MCAT FORMULA SHEET: This formula sheet is to be used as a reference tool. DO NOT MEMORIZE these formulas, instead, understand the concepts behind the equations and the relationships they represent. Kinematics and Mechanics d = vt v f = v0 + at v 2f = v02 + 2a∆x distance vat vax GM 1 M 2 r2 law of gravitation F= F net = ma Newton's 2nd law Fk = µ k FN Fs ≤ µ s FN friction Work, Energy, Momentum 1 2 mv 2 kinetic energy ac = τ = Fl sin θ F = −k x torque hooke's Law Thermodynamics 1 2 kx 2 spring PE PE grav = mgh KE = v2 mv 2 , Fc = r r centripetal motion 1 ∆x = v0 t + at 2 2 tax ∆Q = mc∆T heat energy PEelastic = gravitational PE ∆Q = mL latent heat ∆U = Q − W W P= t power W = Fd cos θ first law of work thermodynamics p = mv m1v1i + m2 v2i = m1v1 f + m2 v2 f momentum conservation of momentum ∆G = ∆H - T ∆S Gibbs free energy ∆G° = − RT ln K eq equilibrium Fluids and Solids m V density ρ= s.g . = ρ substance ρ water specific gravity Fb = ρ fluid Vsubmerged g buoyant force F A pressure P= π = MRT Ptotal = Patm + Pgauge Pfluid = ρ fluid gh osmotic pressure total pressure on fluid fluid gauge pressure A1v1 = A2 v2 continuity equation 1 2 ρ v + ρ gh = const. 2 Bernoulli's equation P+ rate A = rate B MM B MM A Graham's Law ∆L = α L∆T ∆V = β V ∆T thermal expansion Rev. 2A Rev. Date: 2/7/2003 Electricity & Magnetism kq q Fe = 12 2 r electrostatic force q = VC capacitance kq r2 electric field due E= F E= q0 electric field 1 U = CV 2 2 energy stored to point charge µI B= 0 2π r magnetic field by capacitor around a wire Electric Power & Circuits P = IV V = IR electrical power & Ohm's Law kq r electrical potential V= ∆U ∆V = q0 electrical potential F = qvB sin θ F = ILB sin θ magnetic force center of wire loop Light and Optics ∆q ∆t current I= I rms = I max , Vrms = 2 AC circuits Vmax 2 c v index of refraction E = hf = n= hc λ photon energy n1 sin θ1 = n2 sin θ 2 Rs = R1 + R2 + 1 1 1 = + + CS C1 C2 1 1 1 = + + RP R1 R2 CP = C1 + C2 + resistors in series and in parallel capacitors in series and in parallel Periodic Motion, Waves and Sound 1 T wave freq., period f = k m spring angular freq ω = 2π f = g L pendulum angular freq v= fλ wave speed ω = 2π f = v ∓ vD f '= f v ± vS Doppler effect Snell's Law sin θ crit = Chemistry and Biology V1 V = 2 T1 T2 PV = nRT ideal gas law Charles' Law n1 n2 = V1 V2 PV 1 1 = P2V2 Boyle's Law pH = − log H + pH Avogadro's Law dilution X →ZA −− 42 Y + α 1 1 1 = + f o i lensmaker's eq. n2 , n2 < n1 n1 total internal reflection M iVi = M f V f Atomic and Nuclear A Z of a point charge µI B= 0 2r magnetic field @ n2 a P + (V - nb ) = nRT V2 Van der Waals equation of state EMF = E °red + E °ox Ecell = Ecathode - Eanode electromotive force EMF p + q =1 alpha decay p + 2 pq + q 2 = 1 Hardy-Weinberg equations 2 A Z X→ A Z +1 Y+ e 0 −1 beta-minus decay A Z X→ A Z −1 Y+ e 0 +1 beta-plus decay Rev. 2A Rev. Date: 2/7/2003