## MCAT Physics and Math Review

### Glossary

**Aberration**—Visual alterations as the result of an imperfect optical device; may be chromatic or spherical.

**Absolute pressure**—The actual pressure at a given depth in a fluid, including both ambient pressure at the surface and the pressure associated with increased depth in the fluid; also called hydrostatic pressure.

**Absolute** **zero**—The theoretically coldest temperature at which all atomic movements would halt (0 K).

**Acceleration**—The rate of change in the velocity of an object; related to force through mass and measured in .

**Accuracy**—The tendency for data to represent the true answer; also known as validity.

**Adhesion**—The intermolecular force between molecules of a liquid and molecules of another substance.

**Adiabatic**—A thermodynamic process that occurs with no heat exchange.

**Algebraic system**—A method for determining the values of variables that are the same in two or more equations by relating them to each other.

*α***-particle**—A helium nucleus .

**Amplitude**—The maximum displacement from the equilibrium point during wave or oscillatory motion.

**Antinode**—A point of zero displacement in a standing wave.

**Archimedes’ principle**—States that a body immersed in a volume of fluid experiences a buoyant force equal to the weight of the displaced fluid.

**Atomic number**—The number of protons in the nucleus of a given element.

**Attenuation**—The loss of energy of a propagating wave as a result of nonconservative forces; also known as damping.

**Autonomy**—The ethical principle that states that individuals have the right to make decisions about their own healthcare.

**Beneficence**—The ethical principle that states that practitioners should always act in their patients’ best interests; in research ethics, also states that a research project should create a net positive change for both the study population and general population.

** β**-

**particle**—An electron emitted during

*β*

*–*decay, or a positron emitted during

*β*

^{+}decay.

**Bernoulli’s equation**—An equation that relates static and dynamic pressure for a fluid to the pressure exerted on the walls of a tube and the speed of the fluid.

**Blinding**—Withholding information about a research subject’s group assignment from the subject or evaluator to remove some potential bias from the results.

**Boiling point**—The temperature at which the vapor pressure of a liquid equals the ambient (incident) pressure, usually atmospheric pressure; the temperature at which the liquid boils.

**Boundary layer**—A region of laminar flow in an otherwise turbulent system that occurs at the very edges of the vessel.

**Box-and-whisker** **plot**—A visual representation of the range of data, quartiles, and the interquartile range; may contain outliers as separate points.

**Buoyancy**—The upward force that results from immersion in a fluid; described by Archimedes’ principle.

**Capacitance**—A measure of the ability of a capacitor to store charge; the magnitude of the charge on one plate divided by the potential difference between the plates; measured in farads (F).

**Capacitor**—Two conducting surfaces that store charges of equal magnitude but opposite sign when connected to a voltage source.

**Center** **of gravity**—A point such that the entire force of gravity acting on an object can be thought of as acting at that point.

**Center of mass**—The point that acts as if the entire mass of an object was concentrated at that point.

**Centripetal acceleration**—The acceleration of an object that travels in a circle; it is always directed toward the center of the circle if the object is in uniform circular motion.

**Centripetal force**—The force responsible for centripetal acceleration; usually a result of gravity, tension, or a normal force.

**Charges**—Entities that can influence the environment through electrostatic forces or be influenced by electrostatic forces, measured in coulombs (C).

**Cohesion**—The intermolecular forces experienced between the molecules of a liquid.

**Concave**—A surface that has a similar curvature to the interior of a sphere.

**Condensation**—The phase transition from a gas to a liquid.

**Conductor**—A material that allows the free movement of electrical charge; one with very low or zero resistance.

**Confidence**—A statistical indicator of the likelihood that acquired results did not occur by random chance; equal to 1 – *α*.

**Confounding**—An error that results when a causal variable is associated with two other variables in a study but is not accounted for; may falsely indicate that the two variables are associated.

**Conservative force**—A force that does not cause energy to be dissipated from a system, such as gravity, electrostatic forces, and springs (approximately conservative); pathway independent and associated with a potential energy function.

**Control**—A set of experimental conditions meant to ensure that the results of the experimental group are a result of the intervention.

**Convection**—Heat transfer as a result of bulk flow of a fluid over an object.

**Converging**—The tendency to move parallel light rays toward one another; concave mirrors and convex lenses converge parallel light to a focal point.

**Convex**—A surface that has a similar curvature to the exterior of a sphere.

**Coulomb’s** **law**—Relates the electrostatic force between two charged particles to their charges and the distance between them.

**Critical** **angle**—The angle above which any incident light will undergo total internal reflection; occurs when light is moving from a material with a higher refractive index to one with a lower refractive index.

