Introduction physics formula sheet, Cheat Sheet of Physics

Download Introduction physics formula sheet and more Cheat Sheet Physics in PDF only on Docsity! UC Summer Introductory Physics Formula Sheet Module #1 Note: bold symbols represent vector quantities v = ?⃗?𝑣 MECHANICS Trigonometry in a right-angled triangle sinθ= opposite/hypotenuse cosθ = adjacent /hypotenuse tanθ= opposite/adjacent Equations of motion under constant acceleration: v = v0 + at x = x0 + v0t + 1/2 at2 v2 = v20 +2a(x- x0) Newton’s second law ΣF =ma Kinetic friction force Ffr = μkFN Work W= Fd cosθ Kinetic energy K= 1/2mv2 Work-energy theorem Wnet = KE2 – KE1 Mechanical energy Emech = KE +PE Gravitational force FG = Gm1m2/r2 Weight: FG = mg PEG = mgh Case of a spring Fs = -kx PEel = 1/2kx2 Power Pavg = W/∆t P=F∙v Momentum p=mv Coordinates of center of mass xCM = Σi mixi/M Rotational motion AR =v2/r T = 2𝜋𝜋r/v 𝜔𝜔=2𝜋𝜋/T =v/r Physics Formula Sheet K = ½ I 𝜔𝜔2 Torque 𝜏𝜏 =Fr sin𝜙𝜙 Σ𝜏𝜏=I𝛼𝛼 Angular momentum L = r×p Angular momentum L = I𝜔𝜔 Moment of inertia Solid cylinder: I = ½ MR2 Rectangular plate: I = ½ M(l2 + w2) Long thin rod: • Rotation axis through center: I = 1/12ml2 • Rotation axis through end: I= 1/3ml2 Orbiting particle: I = mr2 FLUID MECHANICS Pressure P=F/A In a fluid at depth h: P = P0 + 𝜌𝜌gh Buoyant force B= 𝜌𝜌F gVdisp Continuity equation in a fluid A1v1 = A2v2 Bernoulli’s equation P1 + 1/2𝜌𝜌v12 + 𝜌𝜌gy1 = P2 + + 1/2𝜌𝜌v22 + 𝜌𝜌gy2 Poiseuille’s law Q = [𝜋𝜋r4 (P1-P2) /8𝜂𝜂L WAVES Simple harmonic motion x(t) = Acos(𝜔𝜔t +𝜙𝜙) E = 1/2kA2 For a spring: 𝜔𝜔√(𝑘𝑘/𝑚𝑚) T = 2𝜋𝜋/𝜔𝜔 f= 1/T Mechanical wave y = Asin(kx — 𝜔𝜔 t) Wave number: k = 2𝜋𝜋/𝜆𝜆 v=𝜆𝜆f Mechanical wave in a fixed string v=�𝐹𝐹𝑇𝑇 𝜇𝜇 Doppler effect 𝑓𝑓′ = 𝑓𝑓 � 𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠∓𝑣𝑣𝑜𝑜𝑜𝑜𝑠𝑠 𝑣𝑣𝑠𝑠𝑠𝑠𝑠𝑠∓𝑣𝑣𝑠𝑠𝑜𝑜𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � (both moving) Standing wave y = 2Asin(kx) cos(𝜔𝜔t) In a string: fn =nv/2L, n=1,2,3... Beat frequency: fb = |f1 — f2|