Math and Physics Flashcards PDF

 1.1 Units 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS UNITS Measurement: Quantification of motion (kinematics) and forces (dynamics) using units like meters, seconds, kilograms, and newtons. Analysi...

 1.1 Units 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS UNITS Measurement: Quantification of motion (kinematics) and forces (dynamics) using units like meters, seconds, kilograms, and newtons. Analysis: Examination of motion patterns, velocities, accelerations, and interactions between objects. Predictive Modeling: Using equations with proper units to forecast future motion and interactions based on initial conditions. the SI units include meter, kilogram, second, Kinematics: by the Numbers ampère, mole, kelvin, and candela "Mighty Kites Fly Near Saturn." Explanation: Mighty: Refers to the power of motion and forces. Kites: Represents kinematics, the study of motion. Fly Near Saturn: Relates to dynamics, the study of forces.  1.2 Vectors and Scalars 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS Vectors: Physical quantities that have both magnitude and direction. Examples: displacement, velocity, acceleration, and force. Scalars: Quantities without direction. Scalar quantities may be the magnitude of vectors, like speed, or may be dimensionless, like coefficients of friction Vector Addition: Tip-to-tail method, or you can break the vector into its component parts and use Pythagorean theorem Vector Subtraction: Change the direction of the subtracted vector and then do a tip-to-tail addition Vector Multiplication: By scalar: Changes the magnitude and may reverse the direction. Dot Product: A B = |A||B| cos (q) , results in a scalar quantity Cross Product: A × B = |A||A| sin (q) , results in a new vector. Direction of the new vector can be found using the right-hand rule  1.3 Displacement and Velocity 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS Displacement: The vector representation of a Average Speed and Average Velocity: change in position. Path independent Average speed describes how fast a particle is moving. Average velocity describes how fast the displacement is changing with respect to time. Distance: A scalar quantity that reflects the path Instantaneous velocity traveled limit of the change in displacement over time as the change in time approaches zero Instantaneous speed the magnitude of the instantaneous velocity vector Velocity: The vector representation of the change in DISPLACEMENT with respect to time Instantaneous Velocity: The change in displacement over time as the time approaches 0 Instantaneous Speed: The magnitude of the instantaneous velocity vector  1.4 Forces and Acceleration 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS Force: Any push or pull that has the potential to result in Mass: A measure of the inertia of an object – its an acceleration amount of material Weight: The force experienced by a given mass due to the gravitational attraction to the Earth Gravity: The attractive force between two objects as a result of their masses Friction: A force that opposes motion as a function of Acceleration: The vector representation of the change electrostatic interactions at the surfaces between two in velocity over time. objects Torque: A twisting force that causes rotation Static Friction: Stationary object POS = counterclockwise Kinetic Friction: Sliding object r = r F (sin) θ NEG = clockwise  1.5 Newton’s Laws 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS First Law: An object will remain at rest or move with a Third Law: Any two objects interacting with one another constant velocity if there is no net force on the object experience equal and opposite forces as a result of their interaction Fnet = m a = 0 if at rest or constant velocity FAB = -FBA Second Law: Any acceleration is the result a net force > 0 Fnet = m a  1.6 Motion with Constant Acceleration 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS Linear Motion: Includes free fall and motion in which Inclined Planes: Force components: the velocity and acceleration vectors are parallel or Parallel to the ramp use sinθ. “Sin is sliding ̄ ⬇️ the antiparallel slide”. Perpendicular to the ramp use cosθ. Kinematics Equations for Linear Motion Circular Motion: Best thought of as having radial and tangential dimensions. Centripetal force vector points radially inward, the Projectile Motion: Contains both an x- and y- instantaneous velocity vector points component. Assuming negligible air resistance, the tangentially. only force acting on the object is gravity. X velocity is constant throughout. Centripetal force:  1.7 Mechanical Equilibrium 30 Day MCAT CHAPTER 1 - KINEMATICS & DYNAMICS Translational Equilibrium: Occurs in the absence of any net forces