**Critical speed**—The speed above which flow of a fluid will be turbulent.

**Current**—The orderly movement of charge, often in a circuit; measured by convention as the direction that positive charge would flow within the circuit, and measured in ampères (A).

**Decay** **constant**—The proportionality constant between the rate at which radioactive nuclei decay and the number of radioactive nuclei remaining.

**Density**—A measure of mass per unit volume; useful for buoyancy calculations and usually measured in , , or .

**Dependent variable**—The measured or observed variable in an experiment that is affected by manipulations of the independent variable.

**Detection bias**—An error in data collection that results from the tendency to look more carefully for certain outcomes because a known association with that outcome exists.

**Dielectric material**—An insulating material used to increase capacitance.

**Diffraction**—The spreading or bending of light rays.

**Dispersion**—The separation of light into its component wavelengths when passing through a medium, such as a prism.

**Displacement**—The vector representing the straight-line distance and direction from an initial point; not necessarily equal to total distance traveled, and measured in meters.

**Diverging**—The tendency to move parallel light rays away from one another; convex mirrors and concave lenses diverge parallel light rays from a focal point.

**Doppler** **effect**—Quantifies the perceived change in frequency of sound due to relative movement between the source and detector (observer).

**Electric** **dipole**—A separation of equal and opposite charge by a small distance; can be seen in polar molecules.

**Electric field**—A region generated by an electric charge or multiple charges that can exert a force on another charge brought into the field; measured in .

**Electric meters**—Devices used to measure circuit quantities like current, potential difference, or resistance.

**Electrical potential**—A measure of electrical potential energy per unit charge, given in volts (V); differences in electrical potential (voltage) also drive current as the electromotive force in a circuit.

**Electromagnetic radiation**—A form of energy composed of oscillating electric and magnetic fields perpendicular to each other and perpendicular to the direction of propagation; includes visible light and other types of transverse waves, and can travel through a vacuum.

**Electromotive force**—The difference in electrical potential (voltage) that drives current in a circuit or battery.

**Energy**—The capacity to do work or transfer heat, measured in joules (J).

**Entropy**—A statistical measure of the distribution of unusable energy or heat; randomness introduced to a system, measured in .

**Equilibrium**—The state at which the net torque or net force is equal to zero, such that there is no acceleration.

**Equipoise**—The state of not knowing whether there is a difference between two interventions; ethically necessary for comparative study of the interventions.

**Equipotential lines**—Regions within an electric field with equal electrical potential; movement from one point on these lines to another causes no change in the energy of the system.

**Excited state**—Describes an atom in which an electron occupies an energy state above the minimum energy (ground) state.

**External validity**—The ability to apply findings of a research study to other populations; also called generalizability.

**Field line**—A visual representation of the electric field; points to the direction a force would be exerted on a positive test charge in the electric field.

**FINER method**—A way to determine the usefulness of a research question on the basis of feasibility, interest, novelty, ethics, and relevance.

**Fission**—The splitting of a large nucleus into smaller nuclei with the release of energy.

**Fluid**—A material that conforms to the shape of its container and that can flow.

**Fluorescence**—A process in which the electrons of certain substances are excited to higher energy levels by high-frequency photons, and then emit visible light as the energy is released in two or more steps back to the ground state.

**Focal length**—The distance from a mirror or lens to the focal point.

**Focal point**—The point at which rays of light parallel to the axis of a mirror or lens converge, or from which they appear to diverge when reflected by a mirror or refracted by a lens.

**Force**—A push or a pull, measured in newtons (N).

**Free fall**—A system in which the only force is gravity.

**Freezing**—The phase transition from liquid to solid; also called solidification.

**Frequency**—The rate at which a recurring event occurs; usually measured in hertz (Hz).

**Friction**—A nonconservative force that arises from the interactions between two surfaces in contact.

**Fundamental** **frequency**—The first harmonic of a pipe, string, or other standing wave.

**Fusion**—The merging of small nuclei into a larger nucleus with the release of energy.

*γ***-rays**—High-energy photons released during radioactive decay; part of the electromagnetic spectrum.

**Gauge pressure**—Pressure above and beyond atmospheric pressure.

**Gravity**—An attractive force between two objects that depends on their masses and the distance between them.

**Ground state**—The lowest energy state of an atom.

**Half-life**—The amount of time it takes for one-half of a sample of radioactive nuclei to decay.

**Harmonic** **series**—The set of frequencies that can create standing waves in a given pipe or string.

**Hawthorne effect**—The tendency for research participants to change their behavior because they know they are being observed.

