Harold s AP Physics Cheat Sheet 23 February 206 Kinematics Position (m) (rad) Translation Horizontal: x = x 0 + v x0 t + 2 at2 Vertical: y = y 0 + v y0 t 2 gt2 x = x 0 + vt s = rθ x = v / Rotational Motion θ = θ 0 + ω 0 t + 2 αt2 x = A cos(ωt) x = A cos(2πft) 0 24 = yocto 0 2 = zepto 0 8 = atto 0 5 = femto 0 2 = pico 0 9 = nano 0 6 = micro 0 3 = milli 0 0 = 0 3 = kilo 0 6 = mega 0 9 = giga 0 2 = tera 0 5 = peta 0 8 = exa 0 2 = zetta 0 24 = yotta P + ρgy + 2 ρv 2 = P 2 + ρgy 2 + 2 ρv 2 2 (Conservation of Mass) ρ = m V l = αl 0 T : s i + s o = f L = mλ d sin θ = mλ L = L 0 Copyright 20-206 by Harold Toomey, WyzAnt Tutor
Velocity (m/s) (rad/s) v = d t = x t = dx v = v 0 + at v 2 = v 0 2 + 2a(x x 0 ) v = v 0 + v 2 v = rω v = ω r v = a ω = θ t = θ t = dθ ω = ω 0 + αt ω 2 = ω 0 2 + 2α(θ θ 0 ) ω = ω 0 + ω 2 ω = 2π T = 2πf ω = k m = g l Speed of Light: c 3.00 x 0 8 m s = 299,792,458 m s A v = A 2 v 2 v rms = 3RT M v rms = 3k BT μ : v = fλ n = c v n sin θ = n 2 sin θ 2 v(t) = v 0 Acceleratio n (m/s 2 ) (rad/s 2 ) a = v t = v t = dv a = F m = F net m a = rα g = 9.80665 m s 2 g = 32.740 ft s 2 Tangential: α = a T r = ω t = dω α = τ I = τ net I Centripetal: a c = v2 r = ω2 r a 2 = a + a T 2 Jerk (Jolt) (m/s 3 ) (rad/s 3 ) j = a t = a t = da ζ = α t = α t = dα Copyright 20-206 by Harold Toomey, WyzAnt Tutor 2
Dynamics Mass (kg) / Moment of Inertia (kg m 2 ) Momentum (kg m/s) (kg m 2 /s) m = actual mass I = effective mass p = mv p = m v Conservation of Momentum: p i = p f I = mr 2 I = r 2 dm I = r dm L = Iω L = r p L = r v dm m e = 9. 0 3 kg m p m n =.67 0 27 kg p = ρg m = m 0 Nuclear: λ = h p p = mv Copyright 20-206 by Harold Toomey, WyzAnt Tutor 3
Force (N = kg m/s 2 ) / Torque (J = N m) F = ma F g = mg F = F net = ma F = p t = p t = dp F fric μn F s = kx F G = Gm m 2 r 2 F G = Gm m 2 r 2 r τ = rf sin θ τ = τ net = Iα τ = rf = Iα τ = r F τ = dl F = ma c F = mv2 r F = mrω 2 Electricity: F = k q q 2 r 2 F = q q 2 4πε 0 r 2 F = Eq : F B = qvb sin θ F B = BIl sin θ F B = qv B F B = Il B F = I dl B F = PA P = F A = ρhg F buoy = ρvg PV = nrt = Nk B T J R = 8.3 (mol K) k B =.38 0 23 J K Impulse (N s) (N m s) J = F t = p = m v J = F = p H = τ t = L = I ω H = τ = L Yank (N/s 2 ) / Rotatum (J/s) Y = m J Y = F t = F t = df P = r Y P = τ t = τ t = dτ Copyright 20-206 by Harold Toomey, WyzAnt Tutor 4
Energy W = Fd W = τ θ : W = P V Work (J = N m) W = F x cos θ W = τ (θ θ 0 ) W = QV e = W Q H Kinetic Energy (J) Potential Energy (J) W = F dr K = 2 mv2 U g = mgh U G = Gm m 2 r G = 6.67 0 W = τ dθ K = 2 Iω2 Coiled spring: U s = 2 kx2 ev =.60 0 9 J U E = qv U E = q q 2 4πε 0 r U c = 2 QV U c = 2 CV2 U L = 2 LI2 e c = T H T C T H P + ρgy + 2 ρv2 = constant : K avg = 3 2 k BT P = P 0 + ρgh : U = Q + W Nuclear: K max = hf φ m 0 K = ( ) Nuclear: E = hf = pc E = m E = ( m) E = m ( ) Copyright 20-206 by Harold Toomey, WyzAnt Tutor 5
: H = ka T L Heat Energy (J) Conservation of Energy: E i = E f E = W + Q + K + U g + U G + U s + U E + U c + U L + = constant Q = mh f Q = mh v E = Q = mc T mc T = mc(t f T i ) C H2 O = 480 J/Kg K T f = m C T i + m 2 C 2 T 2 m C + m 2 C 2 P = W t = Fv P = W t = τω P = IV Power (W) P = E t = de P = Fv cos θ P = F v P = W t = dw P = τω cos θ P = τ ω P = I 2 R P = V2 R Copyright 20-206 by Harold Toomey, WyzAnt Tutor 6
Engineering Application T = f = 2π ω : Period / Frequency (Hz) T = f f = T T s = 2π m k T p = 2π l g T = 2π b For: y = sin(bθ) y = cos(bθ) f = λ v t = t 0 x CM = m x + m 2 x 2 m + m 2 Center of Mass (m) x CM = m ix i m i x = M M x dm 0 r CM = mr m : M = h i = s i h o s o (magnification) M where M = dm 0 and dm = ρ dz dy dx Rigid Bodies F y = mg = 0 (Down = ) τ = F y x CM = 0 (CW = ) Copyright 20-206 by Harold Toomey, WyzAnt Tutor 7
Electricity Electricity E = F q C = Q V E avg = V d C = ε 0A d Electric Field (V/m) (N/C) E = dv dr Gauss s Law: Capacitance (F) C = κε 0A d C p = C i i E da = Q ε 0 E = ρj = C s i C i V = IR R = V I Potential (V) V = Q C V = k q i i r i Resistance (Ω) R = ρl A R s = R i i V = q i 4πε 0 i r i = R p i R i I avg = Q t Current (A) I = dq I = V R I = Nev d A EMF (V) Faraday s Law of Induction: E dl = φ m t ε = L di e =.60 0 9 C Copyright 20-206 by Harold Toomey, WyzAnt Tutor 8
B = μ 0 2π I r Solenoid: B s = μ 0 ni Magnetic Field (T) where n = N turns per meter l Ampere s Circuit Law: B dl = μ o I db = μ 0 4π I dl r r 3 (T m) 7 μ 0 = 4π 0 A Magnetic Flux (Wb) φ m = BA cos θ Gauss s Law for : φ m = B da EMF (V) ε avg = φ m t ε = Blv Copyright 20-206 by Harold Toomey, WyzAnt Tutor 9