Physics 211 formula sheet, Cheat Sheet of Physics

Download Physics 211 formula sheet and more Cheat Sheet Physics in PDF only on Docsity! Marshall University Calculus-based Introductory Physics Formula Sheet for Common Final Exam Page 1 of 4 PHY 211 v(t) = dx(t) dt a(t) = dv(t) dt = d2x(t) dt2 x(t) = ˆ t 0 v(t′)dt′ v(t) = ˆ t 0 a(t′)dt′ xf = xi + vit+ 1 2 at2 vf = vi + at v2f = v2i + 2a(xf − xi) vavg = 1 2 (vf + vi) ∆~r = ~vavg∆t ~Fnet ≡ ∑ i ~Fi ~Fnet = m~a Fg = w = mg |~Fs| ≤ µs|~n| |~Fk| = µs|~n| ~FS = −k~x Y = ∆P ∆L/L0 = ∆F A∆L/L0 S = ∆P ∆x/h = ∆F A∆x/ ω = vt r ac = v2t r = rω2 ~FG = −Gm1m2 r2 r̂ g = G mearth r2earth W = ~F · ~d = |~F ||~d| cos(θ) W = ˆ xf xi Fxdx W = ˆ Pf Pi ~F · d~̀= ˆ Pf Pi F‖d` KE = K ≡ 1 2 mv2 Wnet = ∆K Wcons = −∆U = −∆PE PEg = Ug = mgh PEG = UG = −Gm1m2 r PES = US = 1 2 kx2 ~rcm ≡ ∑ imi~ri∑ imi ~vcm ≡ ∑ imi~vi∑ imi ~acm ≡ ∑ imi~ai∑ imi ~p ≡ m~v ~F = ∆~p ∆t ~p1,f + ~p2,f = ~p1,i + ~p2,i . ~J ≡ ~F∆t = ∆~p ~τ ≡ ~r × ~F r⊥ = r sin(θ) τ = r⊥F = Iα θ = s r ω = ∆θ ∆t = vt r α = ∆ω ∆t = at r ~v = −~r × ~ω θf = θi + ωit+ 1 2 αt2 ωf = ωi + αt ω2 f = ω2 i + 2α(θf − θi) ωavg = 1 2 (ωf + ωi) ~L = ~r × ~p = I~ω L = r(mv) sin θ ~τ = ∆~L ∆t W = τ∆θ Krot = 1 2 Iω2 ω = 2πf = 2π T ω = √ k m ω = √ g ` ω = √ mg`cm I x(t) = xmax sin(ωt) v(t) = ωxmax cos(ωt) a(t) = −ω2xmax sin(ωt) E = 1 2 kx2max v = fλ µ ≡ m ` v = √ F µ k ≡ 2π λ ysw(x, t) = [ A sin(kx) ] sin(ωt) fstring = fopen−open = n ( v 2` ) where n ∈ {1, 2, 3, . . .} ` = n λn 2 where n ∈ {1, 2, 3, . . .} fopen−closed = n ( v 4` ) where n ∈ {1, 3, 5, . . .} ` = n λn 4 where n ∈ {1, 3, 5, . . .} ytw(x, t) = A sin(kx∓ ωt) fo = fs ( v ± vo v ∓ vs ) fbeat = |f2 − f1| I = P A I = P 4πr2 I0 ≡ 1.0× 10−12 W m2 β[dB] = 10 log10 ( I I0 ) P = F A ρ = m V Fb = ρV g P = P0 + ρgh P + ρgy + 1 2 ρv2 = const Q = Φv ≡ ~v · ~A = vA cos(θ) Q = ∆V ∆t A1v1 = A2v2 ρvA = ∆m ∆t ∆L = αL0∆T L(∆T ) = L0(1 + α∆T ) ∆V = βv0∆T Marshall University Calculus-based Introductory Physics Formula Sheet for Common Final Exam Page 2 of 4 circumference of a circle C = 2πr area of a circle A = πr2 surface area of a sphere A = 4πr2 volume of a sphere V = 4 3 πr3 If Ax2 +Bx+ C = 0, x = −B ± √ B2 − 4AC 2A loga(xy) = loga(x) + loga(y) loga ( x y ) = loga(x)− loga(y) loga (xy) = y loga(x) If ax = y, x = loga y = log10 y log10 a = ln y ln a If |θ| < 0.5 radians, sin(θ) ≈ θ (in radians) If |θ| < 0.5 radians, tan(θ) ≈ θ (in radians) sin(−θ) = − sin(θ) cos(−θ) = cos(θ) sin(θA + θB) = sin(θA) cos(θB) + cos(θA) sin(θB) cos(θA + θB) = cos(θA) cos(θB)− sin(θA) sin(θB) sin(θA) sin(θB) = cos(θA − θB)− cos(θA + θB) 2 cos(θA) cos(θB) = cos(θA − θB) + cos(θA + θB) 2 sin(θA) cos(θB) = sin(θA − θB) + sin(θA + θB) 2 Law of Cosines c2 = a2 + b2 − 2ab cos(C) Law of Sines a sin(A) = b sin(B) = c sin(C) x = r cos(θ) y = r sin(θ) ⇐⇒  r = √ x2 + y2 θ = tan−1 (y/x) +  0◦, if x > 0 180◦, otherwise If ~R = ~A+ ~B, Rx = Ax +Bx and Ry = Ay +By If ~R = ~A− ~B, Rx = Ax −Bx and Ry = Ay −By ~A · ~B = ~B · ~A = AxBx +AyBy +AzBz = | ~A|| ~B| cos(θ) | ~A× ~B| = | ~A|| ~B||sin(θ)| Newton’s constant G = 6.67430×10−11 m3 kg · s2 speed of light c ≡ 2.99792458× 108 m/s elementary charge e = 1.602176634×10−19 C electrostatic constant k = 8.987551792×109 N ·m2 C2 vacuum permittivity ε0 = 8.854187813×10−12 F/m vacuum permeability µ0 = 1.2566370621×10−6 N ·A−2 (1) ≈ 4π×10−7 N ·A−2 (2) Planck’s constant h = 6.62607015×10−34 J · s ~ ≡ h 2π = 1.054571817×10−34 J · s standard gravity g = +9.80665 m s2 mass of earth mearth = 5.9723×1024 kg mass of moon mmoon = 7.346×1022 kg mass of sun msun = 1.9885×1030 kg mass of electron me = 9.1093837015×10−31 kg mass of proton mp = 1.67262192369×10−27 kg mass of neutron mn = 1.67492749804×10−27 kg volumetric radius of earth rearth = 6.371×106 m earth-moon distance rEM = 3.844×108 m earth-sun distance rES = 1.496×1011 m Density of air at sea level at 15◦ C: ρ0 = 1.225 kg m3 Earth’s total magnetic field strength at Huntington, WV: | ~Bearth| ≈ 5.15×10−5 T Vertical component of Earth’s magnetic field strength at Hunt- ington, WV: Bearth,z ≈ 4.70×10−5 T Bohr radius aB ≡ ~2 meke2 (3) = 5.29177210903×10−11 m (4) Rydberg constant R ≡ ~ 4πmea2Bc (5) = 1.0973731568160× 107 m−1 (6) hydrogen binding energy E0 = 13.605693123 eV