**Heat**—The transfer of thermal energy; measured in joules (J), calories (cal), or kilocalories (kcal or Cal).

**Heat** **of** **transformation**—The amount of heat necessary to cause a phase transition of a unit mass of a substance at the characteristic temperature and pressure of that phase transition.

**Hill’s criteria**—A systematized way of evaluating evidence for causality; only temporality is absolutely necessary to demonstrate causality.

**Histogram**—A visual representation for numerical data; related to a bar chart.

**Hydraulic system**—A simple machine that exerts mechanical advantage using an incompressible fluid; based on Pascal’s principle and conservation of energy.

**Hydrostatics**—The study of fluid systems at rest.

**Hyperopia**—Farsightedness, or the ability to see distant objects while nearby objects are unfocused or blurry.

**Hypothesis** **testing**—A statistical method used to compare results between groups or to a theoretical value with a given level of confidence.

**Image**—The region where light rays converge or appear to converge after being reflected from a mirror or passing through a lens.

**Independent** **variable**—The manipulated variable in an experiment that affects measurements or observations of the dependent variable.

**Index of** **refraction**—A ratio of the speed of light in a vacuum to the speed of light in a given medium.

**Inertia**—An object’s resistance to a change in its motion when a force is applied.

**Informed** **consent**—An ethical requirement for treatments or research, which requires that the patient or participant is able to understand the procedure and its consequences and alternatives; related to autonomy.

**Infrared**—A region of the electromagnetic spectrum that is not visible; may be perceived as heat.

**Infrasonic**—Sound that has a frequency that is lower than the range of human hearing.

**Insulator**—A material that resists the movement of charge because the electrons are tightly associated with their nuclei.

**Intensity**—The average rate of energy expenditure (power) per unit area, measured in ; in waves, intensity is related to the amplitude of the wave.

**Interference**—Interactions between waves traveling in the same space; may be constructive (waves adding together), destructive (waves cancelling each other), partially constructive, or partially destructive.

**Internal validity**—The ability to infer causality from a study or to replicate its results under the same conditions.

**Interquartile range**—A measure of distribution of a sample; outliers lie at least 1.5 interquartile ranges below *Q*_{1} or above *Q*_{3}.

**Inverted**—Describes an image that is upside down relative to the object; in single-mirror or single-lens systems, inverted images are always real.

**Irreversible**—A thermodynamic process that is extraordinarily unfavorable in reverse, usually as a result of changes in entropy.

**Isobaric**—A thermodynamic process that occurs under constant pressure.

**Isothermal**—A thermodynamic process that occurs under constant temperature.

**Isotopes**—Atoms of a given element with different numbers of neutrons and therefore different mass numbers.

**Isovolumetric**—A thermodynamic process that occurs under constant volume; also called isochoric.

**Justice**—The ethical principle that states that practitioners should fairly distribute healthcare resources, and which requires that differences in treatment choices between individuals are only due to morally relevant differences.

**Kinetic energy**—The energy of movement, which depends on both mass and speed; measured in joules (J).

**Kirchhoff’s laws**—Rules that describe the conservation of charge and conservation of energy within an electric circuit; includes the junction rule and loop rule.

**Laminar** **flow**—Smooth flow within a fluid; characterized by streamlines that do not cross each other and an absence of backwards movement.

**Lenses**—Devices that act to create an image by refracting light; usually have spherical surfaces.

**Logarithm**—The inverse function of exponentiation; logarithmic scales are often used to mask large absolute differences between quantities by presenting them as small scale differences.

**Longitudinal wave**—A wave in which the oscillation of the material is parallel to the direction of propagation; sound is a classic example.

**Loudness**—Perceived intensity of a sound, which correlates with sound level; measured in decibels (dB).

**Magnification**—Apparent increase or decrease in size of an image as a result of forming the image with a converging or diverging system.

**Mass**—A measure of inertia or of the amount of “stuff” in an object; measured in kilograms.

**Mass** **defect**—The difference between the sum of the masses of unbound nucleons forming a nucleus and the mass of that nucleus in the bound state.

**Mass number**—The sum of the number of protons and neutrons in an atom; also called the atomic mass.

**Mean**—The average of a group of data; specifically, the arithmetic mean.

**Mechanical advantage**—The reduction in input force required to accomplish a desired amount of output work using a simple machine.

