝑎) = 𝐴𝐴 sin(𝜔𝜔𝑎𝑎) 𝑣𝑣(𝑎𝑎) = –𝐴𝐴𝜔𝜔sin(𝜔𝜔𝑎𝑎) 𝑜𝑜𝐹𝐹 𝑣𝑣(𝑎𝑎) = 𝐴𝐴𝜔𝜔cos(𝜔𝜔𝑎𝑎) 𝑎𝑎(𝑎𝑎) = –𝐴𝐴𝜔𝜔2cos(𝜔𝜔𝑎𝑎) or 𝑎𝑎(𝑎𝑎) = –𝐴𝐴𝜔𝜔2sin(𝜔𝜔𝑎𝑎) Harmonic Waves 𝑣𝑣 = 𝜆𝜆 𝑁𝑁 = 𝜆𝜆 𝑓𝑓 𝑣𝑣 = 𝑐𝑐 = 3 × 108 m/s for electromagnetic waves (light, microwaves, etc.) 𝑣𝑣2 = 𝐹𝐹 𝑚𝑚 𝐿𝐿� for wave on a string 𝜆𝜆𝑛𝑛 = 2 𝑛𝑛 𝐿𝐿 (wavelength, of the 𝑛𝑛𝛥𝛥ℎ harmonic) Sound Waves Loudness: 𝛽𝛽 = 10 log10 � 𝐼𝐼 𝐼𝐼0 � (in dB), where 𝐼𝐼0 = 10–12 W/m2 𝐼𝐼 = 𝑃𝑃 4𝜋𝜋𝑔𝑔2 (sound intensity) 𝛽𝛽2 − 𝛽𝛽1 = (10 dB) log10 � 𝐼𝐼2 𝐼𝐼1 � 𝑓𝑓𝑡𝑡𝑜𝑜𝑠𝑠𝑎𝑎𝑔𝑔𝑎𝑎𝑎𝑎𝑔𝑔 = 𝑓𝑓𝑠𝑠𝑡𝑡𝑠𝑠𝑔𝑔𝑐𝑐𝑎𝑎 (𝑎𝑎𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤−𝑎𝑎𝑜𝑜𝑜𝑜𝑜𝑜𝑤𝑤𝑜𝑜𝑤𝑤𝑤𝑤𝑜𝑜) 𝑎𝑎𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤−𝑎𝑎𝑜𝑜𝑜𝑜𝑠𝑠𝑜𝑜𝑠𝑠𝑤𝑤 (Doppler Effect) 𝜔𝜔2 = 𝑘𝑘 𝑚𝑚 𝑇𝑇 = 2𝜋𝜋 𝜔𝜔 = 2𝜋𝜋�𝑚𝑚 𝑘𝑘 𝑓𝑓 = 1/𝑇𝑇 𝑥𝑥𝑚𝑚𝑎𝑎𝑚𝑚 = 𝐴𝐴 𝑣𝑣𝑚𝑚𝑎𝑎𝑚𝑚 = 𝜔𝜔𝐴𝐴 𝑎𝑎𝑚𝑚𝑎𝑎𝑚𝑚 = 𝜔𝜔2𝐴𝐴 𝜔𝜔 = 2𝜋𝜋 𝑓𝑓 For a simple pendulum 𝜔𝜔2 = 𝑔𝑔 𝐿𝐿 , 𝑇𝑇 = 2𝜋𝜋 /L g 𝜌𝜌𝑤𝑤𝑎𝑎𝛥𝛥𝑎𝑎𝑔𝑔 = 1000 kg/m3 1 m3 = 1000 liters 1 atm = 1.01 𝑥𝑥 105 Pa 1 Pa = 1 N/m2 (area of circle A=πr2)