Formula sheet-physics, Cheat Sheet of Physics

Download Formula sheet-physics and more Cheat Sheet Physics in PDF only on Docsity! Formula Sheet - Physics 111 x y ~Ax ~Ay ~A θ 2D Vectors: A = Ax + Ay = (Ax, Ay)∣∣∣A∣∣∣ = A = √ A2 x +A2 y Ax = A cos θ Ay = A sin θ tan θ = Ay Ax Algebra & Trigonometry: ax2 + bx+ c = 0 ⇒ x = −b± √ b2 − 4ac 2a 2 sin2 x+ cos (2x) = 1 cos (x+ y) = cosx cos y − sin x sin y 2 cos2 x− cos (2x) = 1 sin (x+ y) = sin x cos y + cosx sin y sin2 x+ cos2 x = 1 2 cosx cos y = cos (x− y) + cos (x+ y) sec2 x− tan2 x = 1 2 sin x sin y = cos (x− y)− cos (x+ y) csc2 x− cot2 x = 1 2 sin x cos y = sin (x− y) + cos (x+ y) Conversion factors: femto- (f) = 10−15 pico- (p) = 10−12 nano- (n) = 10−9 micro- (µ) = 10−6 milli- (m) = 10−3 centi- (c) = 10−2 kilo- (k) = 103 mega- (M) = 106 giga- (G) = 109 tera- (T) = 1012 1 yd=3 ft = 36 in 1 in=2.54 cm 1 mi=1609 m 1 lb=4.448 N 1 gal=3.78541 L 1 m3=1000 L 1 atm=1.013× 105 Pa 1 cal=4.186 J =760 mm Hg 1 Cal=1000 cal Geometry Circle: Perimeter = 2πr Area = πr2 Sphere: Surface Area = 4πr2 Volume = 4 3πr 3 Cylinder: Surface Area = 2πr2 + 2πrh Volume = πr2h Few Physical Constants & Quantities: REarth = 6.38× 106 m g = 9.80 m/s2 MEarth = 5.97× 1024 kg G = 6.67× 10−11 Nm2/kg2 Msun = 1.99× 1030 kg R = 8.314 J/mol ·K rsun−Earth = 1.496× 1011 m kB = 1.381× 10−23 J/K STP : 1 atm, 273 K NA = 6.022× 1023 mol−1 vsound,air = 343 m/s σ = 5.67× 10−8 W/m2K4 ρwater = 1000 kg/m3 General Kinematics vavg = ∆r ∆t = r2 − r1 t2 − t1 v = lim ∆t→0 ∆r ∆t aavg = ∆v ∆t = v2 − v1 t2 − t1 a = lim ∆t→0 ∆v ∆t constant acceleration 1D motion Kinematics x = x0 + v0t+ 1 2at 2 v = v0 + at v2 = v2 0 + 2a∆x v = v + v0 2 Constant acceleration Kinematics 2D: x = x0 + v0xt+ 1 2axt 2 vx = v0x + axt v2 x = v2 0x + 2ax∆x y = y0 + v0yt+ 1 2ayt 2 vy = v0y + ayt v2 y = v2 0y + 2ay∆y vx = vx + v0x 2 vy = vy + v0y 2 Projectile motion (ax = 0 and ay = −g) x = x0 + vxt vx = constant. y = y0 + v0yt− 1 2gt 2 vy = v0y − gt v2 y = v2 0y − 2g∆y vy = vy + v0y 2 v2 = v2 x + v2 y v2 = v2 0 − 2g∆y Relative motion ra,c = ra,b + rb,c va,c = va,b + vb,c aa,c = aa,b + ab,c Forces ∑ F = ma FAB = −FBA Fspring = −kx F g(≡W ) = mg fk = µkN fs ≤ µsN Circular motion ω = ∆θ ∆t α = ∆ω ∆t s = Rθ v = Rω atan = Rα a = atan + ar arad = v2 R = ω2R a = √ a2 tan + a2 