**Median**—The central value of a data set.

**Melting**—The phase transition from solid to liquid; also known as fusion.

**Metric system**—A system of measurements based on the powers of ten; most commonly used in scientific disciplines.

**Microwaves**—Long-wavelength electromagnetic radiation capable of inducing vibration in bonds.

**Mode**—The most common data point in a data set.

**Monochromatic**—Electromagnetic radiation wherein the wavelength is the same for all incident photons.

**Mutually exclusive**—Describes outcomes that cannot occur simultaneously.

**Myopia**—Nearsightedness, or the ability to see nearby objects while distant objects are unfocused or blurry.

**Natural frequency**—The frequency at which a system resonates; also called the resonant frequency.

**Node**—A point of maximum displacement of a standing wave.

**Nonconservative force**—A force that causes energy to be dissipated from a system, such as friction, air resistance, and viscous drag; pathway dependent.

**Nonmaleficence**—The ethical principle that states that practitioners have an obligation to avoid treatments or interventions in which the potential for harm is greater than the potential for good.

**Normal**—A line perpendicular to the surface of interest.

**Normal force**—The force that two surfaces in contact exert on each other that is perpendicular to the plane of contact.

**Nucleon**—A proton or neutron.

**Null hypothesis**—The hypothesis of no difference; given enough statistical evidence, the null hypothesis may be rejected.

**Ohm’s law**—Relates voltage, current, and resistance for a given circuit element.

**Outlier**—A data point that deviates significantly from the perceived pattern of distribution; depending on the context, an outlier may be disregarded, analyzed normally, or given disproportionate weight when calculating statistics.

**Parallel**—An arrangement of circuit elements in which the current can go through one element or the other, but not through both.

**Parameter**—A measure of population data.

**Pascal’s principle**—States that pressure applied to a noncompressible fluid is distributed equally to all points within that fluid and the walls of the container.

**Period**—The amount of time it takes for a wave or oscillation to complete one cycle, measured in seconds; the inverse of frequency.

**Pitch**—A perception of sound that results from its frequency; as frequency increases, pitch gets higher.

**Pitot tubes**—Measurement devices for pressure or flow rate of a dynamic fluid system.

**Plane mirrors**—Reflecting surfaces with an infinite radius of curvature, which results in equal image and object distances.

**Plane-polarized light**—Electromagnetic radiation in which all of the electric field vectors are oriented parallel to one another.

**Poiseuille’s law**—Relates viscosity, tube dimensions, and pressure differentials to the rate of flow between two points in a system.

**Population**—The group of all individuals who have certain desired characteristics.

**Positron**—Antiparticle of an electron; it has the same mass as an electron and the opposite charge (*e*^{+} or *β*^{+}).

**Potential difference**—The difference of electrical potential between two distinct points, measured in volts (V); also called voltage.

**Potential energy**—Energy associated with position, measured in joules (J); includes gravitational, elastic, chemical, and electrical forms.

**Power**—Rate at which work is accomplished, or energy expenditure per unit time; measured in watts (W).

**Precision**—The tendency of measurements to agree with one another; also called reliability.

**Pressure**—The ratio of force to the area over which it is applied; measured in pascals (Pa), millimeters of mercury (mmHg) or torr, or atmospheres (atm).

**Process** **functions**—Physical quantities that depend on the path taken to get from one state to another; include work and heat.

**Quantum**—A discrete bundle of energy such as the photon.

**Quartiles**—Values that separate data in ascending order into four evenly sized groups.

**Radiation**—A method of heat transfer that relies on electromagnetic waves; can occur in a vacuum.

**Radio waves**—Very long wavelength electromagnetic radiation.

**Randomization**—A method of reducing bias and confounding during research in which participants are assigned to a group by a random number generator or similar method; participants or researchers cannot choose the groups.

**Range**—The difference between the smallest number in a data set and the largest.

**Ray** **diagram**—Visual representation of a geometrical optics system.

**Real**—Describes an image on the same side of a lens or mirror as the refracted or reflected light that can be projected on a screen; in single-mirror or single-lens systems, real images are always inverted.

**Reflection**—The return of light rays from a medium at an angle equal to the incident angle.

**Refraction**—The bending of light rays as a result of a change in the index of refraction between media.

**Resistance**—A measure of the opposition to current flow through a material, measured in ohms (Ω); the inverse of conductance.

**Resistivity**—A measure of the intrinsic resistance of a material independent of its shape or size; resistivity generally increases with temperature.

**Resonance**—Oscillation at maximum amplitude as the result of a periodically applied force at the natural (resonant) frequency of an object.

