Formula Sheet , Final Exam - General Physics | PHYS 2101, Exams of Physics

Download Formula Sheet , Final Exam - General Physics | PHYS 2101 and more Exams Physics in PDF only on Docsity! Formula Sheet for LSU Physics 2101, Spring ’08, Final Exam. Units: 1m = 39.4 in = 3.28 ft 1 mi = 5280 ft 1min = 60 s, 1 day = 24 h 1 rev = 360◦ = 2π rad 1 atm = 1.013×105 Pa 1 cal = 4.186 J T = ( 1K 1◦C ) TC + 273.15K TF = ( 9 ◦F 5◦C ) TC + 32 ◦F Constants: g = 9.8 m/s2 REarth = 6.37× 106 m MEarth = 5.98×1024 kg G = 6.67×10−11 m3/(kg·s2) RMoon = 1.74× 106 m MMoon = 7.36×1022 kg Earth-Sun distance = 1.50×1011 m MSun = 1.99×1030 kg Earth-Moon distance = 3.82×108 m k = 1.38× 10−23 J/K R = 8.31 J/(mol·K) Avogadro’s number = 6.02 ×1023 atoms/mol Properties of H2O: Density: ρwater = 1000 kg/m3 Specific heat: cwater = 4190 J/(kg K) cice = 2220 J/(kg K) Heats of transformation: Lvaporization = 2.256× 106 J/kg Lfusion = 3.33× 105 J/kg Quadratic formula: for ax2 + bx + c = 0, x1,2 = −b ± √b2 − 4ac 2a Dot Product: ~a ·~b = axbx + ayby + azbz = |~a| ∣∣∣~b ∣∣∣ cos(φ) (φ is smaller angle between ~a and ~b) Cross Product: ~a ×~b = (aybz − azby)ı̂ + (azbx − axbz)̂ + (axby − aybx)k̂, ∣∣∣~a ×~b ∣∣∣ = |~a| ∣∣∣~b ∣∣∣ sin(φ) Equations of Constant Acceleration: linear equation along x missing missing rotational equation vx = vox + axt x − xo θ − θo ω = ωo + αxt x − xo = voxt + 1 2 axt 2 vx ω θ − θo = ωot + 1 2 αt2 v2x = v 2 ox + 2ax(x − xo) t t ω2 = ω2o + 2α(θ − θo) x − xo = 1 2 (vox + vx)t ax α θ − θo = 1 2 (ωo + ω)t x − xo = vxt − 1 2 axt 2 vox ωo θ − θo = ωt − 1 2 αt2 Vector Equations of Motion with Constant Acceleration: ~r = ~ro + ~vot + 1 2 ~at2, ~v = ~vo + ~at Projectile Motion: x = voxt y = voyt − 1 2 gt2 R = v2o sin(2θo) g vx = vox = constant vy = voy − gt Newton’s Second Law: ∑ ~F = m~a Centripetal Force: Fc = mv2 r = mac Time per revolution: T = 2 π r vavg Force of Friction: Static: fs ≤ fs,max = µsFN , Kinetic: fk = µkFN Elastic (Spring) Force: Hooke’s Law F = −kx (k = spring (force) constant) Kinetic Energy (nonrelativistic): Translational: K = 1 2 mv2 Rotational: K = 1 2 Iω2 Work: W = ~F · ~d (constant force), W = ∫ xf xi F (x)dx (variable 1-D force), W = ∫ rf ri ~F (~r) · d~r (variable 3-D force) Work - Kinetic Energy Theorem: W = ∆K = Kf − Ki Work done by weight (gravity close to the Earth surface): W = m ~g · ~d Work done by spring force F = −kx: W = −k ∫ xf xi x dx = −k ( x2f 2 − x 2 i 2 ) Power: Average: Pavg = W ∆t , P = ~F · ~vavg (const. force) Instantaneous: P = dW dt , P = ~F · ~v (const. force) Potential Change: ∆U = −W (conservative force) Potential-Force Relation: F (x) = −dU(x) dx Gravitational (near Earth) Potential Energy: U(y) = mgy (at height y) Elastic (Spring) Potential Energy: U = 1 2 kx2 (relative to the relaxed spring) Mechanical Energy: Emec = K + U Conservation of Mech. Energy of the System: ∆K + ∆U = 0 or Ki + Ui = Kf + Uf (isolated system with only conservative forces with non-zero work, W = −∆U) Conservation of Energy: W = ∆K + ∆U + ∆Eth + ∆Eint, where W is the external work done on the system, and ∆Eth = −Wfk = (fkd for constant friction). Center of mass: M = N∑ i=1 mi, xcom = 1 M N∑ i=1 mixi, ycom = 1 M N∑ i=1 miyi, zcom = 1 M N∑ i=1 mizi ~rcom = 1 M N∑ i=1 mi~ri ~vcom = 1 M N∑ i=1 mi~vi ~acom = 1 M N∑ i=1 mi~ai = 1 M N∑ i=1 ~Fi Definition of Linear Momentum: one particle: ~p = m~v, system of particles: ~P = N∑ i=1 ~pi = M~vcom Newton’s 2nd Law for a System of Particles: ~Fnet = M~acom = d ~P dt Conservation of Linear Momentum of an Isolated System: ∑ ~pi = ∑ ~pf Impulse - Linear Momentum Theorem: ∆~p1 = ~J12 = ∫ t2 t1 ~F12(t)dt = ~Favg,12∆t Elastic Collision (1 Dim): v1f = m1 − m2 m1 + m2 v1i + 2m2 m1 + m2 v2i v2f = 2m1 m1 + m2 v1i + m2 − m1 m1 + m2 v2i Linear and Angular Variables Related: s = rθ v = ωr at = αr ar = v2 r = ω2r (magnitude of the radial or centripetal acceleration) Rotation: Rotational Inertia (Icom) for Simple Shapes: see next page Rotational Inertia: Descrete particles: I = N∑ i=1 mir 2 i Continuous object: I = ∫ r2dm Parallel Axis Theorem: I = Icom + Mh2 Torque: ~τ = ~r × ~F τ = rFt = r⊥F = rF sin φ Angular Momentum: rigid body, fixed axis: ~L = I~ω point-like particle: ~L = ~r × ~p Newton’s 2nd Law: ~τnet = I~α = d~L dt Conservation Law (isolated system, ∑ τ = 0): ∑ ~Li = ∑ ~Lf Rotational Work: W = ∫ θf θi τdθ = τavg∆θ Kinetic Energy: K = 1 2 Iω2 Rotational Power: Instantaneous: P = dW dt = τω Average: Pavg = W t = τavgωavg Rolling: vcom = ωR acom = αR Kinetic Energy of Rolling: K = 1 2 mv2com + 1 2 Icomω 2