A complete guide to MCAT physics equations, covering formulas, when to use them, and high-yield practice to improve your MCAT performance.
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Part 1: Introduction
For many premeds, physics (and organic chemistry) was one of the more difficult classes they had to take in college. From long equations to complex math problems to a sea of formulas, college physics can make even the best student waver.
Fortunately, MCAT physics relies less on your math skills and more on your critical reasoning skills. On the MCAT, you’re not allowed to use a calculator, so physics problems written by the test-makers at the American Association of Medical Colleges (AAMC) must be solvable using simple math, estimations, or no math at all. Not to fear—for additional help with using equations, be sure to refer to our guide on MCAT math.
As such, it is very important for premeds studying for the MCAT to build time for learning the important physics equations into their study schedules. Now, what is an important physics equation? An important physics equation is an equation that we’ve either seen on 1) AAMC practice materials from the MCAT Official Prep Hub or 2) the AAMC’s list of content covered on the MCAT.
Here, we’ll show you those important equations that you should know for any MCAT physics questions you get. By knowing these equations (like you know functional groups or amino acids), you’ll put yourself in the best position to score well on the MCAT and increase your odds of receiving that acceptance letter from the medical school of your dreams!
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Part 2: The MCAT Physics Equations You Need to Know
Heat during phase change: q = m × L
Thermal expansion: ΔL = α × L × ΔT
Volumetric expansion: ΔV = β × V × ΔT
First law of thermodynamics: ΔU = Q − W
Entropy: ΔS = Qrev/T
Definition of velocity: v = Δx/Δt
Definition of acceleration: a = Δv/Δt
Under constant acceleration: v = v0 + at
Δx = ((v + v0)/2)t
Δx = v0t + (1/2)at2
v2 = v02 + 2aΔx
Projectile motion, assuming g ≈ 10 m/s2: vy = vy0 − 10t
Δy = vy0t − 5t2
Δx = vx0t
Period of circular motion: T = 2πR/vT
Frequency of circular motion: f = 1/T
Converting angular motion to linear motion: Δx = Δθ × R
vt = ω × R
*Note that θ must be in radians
Centripetal acceleration: ac = vT2/R = Rω2
Torque: T = R × F × sinθ = I × α
Newton’s 2nd Law: ΣF = m × a
Gravitational Force on earth: Fg = m × g; g = 9.8 m/s2
Force of Friction: f = FN × μ
Translational Kinetic Energy: KT = (1/2) × m × v2
Gravitational Potential Energy: Ug = m × g × h
Conservation of Energy: E2 = E1 − WNC
Work done by Constant Force: W = F × d × cosθ
Work-Kinetic Energy Theorem: W = ΔK
Power: P = ΔW/Δt
Density: ρ = m/V
Specific Gravity: SG = ρ/ρwater
Buoyant force: FB = mdisplaced × g = ρfluid × Vobject × g
Hydrostatic pressure: P = ρ × g × h
Atmospheric pressure: 1 atm = 101,000 Pa
Pascal’s law: F1/A1 = F2/A2 = constant
Continuity equation: ΔV/Δt = constant = A × v
Dynamic pressure: q = (1/2) × ρ × v2
Bernoulli’s equation: P + (1/2)ρv2 + ρgh = constant
Coulomb’s Law: F = −kq1q2/r2
Force due to arbitrary electric field: F = E × q
Electric potential: V = E × d × cosθ
Electric Potential Energy: UE = q × V
Electrical Current: I = ΔQ/Δt
Resistance: R = ρ × l/A
Conductivity: σ = 1/ρ
Ohm’s law: V = I × R
Equivalence for components in series: RT = R1 + R2 + ... + RN
1/CT = 1/C1 + 1/C2 + ... + 1/CN
Equivalence for components in parallel: 1/RT = 1/R1 + 1/R2 + ... + 1/RN
CT = C1 + C2 + ... + CN
Capacitance: C = Q/V
Parallel plate capacitance: C = kε0A/d
Energy in capacitor: U = (1/2)Q2/C = (1/2)QV = (1/2)CV2
Lorentz Force (moving charge in b-field): F = q × v × B × sinθ
Force on wire in b-field: F = I × L × B × sinθ
Biot-Savart law (b-field created by straight wire): B = μ0I/(2R)
Induced voltage: Ε = −ΔΦ/Δt
Permittivity of space: ε0 = 8.85 × 10−12
Permeability of free space: μ0 = 4π × 10−7
Snell's law: n1 × sinθ1 = n2 × sinθ2
Magnification: M = h′/h = −q/p
Thin lens equation: 1/f = 1/p + 1/q
Lens strength: P = 1/f