**Respect for persons**—A principle of research ethics that encompasses autonomy and informed consent.

**Resultant**—The sum, difference, or product of vector mathematics; also refers to the sum or difference of two waves.

**Right-hand rule**—A method for determining the direction of a vector that is the product of two vectors.

**Rotation**—The turning of an extended body about an axis or center.

**Sample**—A subset of a population that is used to make generalizations about the population as a whole.

**Scalar**—A mathematical quantity that lacks directionality.

**Scientific method**—A systematized way of evaluating data and investigating new hypotheses.

**Scientific notation**—A mathematical representation of quantities as multiples of powers of ten.

**Selection bias** — Occurs when research participants differ from the general population in a meaningful way.

**Series**—An arrangement of circuit elements in which the current must go through all of the elements.

**Shock wave**—The buildup of wave fronts that occurs when the source is travelling at or above the speed of sound.

**Significant** **figures**—A tool for maintaining appropriate levels of precision when performing mathematical calculations.

**Snell’s law**—Relates the incident angle, refracted angle, and indices of refraction for two media.

**Solid**—A material with distinct boundaries and strong intermolecular forces capable of resisting shear forces.

**Sound**—The perception of longitudinal waves of pressure changes in air and other media.

**Specific gravity**—The ratio of an object’s density to the density of water; unitless.

**Specific heat**—The relationship between thermal energy and temperature change per unit mass of a substance, measured in .

**Speed**—The ratio of distance traveled to time; at any given point, instantaneous speed is the magnitude of instantaneous velocity; measured in .

**Spherical** **mirror**—A mirror that causes convergence or divergence of light rays incident upon its surface.

**Standard deviation**—A measure of distribution of data from the mean of a sample; outliers lie at least three standard deviations above or below the mean.

**Standing waves**—Waveforms with steady nodes and antinodes formed from the interference of incident and reflected waves at a boundary.

**State** **functions**—Physical quantities that can be determined based on the state of an object, such as pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy; pathway independent.

**Statistic**—A measure of sample data.

**Streamlines**—Visual representations of the movement of fluid during laminar flow.

**Surface** **tension**—The result of the cohesive forces in a liquid creating a barrier at the interface between a liquid and the environment.

**Surroundings**—Everything that is not being measured as part of a given system.

**System**—The observed and quantified region of the universe of interest to the experimenter.

**Temperature**—A measure of the average kinetic energy of particles in a substance; measured in degrees Fahrenheit (°F), degrees Celsius (°C), or kelvins (K).

**Terminal velocity**—The velocity at which air resistance is equal to gravitational force and no acceleration occurs for an object in free fall.

**Thermal expansion**—An increase in length or volume of a substance as a result of an increase in temperature.

**Torque**—The primary motivator for rotational movement that combines force, lever arm, and the angle between them; measured in N·m.

**Traveling wave**—A wave that propagates through a medium with changes in the locations of crests and troughs.

**Translation**—Motion through space without rotation.

**Transverse wave**—A wave that propagates in a direction perpendicular to the direction of oscillation.

**Turbulent** **flow**—Fluid movement that does not follow parallel streamlines; has backflow, eddies, and swirls.

**Twin study**—A research design used heavily in psychology to differentiate between genetic and environmental effects.

**Ultrasonic**—Above the frequencies that humans can hear.

**Ultrasound**—A treatment and diagnostic modality using ultrasonic waves for medical purposes.

**Ultraviolet**—A region of the electromagnetic spectrum that is not visible; primarily responsible for the damaging effects of sunlight on skin.

**Upright**—Describes an image that is the same orientation as the object; in single-mirror or single-lens systems, upright images are always virtual.

**Vaporization**—The phase transition from solid to gas; also called boiling or evaporation.

**Vector**—A mathematical quantity that has both magnitude and direction.

**Velocity**—The rate of change in the displacement of an object; measured in .

**Venturi effect**—Describes the relationship between the continuity equation and Bernoulli’s equation; as cross-sectional area of a tube decreases, the speed of the fluid increases, and the pressure exerted on the walls of the tube decreases.

**Virtual**—Describes an image on the opposite side of a lens or mirror as the refracted or reflected light; in single-mirror or single-lens systems, virtual images are always upright.

**Viscosity**—A measure of the resistance to flow in a fluid.

**Wavelength**—The distance between two corresponding points of successive cycles in a waveform, measured in meters.

**Weight**—The force of gravity acting on an object.

**Work**—A function of the applied force and the distance through which it is applied or the pressure and volume changes in a gas system; work is the use of energy to accomplish something and is measured in joules (J).

**Work—energy theorem**—States that net work is equal to the change in energy (usually kinetic energy) of an object.

**X-rays**—A type of electromagnetic radiation; primarily used for medical imaging.