MCAT Physics Equations Sheet (List of MCAT Physics Formulas)

This MCAT Physics equations sheet provides helpful physics equations for MCAT preparation. Physics equations on motion, force, work, energy, momentum, electricity, waves and more are presented below. Please keep in mind that understanding the meaning of equations and their appropriate use will always be more important than memorization. Sometimes, formulas will be provided during the MCAT but, as you will see, you are expected to already know quite a few. Doing and reviewing practice questions and practice tests will improve your understanding of what you need to know.

alpha: a          mu: �         delta: Δ If you don't see the Greek symbols above then the equations below will not make sense; thus adjust fonts on your browser to Unicode.

MCAT Physics Equations to memorize

Translational motion x = x o + v o t + 1/2at2 | (Vf)2 = (Vo)2 + 2ax Vƒ = Vo + at Frictional force f max = μ Ν μk < μs always 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 (MCAT !) Q = mL Torque forces L1 = F1× r1 (CCW + ve) L2 = F2 × r2 (CW -ve) 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

MCAT Physics Equations to 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 = 1/2 mv2 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 r 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.