Categorizing Equations by Frequency of Use
When organizing your study plan, it is vital to distinguish between high yield MCAT physics equations and those that appear only in niche scenarios. High-yield formulas, such as Newton’s Second Law ($F = ma$) or Ohm’s Law ($V = IR$), are the workhorses of the exam, appearing across multiple passage types from biomechanics to neural signaling. These should be memorized until they become reflexive. Secondary equations, such as those governing specific heat or torque, require a deep understanding of proportionality. The MCAT rarely asks for a plug-and-chug calculation in isolation; instead, it tests how a change in one variable—like doubling the radius of a blood vessel—affects another, such as flow rate. By categorizing formulas into "Core," "Relational," and "Specialized" groups, you can prioritize your mental energy on the mathematical tools that offer the highest point-per-minute return during the 95-minute science sections.
The Role of Units and Dimensional Analysis
One of the most powerful tools for an MCAT candidate is dimensional analysis, the practice of checking the units of a calculation to ensure the final answer is physically plausible. Every formula is an equality of units. For instance, if a question asks for Power and your calculated result does not yield Watts ($J/s$ or $kg · m^2/s^3$), an algebraic error has occurred. Memorizing the base units of the International System (SI) is non-negotiable. You must be able to decompose a Newton ($N$) into $kg · m/s^2$ or a Pascal ($Pa$) into $N/m^2$. In many instances, if you forget a specific equation, you can reconstruct it simply by looking at the units provided in the answer choices. This "unit-matching" strategy serves as a critical safety net, allowing you to eliminate distractors that do not match the required dimensions of the sought-after physical quantity.
Mechanics and Motion Equations
Kinematics: The Big Four Equations of Motion
Kinematics focuses on the description of motion without regard to the forces causing it. For the MCAT, you must master the linear motion equations, often referred to as the "Big Five" or "Big Four," which assume constant acceleration ($a$). These include: $v = v_0 + at$, $Δx = v_0t + ½ at^2$, $v^2 = v_0^2 + 2aΔx$, and $Δx = ½(v + v_0)t$. When tackling projectile motion or a car braking, identifying which variables are known ($v_0$, $v$, $a$, $t$, or $Δx$) and which is missing is the first step. For example, in free-fall problems, the acceleration is always $g ≈ 10 m/s^2$. If a problem asks for the maximum height of a projectile, you must recognize the hidden piece of information: at the peak of the trajectory, the vertical velocity ($v_y$) is exactly zero. Applying the $v^2$ equation here allows for a quick solution without needing the time of flight.
Forces: Newton's Laws, Friction, and Circular Motion
Newton's laws of motion form the backbone of classical mechanics. $F_{net} = ma$ is the most significant equation, but it is often applied in conjunction with friction and circular motion. Static friction ($f_s leq mu_s N$) and kinetic friction ($f_k = mu_k N$) describe the resistance between surfaces, where $N$ is the normal force. Note that $mu_s$ is always greater than or equal to $mu_k$, reflecting the reality that it is harder to start an object moving than to keep it moving. In uniform circular motion, the centripetal force is defined as $F_c = mv^2/r$. Candidates must remember that centripetal force is not a new, separate force but rather a role played by other forces like gravity, tension, or friction. On the MCAT, this often appears in the context of mass spectrometry, where magnetic forces act as centripetal forces to deflect ions into circular paths.
Energy is a conserved quantity, a principle that simplifies many complex mechanics problems. The Work-Energy Theorem states that $W_{net} = ΔKE$, where Kinetic Energy ($KE$) is $½ mv^2$. Potential Energy ($PE$) on the MCAT usually takes the form of gravitational potential ($U = mgh$) or elastic potential ($U = ½ kx^2$). Work itself is defined as $W = Fd cos heta$, emphasizing that only the force component parallel to displacement does work. Power ($P$), the rate of energy transfer, is calculated as $P = W/t$ or $P = Fv$. In biological systems, these formulas are used to calculate the metabolic cost of muscle contraction or the power output of the heart. Remember that the unit for Work and Energy is the Joule ($J$), while Power is measured in Watts ($W$). If a passage describes a process with $100%$ efficiency, you can set the initial total mechanical energy equal to the final total mechanical energy ($E_i = E_f$).
Fluids and Solids
Density, Pressure, and Pascal's Principle
Fluids are a major focus of MCAT kinematics and fluids formulas because of their relevance to the circulatory and respiratory systems. Density ($
ho = m/V$) and Pressure ($P = F/A$) are the fundamental variables. Hydrostatic pressure, the pressure exerted by a fluid at rest, increases with depth: $P = P_0 +
ho gh$. Pascal’s Principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the container. This is mathematically expressed as $P_1 = P_2$, or $F_1/A_1 = F_2/A_2$. This principle explains the mechanical advantage of hydraulic lifts and the way pressure is distributed in the cerebrospinal fluid. When solving these, pay close attention to the units of area; converting $cm^2$ to $m^2$ requires dividing by $10,000$ ($10^4$), a common point of failure for many examinees.