r Constant α: ω = ω0 + αt ω2 = ω2 0 + 2α∆θ ω = ω + ω0 2 θ = θ0 + ω0t+ 1 2αt 2 Uniform Circular Motion(α = 0) : T = 1 f = 2π ω = 2πR v Work and Energy W =Fd cos θ ∆KE = Wtotal KE = 1 2mv 2 = p2 2m P =W t = Fv cos θ ∆PE = −Wcons ∆E = Wnon−cons E =PE +KE ∆E = ∆PE + ∆KE PEs = 1 2kx 2 PEgrav = mgy Gravitation F g = −GmM r2 r̂ g = GM r2 T 2 r3 = 4π2 GM vcirc orbit = √ GM r Momentum, Impulse, System of particles F net = ∆p ∆t = mtotacm p = mv J = ∆p = F net,avg∆t rcm = ∑ miri∑ mi vcm = ∑ mivi∑ mi acm = ∑ miai∑ mi∑ pi = mtotvcm If F net = 0 ⇒ ∆p = 0 ⇒ p = p′ Elastic Collision: KEbefore = KE′after vA,x − vB,x = − ( v′A,x − v′B,x ) Rigid-body and Rotational motion KE = KEtr +KErot KErot = 1 2Iω 2 KEtr = 1 2mv 2 cm τ = rF sin θ = r⊥F = rF⊥ ∑ τ = I~α W = τ∆θ L = rp sin θ = r⊥p = rp⊥ L = Iω P = τω ∑ τ = ∆L ∆t if ∑ ~τ = 0 ⇒ ∆L = 0 ⇒ L = L′ Icm for few objects about symmetry axis: Isolid sphere = 2 5mr 2 Isolid cylinder = 1 2mr 2 Ihollow sphere = 2 3mr 2 Ihollow cylinder = mr2 Irod = 1 12m` 2 Irectangle = 1 12m ( a2 + b2 ) a b Elasticity E = F/A ∆`/`0 B = − ∆P ∆V/V0 G = F||/A x/h Fluids P = F A P = P0 + ρgh ρ = m V FB = ρFVdisplg A1v1 = A2v2 = const P + ρgy + 1 2ρv 2 = const Simple Harmonic Motion x = A cos(ωt) v = −Aω sin(ωt) a = −Aω2 cos(ωt) ωspring = √ k m T = 1 f = 2π ω Tpendulum = 2π √ ` g Mechanical Waves v = λf ω = 2πf v = √ F m/` f = 1 T 〈P 〉 = 1 2ω 2A2 √ µF I = P 4πr2 sound: v = √ γRT M γair = 1.40 β = (10 dB) log10 I I0 fbeat = |fa − fb| I0 = 10−12 W/m2 fobs = vsnd ± vobs vsnd ± vsrc fsrc Interference: d2 − d1 = n λ 2 n = 0,±2,±4, . . . (constructive) n = ±1,±3,±5, . . . (destructive) Standing wave normal modes: fn = nf0 = nv 2` n = 1, 2, 3, . . . (both ends either fixed or free) = nv 4` n = 1, 3, 5, . . . (one end fixed) Temperature and Heat TK = TC + 273.15 K TC = 5 9 (TF − 32 ◦C) ∆` = α`0∆T Qrad t = εσA ( T 4 − T 4 s ) Qcond t =kATH − TC ` ∆V = βV0∆T Q = mc∆T Q =nCmolar∆T Q = mL Ideal Gas pV = nRT = NkT vrms = √ 3kT m = √ 3RT M n = N NA = m M 〈KE〉 = 3 2kT = 1 2mv 2 rms k = R NA = 1.381× 10−23J/K U = 3 2nRT (monoatomic) Thermodynamics ∆U = Q−W W = p∆V W = |QH| − |QL| eengine = W QH COPrefrig = QL |W | COPideal pump = TH TH − TL eideal = 1− TL TH COPpump = ∣∣∣∣QH W ∣∣∣∣ COPideal refrig = TL TH − TL ∆S = Q T ideal : TL TH = ∣∣∣∣QL QH ∣∣∣∣