## Pages   # Memorize These!

 Translational motion x = x 0 + v 0 t + at2/2 Vƒ = Vo + at Frictional force f max = μ Ν μk < μs Uniform circular motion Fc = mac = mv2 /r ac= v2 /r Momentum, Impulse I = F Δt = ΔM M = mv Work, Power W = F d cosθ P = ΔW/Δt Energy (conservation) ET = Ek + Ep E = mc2 Spring Force, Work F = -kx W = kx2 /2 Continuity (fluids) A v = const. ρAv = const. Current and Resistance I = Q/t R = ρL/A Resistors (series, par.) Req = R1 + R2 . . . 1/ Req = 1/ R1 +1/ R2 Sound dB = 10 log 10 (I/I0 ) beats = Δ f Kirchoff's Laws Σi = 0 at a junction ΣΔV = 0 in a loop Thermodynamics Q = mc Δ T Q = mL Torque forces L1 = F1× r1 L2 = F2 × r2 Torque force at EQ ΣFx = 0 and ΣFy = 0 ΣL = 0 Refraction ( sin θ1 )/(sin θ2 ) = v1 /v2 = n2 /n1 = λ1 /λ2 n = c/v

# Memorize as Pairs

 F = ma F = qE Similar Form F = KG ( m1 m2 / r2 ) F = k ( q1 q2 / r2 ) V = IR P = IV Paired Use vav = Δ d / Δ t aav = Δ v / Δ t (avg vel, acc) v = λ f E = hf (f = 1/T) Ek = ½mv2 Ep = mgh (kin, pot E) Ρ = F/A Δ Ρ = ρgΔh (pressure Ρ) SG = ρ substance / ρ water ρ = 1 g/cm3 = 103 kg/m3 (Spec Grav) ρ = mass / volume Fb = Vρg = mg (buoyant F) Irms = Imax / √2 Vrms = Vmax / √2 Root Mean Sq 1/ i + 1/ o = 1/ f = 2/r = Power M = magnification = - i/o Optics Note: Specific gravity (SG) is equivalent to the fraction of the height of a buoyant object below the surface of the fluid.

# Don't Memorize, Know How to Use...

 Ρ + ρgh + 1/2 ρv2 = constant Bernouilli's Equation Fluids in Motion L = L0 (1 + αΔ T ) Linear Expansion Solids, Temp Δ A = A0(1 + γΔ T ) Area Expansion V = V0(1 + βΔ T ) Volume Expansion β = 3 α fo = fs (V ± vo )/ ( V ± vs ) Doppler Effect: when d is decreasing use + vo and - vs V = Ed for a parallel plate capacitor d = the distance between the plates dF = dq v(B sin α) = I dl(B sin α) Laplace's Law RH rule 1/ Ceq = 1/ C1 + 1/ C2 + 1/ C3 . . . Capacitors in Ser. and Par. Ceq = C1 + C2 . . . Potential Energy ( PE ) = W = 1/2 QV Work in Electricity W = 1/2 CV2 ΔG = ΔH - TΔS Gibbs Free Energy ΔG° = -RTln Keq

# Atomic Physics

 1) alpha (α) particle = 2He4 (helium nucleus); 2) beta (β) particle = -1e0 (an electron); 3) a positron +1e0 (same mass as an electron but opposite charge); 4) gamma (γ) ray = no mass, no charge, just electromagnetic energy; 5) Δ m /Δ t = rate of decay where Δ m = change in mass, Δ t = change in time. 6) If the number of half-lifes n are known we can calculate the percentage of a pure radioactive sample left after undergoing decay since the fraction remaining = (1/2) n . Nelectrons = 2 n2 , where Nelectrons designates the number of electrons in shell n . The state of each electron is determined by the four quantum numbers: principal quantum number n determines the number of shells, possible values are: 1 (K), 2 (L), 3 (M), etc... angular momentum quantum number l, determines the subshell, possible values are: 0 (s), 1 (p), 2 (d), 3 (f), n-1, etc... magnetic momentum quantum number ml , possible values are: ± l , ... , 0 spin quantum number ms ,determines the direction of rotation of the electron, possible values are: ±1/2.

# The Basics sin θ = opp/hyp cos θ = adj/hyp tan θ =opp/adj θ = sin -1 x arcsec θ = sec-1θ r2 = x2 + y2

• angle θ may be given in radians (R) where 1 revolution = 2πR = 360°

• estimate square root 3 as 1.7 and root 2 as 1.4

• cross-sectional area of a tube = area of a circle = πr2 where π can be estimated as 3.14 and is the radius of the circle; circumference = 2πr

# Some Units to Memorize

 Both work and energy are measured in joules where 1 joule (J) = 1 N × 1 m . {Imperial units: the foot- pound , CGS units: the dyne-centimeter or erg } The SI unit for power is the watt (W) which equals one joule per second (J/s) = volts × amperes . Current is measured in amperes = coulombs/sec. The units of resistance are ohms, symbolized by Ω (omega), where 1 ohm = 1 volt/ampere. The SI unit for pressure is the pascal (1 Pa = 1 N/m2 ). Other units are: 1.00 atm = 1.01 × 105 Pa = 1.01 bar = 760 mmHg = 760 torr. The SI unit for the magnetic induction vector B is the tesla where 1 T = 1 N/(A)(m) = 104 gauss.

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