Buoyancy and Archimedes' Principle
Archimedes' Principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. The formula is $F_B =
ho_{fluid} V_{submerged} g$. This concept is essential for determining whether an object will sink or float. The "floating equation" relates the density of the object to the density of the fluid: the fraction of the object submerged is equal to $
ho_{object} /
ho_{fluid}$. If an object’s density is $0.7 g/cm^3$ and it is placed in water ($1.0 g/cm^3$), $70%$ of the object will be below the surface. On the MCAT, buoyancy is often linked to specific gravity, a dimensionless number representing the ratio of a substance's density to the density of water. Understanding this allows you to quickly assess the purity of a sample or the concentration of solutes in a biological fluid like urine.
Fluid Flow: Continuity and Bernoulli's Equation
Fluid dynamics on the MCAT assumes "ideal" fluid behavior: non-viscous, incompressible, and laminar flow. The Continuity Equation, $A_1v_1 = A_2v_2$, dictates that for an incompressible fluid, the volume flow rate ($Q$) remains constant. If the cross-sectional area of a pipe decreases, the velocity of the fluid must increase. This is paired with Bernoulli’s Equation: $P + ½
ho v^2 +
ho gh = constant$. This equation is essentially a statement of energy conservation for fluids. It reveals that as the velocity of a fluid increases, its static pressure decreases (the Venturi effect). This explains why an aneurysm (a widening of an artery) leads to slower blood flow and higher internal pressure, potentially causing the vessel to rupture. Mastering the trade-off between pressure, height, and velocity is crucial for high-scoring students.
Elasticity and Stress-Strain Relationships
While fluids dominate the exam, the physical properties of solids—specifically tissues like bone and cartilage—are also tested. Stress is defined as force per unit area ($sigma = F/A$), and strain is the fractional change in length ($epsilon = ΔL/L_0$). The relationship between the two is governed by Young’s Modulus ($Y$ or $E$), where $Stress = Y × Strain$. This is essentially a specialized version of Hooke’s Law ($F = kΔx$), where the spring constant $k$ is replaced by the material's inherent stiffness. A material with a high Young’s Modulus is stiff and resists deformation, whereas a material with a low modulus is more elastic. On the MCAT, you might be asked to compare the tensile strength of different biological fibers or calculate the compression of a bone under a specific load, requiring a firm grasp of these linear elastic relationships.
Electricity and Magnetism
Electrostatics: Coulomb's Law and Electric Fields
Electricity and magnetism are central to understanding nerve conduction and laboratory techniques like gel electrophoresis. Electricity and magnetism MCAT equations begin with Coulomb’s Law: $F = k q_1 q_2 / r^2$, which calculates the force between two point charges. The electric field ($E$) produced by a source charge is $E = kQ / r^2$, or more simply, $E = F/q$. You must distinguish between the electric force (which requires two charges) and the electric field (which exists regardless of a test charge). Electric Potential ($V$) is the work required to move a charge per unit charge, $V = kQ/r$. In a uniform electric field, such as between the plates of a capacitor, the relationship simplifies to $V = Ed$. Understanding these inverse-square and linear relationships is key to predicting how ions will behave in an electrochemical gradient across a cell membrane.
Circuit Fundamentals: Ohm's Law and Power
Circuits are a high-yield topic, often used as an analogy for blood flow (where pressure is voltage and flow is current). Ohm’s Law, $V = IR$, is the primary relationship you must know. Resistance ($R$) depends on the material's properties: $R =
ho L / A$, where $
ho$ is resistivity, $L$ is length, and $A$ is cross-sectional area. For resistors in series, you sum the resistances ($R_{total} = R_1 + R_2 ...$), while for resistors in parallel, you sum the reciprocals ($1/R_{total} = 1/R_1 + 1/R_2 ...$). Electrical power is given by $P = IV = I^2R = V^2/R$. When analyzing a circuit, always look for the "node" or "junction" to apply Kirchhoff’s Junction Rule (sum of currents in equals sum of currents out) and the Loop Rule (sum of voltage drops in a loop equals the source voltage). These rules ensure the conservation of charge and energy within the system.
