Physics 101 Formulas, Lecture notes of Physics

Download Physics 101 Formulas and more Lecture notes Physics in PDF only on Docsity! Physics 101 Formulas 4/9/2019 1 Kinematics 𝒗"#$ = '𝒙 ') 𝒂"#$ = '𝒗 ') 𝑣 = 𝑣, + 𝑎𝑡 𝑥 = 𝑥, + 𝑣,𝑡 + 1 2 𝑎𝑡3 𝑣3 = 𝑣,3 + 2𝑎𝛥𝑥 𝑔 = 9.8 m/s3 = 32.2 ft/s3 (near Earth’s surface) Dynamics 𝛴𝑭 = 𝑚𝒂 𝑊𝑒𝑖𝑔ℎ𝑡 = 𝑚𝑔 (near Earth’s surface) 𝑓G,I"J = 𝜇G𝐹M 𝑓N = 𝜇N𝐹M 𝑎O = #P Q = 𝜔3𝑅 Universal Gravitation Universal Gravitational Constant 𝐺 = 6.7 × 10–ZZ N ∙ ] P ^_P 𝐹 = aIbIP QP 𝑈 = − aIbIP Q Work & Energy 𝑊e = 𝐹𝐷cos(𝜃) 𝐾 = Z 3 𝑚𝑣3 = mP 3I 𝑊Mno = 𝛥𝐾 = 𝐾p – 𝐾q 𝐸 = 𝐾 + 𝑈 𝑊sO = 𝛥𝐸 = 𝐸p – 𝐸q = (𝐾p + 𝑈p) – (𝐾q + 𝑈q) 𝑈 t"# = 𝑚𝑔𝑦 Impulse & Momentum Impulse: 𝑰 = 𝑭"#$𝛥𝑡 = 𝛥𝒑 𝑭"#$𝛥𝑡 = 𝛥𝒑 = 𝑚𝒗p – 𝑚𝒗q 𝑭"#$ = 𝛥𝒑/𝛥𝑡 𝛴𝑭$J)𝛥𝑡 = 𝛥𝑷)y)"z = 𝑷)y)"z,pqs"z – 𝑷)y)"z,qsq)q"z (momentum conserved if 𝛴𝑭$J) = 0) 𝒙OI = Ib𝒙b { IP𝒙P Ib { IP Elastic Collisions: Mass 𝒎𝒊 moving with 𝒗𝒊; Stationary mass 𝑴 𝑣I,p = 𝑣I,q I€ I{€ 𝑣€,p = 𝑣I,q 3I I{€ Rotational Kinematics 𝜔 = 𝜔, + 𝛼𝑡 𝜃 = 𝜃, + 𝜔,𝑡 + Z 3 𝛼𝑡3 𝜔3 = 𝜔,3 + 2𝛼𝛥𝜃 𝛥𝑥o = 𝑅𝛥𝜃 𝑣o = 𝑅𝜔 𝑎o = 𝑅𝛼 (rolling without slipping: 𝛥𝑥 = 𝑅𝛥𝜃 𝑣 = 𝑅𝜔 𝑎 = 𝑅𝛼 ) 1 revolution = 2π radians Rotational Statics & Dynamics 𝜏 = 𝐹𝑟 sin 𝜃 𝛴𝜏 = 0 and 𝛴𝐹 = 0 (static equilibrium) 𝛴𝜏 = 𝐼𝛼 𝑊 = 𝜏𝜃 𝑳 = 𝐼𝝎 𝛴𝝉$J)𝛥𝑡 = 𝛥𝑳 (angular momentum conserved if 𝛥𝝉$J) = 0) 𝐾ty) = Z 3 𝐼𝜔3 = “P 3” 𝐾)y)"z = 𝐾)t"sG + 𝐾ty) = Z 3 𝑚𝑣3 + Z 3 𝐼𝜔3 Moments of Inertia (I) 𝐼 = 𝛴𝑚𝑟3 (for a collection of point particles) 𝐼 = 1 2 𝑀𝑅3 (solid disk or cylinder) 𝐼 = 2 5 𝑀𝑅3 (solid ball) 𝐼 = 2 3 𝑀𝑅3 (hollow sphere) 𝐼 = 𝑀𝑅3 (hoop or hollow cylinder) 𝐼 = 1 12 𝑀𝐿3 (uniform rod about center) 𝐼 = 1 3 𝑀𝐿3 (uniform rod about one end) Last Name: First Name: Lab Section: Exam Day: Exam Time Physics 101 Formulas 4/9/2019 2 Fluids 𝑃 = e ™ , 𝑃(𝑑) = 𝑃(0) + 𝜌𝑔𝑑 change in pressure with depth 𝑑 𝜌 = € œ (density) Buoyant force 𝐹 = 𝜌𝑔𝑉ŸqG = weight of displaced fluid Flow rate 𝑄 = 𝑣Z𝐴Z = 𝑣3 𝐴3 continuity equation 𝑃Z + Z 3 𝜌𝑣Z3 + 𝜌𝑔𝑦Z = 𝑃3 + Z 3 𝜌𝑣33 + 𝜌𝑔𝑦3 Bernoulli equation Simple Harmonic Motion Hooke’s Law: 𝐹G = – 𝑘𝑥 𝑈Gmtqs` = Z 3 𝑘𝑥3 𝑥(𝑡) = 𝐴 cos(𝜔𝑡) or 𝑥(𝑡) = 𝐴 sin(𝜔𝑡) 𝑣(𝑡) = – 𝐴𝜔sin(𝜔𝑡) 𝑜𝑟 𝑣(𝑡) = 𝐴𝜔cos(𝜔𝑡) 𝑎(𝑡) = – 𝐴𝜔3cos(𝜔𝑡) or 𝑎(𝑡) = – 𝐴𝜔3sin(𝜔𝑡) Harmonic Waves 𝑣 = ¤ o = 𝜆 𝑓 𝑣 = 𝑐 = 3 × 10§ m/s for electromagnetic waves (light, microwaves, etc.) 𝑣3 = e I “̈ for wave on a string 𝜆s = 3 s 𝐿 (wavelength, of the 𝑛)ª harmonic) Sound Waves Loudness: 𝛽 = 10 log10 ­ ” ”® ¯ (in dB), where 𝐼, = 10–Z3 W/m3 𝐼 = ± ²³tP (sound intensity) 𝛽3 − 𝛽Z = (10 dB) log µ 𝐼3 𝐼Z ¶ 𝑓zqG)s$t = ·#¸¹º»¼±#¾¿¸À»Á #¸¹º»¼∓#¸¹ºÂÄÁ Å 𝑓GyÆtO$ (Doppler Effect) Numerator: Use + if listener moves toward source – if listener moves away from source. Denominator: Use – if source moves toward listener + if source moves away from listener. 𝜔3 = N I 𝑇 = 3³ È = 2𝜋ÊIN 𝑓 = 1/𝑇 𝑥I"J = 𝐴 𝑣I"J = 𝜔𝐴 𝑎I"J = 𝜔3𝐴 𝜔 = 2𝜋 𝑓 For a simple pendulum 𝜔3 = ` “ , 𝑇 = 2𝜋 /L g 𝜌Ë")$t = 1000 kg/mÍ 1 mÍ = 1000 liters 1 atm = 1.01 𝑥 10Î Pa 1 Pa = 1 N/m3 (area of circle A=πr2)