 # MCAT Physics Equations Sheet

## Gold Standard MCAT Physics Equations Sheet (List of MCAT Physics Formulas)

This MCAT Physics Equations Sheet is by no means an exhaustive review of MCAT Physics. Our sheet is only meant to highlight key equations that are most helpful for the new MCAT. For a list of topics for the new MCAT: MCAT Physics Topics List. You can also access practice questions in our Free MCAT Practice Test, or our many full-length MCAT Practice Tests.

This MCAT Physics Equations Sheet provides helpful physics MCAT equations for MCAT Physics practice. MCAT Physics equations for 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.

Do you see the symbols alpha: α          mu: μ         delta: Δ

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## Gold Standard MCAT Physics Equations - Memorize

 Translational motion x = xo + vot + 1/2at2       |       (Vƒ)2 = (Vo)2 + 2ax Vƒ = Vo + at Frictional force fmax = 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 Capacitors in Ser. and Par. 1/ Ceq = 1/ C1 + 1/ C2 + 1/ C3 . . . Ceq = C1 + C2 . . Sound dB = 10 log10 (I/I0 ) beats = Δ ƒ 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

*Not technically in the new MCAT Physics syllabus but since these are simple concepts that have been the source of traditional MCAT questions, we do not believe that they should be discarded from your preparation.

## Gold Standard MCAT Physics Equations - 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) 1/ i + 1/ o = 1/ f = 2/r = Power M = magnification = - i/o Optics ΔG = ΔH - TΔS Gibbs Free Energy ΔG° = -RTln Keq

## Gold Standard MCAT Physics Equations - Know How to Use - Do Not Memorize

 Ρ + ρgh + 1/2 ρv2 = constant Bernouilli's Equation Fluids in Motion f0 = fs (V ± V0 )/( V ± Vs ) Doppler Effect: when d is decreasing use + V0 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 Potential Energy ( PE ) = W = 1/2 QV Work in Electricity W = 1/2 CV2

## Gold Standard MCAT Physics Equations - Atomic Nucleus & Electronic Structure

• Alpha (α) particle = 2He4 (helium nucleus);
• Beta (β) particle = -1e0 (an electron);
• A positron = +1e0 (same mass as an electron but opposite charge);
• Gamma (γ) ray = no mass, no charge, just electromagnetic energy;
• Δ m /Δ t = rate of decay where Δ m = change in mass, Δ t = change in time.
• 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
• Determines the orbital
• Possible values are: ± l , ... , 0
• Spin quantum number = ms
• Determines the direction of rotation of the electron
• Possible values are: ± 1/2

## Gold Standard MCAT Physics Equations - Trigonometry - The Basics sin θ = opp/hyp
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

## Gold Standard MCAT Physics Equations - 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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