Magnetic Force on Moving Charges
Magnetic fields ($B$) exert forces only on moving charges. The formula $F_B = qvB sin heta$ is essential. The $sin heta$ term indicates that no force is exerted if the charge moves parallel to the magnetic field. To determine the direction of the force, use the Right-Hand Rule: thumb in the direction of velocity ($v$), fingers in the direction of the field ($B$), and the palm represents the force ($F$) for a positive charge (use the back of the hand for a negative charge). Magnetic fields are measured in Teslas ($T$). In the context of the MCAT, magnetism often appears in questions regarding the operation of a cyclotron or the behavior of electrons in an external field. Remember that magnetic forces do no work because the force is always perpendicular to the velocity, meaning the speed of the particle remains constant while its direction changes.
Capacitance and Energy Storage
Capacitors store charge and energy, making them excellent models for the lipid bilayer of a cell. Capacitance ($C$) is defined as $C = Q/V$. For a parallel-plate capacitor, $C = epsilon_0 A / d$. To increase capacitance, one can increase the area of the plates or decrease the distance between them. Introducing a dielectric material (an insulator) between the plates always increases capacitance by a factor $kappa$. The energy stored in a capacitor is $U = ½ CV^2 = ½ QV = ½ Q^2/C$. Unlike resistors, capacitors in parallel are summed directly ($C_{total} = C_1 + C_2 ...$), while capacitors in series follow the reciprocal rule. This inversion is a common trap on the MCAT. Understanding how capacitors discharge through a resistor (RC circuits) is also relevant for understanding the time constant of a neuron’s membrane potential recovery.
Waves, Sound, and Optics
Wave Properties: Velocity, Frequency, and Wavelength
Waves transport energy without transporting matter. The fundamental wave equation is $v = flambda$, where $v$ is propagation speed, $f$ is frequency, and $lambda$ is wavelength. Frequency is determined by the source and does not change when a wave enters a new medium; however, velocity and wavelength do change. The period ($T$) is the reciprocal of frequency ($T = 1/f$). For electromagnetic waves in a vacuum, $v$ is the speed of light ($c approx 3 imes 10^8 m/s$). When a wave travels through a medium, its speed is reduced by the index of refraction ($n = c/v$). An MCAT optics and waves formula sheet should also include the formula for the energy of a wave, which is proportional to the square of its amplitude. Recognizing these proportionalities allows you to predict how light behaves as it transitions from air into the vitreous humor of the eye.
Sound Intensity and Doppler Effect
Sound is a longitudinal pressure wave. Its intensity ($I$) is measured in $W/m^2$ and is often expressed on a logarithmic scale in decibels ($dB$): $eta = 10 log(I/I_0)$, where $I_0$ is the threshold of hearing ($10^{-12} W/m^2$). Every $10 dB$ increase represents a tenfold increase in intensity. The Doppler Effect describes the change in perceived frequency when a source and detector move relative to each other: $f' = f rac{v pm v_d}{v mp v_s}$. You use the top signs when the source and detector are moving toward each other (resulting in a higher perceived frequency) and the bottom signs when they move apart. This is used clinically in Doppler ultrasound to measure the velocity of blood flow. If the blood is moving toward the transducer, the reflected frequency is shifted higher, allowing the machine to calculate the flow velocity based on the frequency shift.
Geometric Optics: Lens and Mirror Equations
Optics is a consistent feature of the MCAT due to its relevance to human vision. The thin lens equation, $1/f = 1/o + 1/i$, relates the focal length ($f$), object distance ($o$), and image distance ($i$). For mirrors, focal length is half the radius of curvature ($f = R/2$). Magnification is $m = -i/o$. You must master the sign conventions: $f$ is positive for converging systems (convex lenses, concave mirrors) and negative for diverging systems (concave lenses, convex mirrors). $i$ is positive for real images and negative for virtual images. Real images are always inverted, and virtual images are always upright. Snell’s Law, $n_1 sin heta_1 = n_2 sin heta_2$, governs refraction. Total internal reflection occurs when light travels from a higher refractive index to a lower one at an angle exceeding the critical angle ($ heta_c = arcsin(n_2/n_1)$).
Wave Optics: Diffraction and Interference Conditions
Wave optics deals with the behavior of light when it encounters obstacles or slits. Young’s Double-Slit experiment demonstrates interference, with constructive interference (bright fringes) occurring when the path difference is an integer multiple of the wavelength ($d sin heta = nlambda$). Destructive interference (dark fringes) occurs at half-integer multiples. Diffraction through a single slit creates a central bright fringe with a width governed by $a sin heta = nlambda$, where $a$ is the slit width. Notice that as the slit becomes narrower, the light spreads out more—an inverse relationship. This section also includes polarization, where a polarizer filters light to oscillate in a single plane. This is used in polarimetry to measure the concentration of chiral molecules in a solution, bridging the gap between physics and organic chemistry.