Photon energy: E = h × f
Double slit equation (applied to diffraction gratings): d × sinθ = m × λ
Single slit equation: a × sinθ = m × λ
Doppler equation: f′ = ((c + ν0)/(c − νs)) × f
Speed of light: c = 3 × 108 m/s
Planck's constant: h = 6.63 × 10−34 J/s
Velocity of sound: v = f × λ
Decibel scale: β = 10 log(I/I0)
I0 = 10−12 W/m2
Doppler effect: f′ = ((v + v0)/(v − vs)) × f
Resonance:
in strings and open tubes: L = (n/2) × λ
in tubes with one open one closed end: L = ((2n − 1)/4) × λ
Electron energy levels: E = −13.6 eV/n2
Absorbed or emitted light: 1/λ = R(1/nf2 − 1/ni2)
E = hν = hc/λ
Mass defect: mD = mP − me
mD = E/c2
Alpha decay: AZX → A−4Z−2Y + 42α
Beta-minus decay: AZX → AZ+1Y + 0−1β
Beta-plus decay: AZX → AZ−1Y + 0+1β
Half-life: N = N0 × (1/2)# of half-lives
N = N0 × (1/2)t/τ
N = N0 × e−λt
τ = ln(2)/λ
Rydberg constant: RH = 1.09 × 107 m−1
Planck's constant: h = 6.6 × 10−34 m2 kg/s
Speed of light (in a vacuum): c = 3 × 108 m/s
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Part 3: MCAT Physics Equations practice questions
1. Which of the following is the equation given by Newton’s second law?
A) PE = mgh
B) F = ma
C) PV = nRT
D) V = IR
2. Which of the following is the ideal gas law?
A) PE = mgh
B) F = ma
C) PV = nRT
D) V = IR
3. Which of the following best describes the second law of thermodynamics?
A) Objects in motion tend to stay in motion
B) Energy cannot be created or destroyed
C) Entropy increases over time
D) The entropy of a perfect crystal at absolute zero is equal to zero
4. A researcher sets up a simple series circuit with a single resistor. Over time, the resistance of the resistor decreases. Which of the following best describes the effect of a decreasing resistance on current, given a constant voltage?
A) Current increases
B) Current decreases
C) Current remains the same
D) Current can no longer be calculated
5. Given the same wire resistance and length of a metal tube, which of the following cross-sectional areas would provide the greatest resistivity?
A) 1 m2
B) 10 m2
C) 25 m2
D) 100 m2
Answer key for MCAT Physics Equations practice questions
1. The correct answer is B. Newton’s second law states that force is equal to mass multiple by acceleration (choice B is correct). PE = mgh is the equation for gravitational potential energy (choice A is incorrect). PV = nRT is the ideal gas law (choice C is incorrect). V = IR is Ohm’s Law for circuits (choice D is incorrect).
2. The correct answer is C. PV = nRT is the ideal gas law (choice C is correct). PE = mgh is the equation for gravitational potential energy (choice A is incorrect). Newton’s second law states that force is equal to mass multiple by acceleration (choice B is incorrect). V = IR is Ohm’s Law for circuits (choice D is incorrect).
3. The correct answer is C. The second law of thermodynamics discusses entropy and states that entropy increases over time unless there are restrictive forces (choice C is correct). Choice A is Newton’s first law. Choice B describes the law of conservation of energy. Choice D describes the third law of thermodynamics.
4. The correct answer is A. Ohm’s law is V = IR where V = voltage, I = current, and R = resistance. By rearranging the equation to I = V/R, we see that decreasing R while holding V constant leads to an increase in I (choice A is correct; choices B, C, and D are incorrect).
5. The correct answer is D. Resistivity is equal to resistance times cross-sectional area divided by length. So, cross-sectional area is directly proportional to resistivity, meaning answer choice D is correct since it has the greatest cross-sectional area. Further, recall that:
ρ = R × A/l
R = ρ × l/A
The question asks us to consider what might happen when both resistance (R) and length (l) of a wire are held constant. Let's make up some arbitrary values for those numbers, and set R=100 and l=1. If the cross-sectional area A=1, then resistivity ρ=100. Alternatively, if the cross-sectional area A=100, then ρ=10000.
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