Modern Physics and Atomic Phenomena
Photoelectric Effect and Energy of a Photon
Modern physics on the MCAT focuses on the quantized nature of light and matter. The energy of a photon is $E = hf$, where $h$ is Planck’s constant ($6.6 imes 10^{-34} J·s$). In the photoelectric effect, light hitting a metal surface can eject electrons if the photon energy exceeds the work function ($Phi$) of the metal. The maximum kinetic energy of the ejected electron is $KE_{max} = hf - Phi$. This phenomenon proves that light behaves as a particle (photon) rather than just a wave. If the frequency of the light is below the threshold frequency ($f_0 = Phi/h$), no electrons are ejected, regardless of the light's intensity. This concept is fundamental to understanding how various detectors and imaging technologies, such as PET scans, function by converting high-energy photons into measurable electrical signals.
Bohr Model and Energy Level Transitions
The Bohr model describes electrons orbiting the nucleus in discrete energy levels. When an electron jumps from a lower energy level to a higher one, it absorbs a photon of a specific frequency. When it drops back down, it emits a photon. The energy of the emitted photon corresponds to the difference between the two energy levels: $Delta E = E_{final} - E_{initial}$. These energy levels are quantized, often expressed as $E_n = -R_H / n^2$. Because the energy levels are negative (representing a bound state), the energy becomes "less negative" (increases) as $n$ increases. This explains the discrete spectral lines observed in atomic emission spectra. On the MCAT, you may need to relate these transitions to the electromagnetic spectrum, identifying whether a transition produces ultraviolet, visible, or infrared light based on the energy magnitude.
Nuclear Decay and Half-Life Calculations
Nuclear physics is tested primarily through the lens of radioactive decay and half-lives. There are four main types of decay: Alpha ($alpha$), Beta-minus ($eta^-$), Beta-plus ($eta^+$/positron emission), and Gamma ($gamma$). In $alpha$ decay, the nucleus loses two protons and two neutrons ($^4He$). In $eta^-$ decay, a neutron turns into a proton, increasing the atomic number by one. In $eta^+$ decay, a proton turns into a neutron, decreasing the atomic number by one. Gamma decay involves the release of high-energy photons without changing the identity of the atom. The amount of a radioactive substance remaining after time $t$ is $N(t) = N_0 e^{-lambda t}$. A more practical version for the MCAT is $N = N_0 (1/2)^n$, where $n$ is the number of half-lives elapsed. If three half-lives have passed, $1/8$ ($12.5%$) of the original sample remains.
Applying Formulas in Biological Contexts
Cardiovascular Physics: Blood Flow and Pressure
The MCAT frequently asks students to apply how to remember MCAT physics formulas to the human body. The circulatory system is modeled as a closed circuit. Mean Arterial Pressure ($MAP$) can be approximated as $MAP = CO imes TPR$, where $CO$ is cardiac output and $TPR$ is total peripheral resistance—this is a direct biological analog of $V = IR$. Poiseuille’s Law is a high-yield equation describing the flow rate ($Q$) of a viscous fluid through a pipe: $Q = pi Delta P r^4 / 8eta L$. The most critical takeaway here is the $r^4$ relationship; a small change in the radius of an arteriole (vasoconstriction or vasodilation) leads to a massive change in flow rate and resistance. This explains how the body can precisely regulate blood distribution to different organs by making minute adjustments to vessel diameter.
Respiratory Physics: Lung Volumes and Gas Laws
Respiratory mechanics rely on pressure gradients and the Ideal Gas Law ($PV = nRT$). During inhalation, the diaphragm contracts, increasing the volume of the thoracic cavity. According to Boyle’s Law ($P_1V_1 = P_2V_2$), this increase in volume leads to a decrease in intrapleural pressure. Since the pressure inside the lungs is now lower than atmospheric pressure, air flows in. The MCAT also tests Dalton’s Law of Partial Pressures ($P_{total} = sum P_i$) and Henry’s Law ($[C] = kH imes P_{gas}$), which explains how the concentration of dissolved oxygen in the blood is proportional to the partial pressure of oxygen in the alveoli. Understanding these relationships is essential for solving problems related to gas exchange, altitude sickness, and the effects of pulmonary surfactants on surface tension.
Sensory Physics: Vision and Hearing Thresholds
Finally, the physics of the senses integrates optics and acoustics with biology. For vision, the refractive power of the lens is measured in diopters ($P = 1/f$). The human eye adjusts its focal length through accommodation to keep images focused on the retina. Myopia (nearsightedness) is corrected with diverging lenses, while hyperopia (farsightedness) is corrected with converging lenses. In hearing, the ear acts as a series of impedance-matching structures that amplify sound waves before they reach the fluid-filled cochlea. The resonance of the ear canal and the mechanical advantage of the ossicles (malleus, incus, and stapes) ensure that sound energy is efficiently transmitted. By viewing the body as a collection of physical systems governed by these formulas, you can approach the MCAT with the analytical mindset necessary for medical school success.