acting on an object Rotational Equilibrium: Occurs in the absence of any net torques acting on an object. Free Body Diagrams: The center of mass is the most commonly used Representations of the forces acting on an pivot point. object. useful for equilibrium and dynamics problems  2.1 Energy 30 Day MCAT CHAPTER 2: WORK AND ENERGY Structural Proteins: Electrical Potential Energy: The property of a system that enables it to do The energy between two charged particles. something or make something happen, including the capacity to do work. Chemical Potential Energy: SI units are joules (J). The energy stored in the bonds of compounds. Conservative Forces: Path independent and do not dissipate the Kinetic Energy: mechanical energy of a system. Energy associated with the mvmt of objects. It Examples: Gravity and electrostatic forces. depends on mass and speed squared. Potential Energy: Energy stored within a system. Nonconservative Forces: Path dependent and cause dissipation of mechanical energy from a system. Examples: Friction, air resistance, and viscous drag. Gravitational Potential Energy: Related to the mass of an object and its height above a zero point.  2.2 Work 30 Day MCAT CHAPTER 2: WORK AND ENERGY Work: Work-Energy Theorem: The process by which energy is transferred from one When net work is done on or by a system, the system to another. system’s kinetic energy will change by the same Can be expressed as the dot product of force and amount. displacement: Power: The rate at which work is done or energy is transferred. SI unit is watt (W). work may be expressed as the dot product of force and displacement, or the product of force and distance traveled with the cosine of the angle between the two  2.3 Mechanical Advantage 30 Day MCAT CHAPTER 2: WORK AND ENERGY Mechanical Advantage: Simple Machines: The factor by which a simple machine multiplies the Inclined plane, wedge, wheel and axle, lever, input force to accomplish work. pulley, and screw. The input force necessary to accomplish the work is reduced and the distance through which the reduced input force must be applied is increased by the same factor. Mechanical advantage makes it easier to accomplish a given amount of work the input force necessary to accomplish the work is reduced MA of an Inclined Plane: the distance through which the reduced input force must be applied, however, is increased by the same factor (assuming 100% efficiency) Efficiency: The ratio of the machine’s work output to work input when nonconservative forces are taken into account.  3.1 Zeroth Law of Thermodynamics 30 Day MCAT CHAPTER 3- THERMODYNAMICS Thermal Equilibrium: Temperature: When systems have the same average KE and thus The average kinetic energy the same temperature. of the particles that make No heat transfer. up a substance. a qualitative measure of how hot or cold an object is; quantitatively Is obtained when touching objects within a system reach the same temperature Thermal Expansion: Describes how a substance changes in length or volume as a function of the change in temperature.  3.2 Systems 30 Day MCAT CHAPTER 3- THERMODYNAMICS Isolated System: Do not exchange matter or energy with surroundings. Closed System: Exchange energy but not matter with their surroundings. Open System: Exchange both energy and matter with their surroundings. TYPES OF THERMODYNAMIC SYSTEM Process Functions State Functions: Pathway independent and are not themselves defined by a process. Include: Pressure, density, temp, volume, enthalpy, internal energy, Gibbs free energy, and entropy. Process Functions: Describe the pathway from one equilibrium state to another. Include: work and heat.  3.3 First Law of Thermodynamics 30 Day MCAT CHAPTER 3- THERMODYNAMICS A statement of conservation of energy: Heat of Transformation: The total energy in the universe can never The energy required for a phase change of a decrease or increase. substance (temperature does not change during the ∆ For an individual system: U = Q − W transformation). ∆ U = change in system's internal energy q=ml L = heat of transformation Q = energy transferred into the system as heat Processes with Constant Variable: W = work done by the system ∆ Isobaric: Pressure is constant, P = 0 Heat: The process by which energy transfer between ∆ Isothermal: Temp is constant, U = 0 Adiabatic: No heat is exchanged, Q = 0 two objects at different temperatures that occurs until the two objects come into thermal equilibrium Isovolumetric (isochoric): Volume is constant, ∆V = 0, so Work = 0 (reach the same temperature). q=mc T ∆ Work of a Gas: W = −P V ∆ Specific Heat: The amount of energy necessary to raise one gram of a substance by 1° C or 1 K. Specific heat of H2O = First Law of Thermodynamics - Equations, Limitations and Examples  3.4 Second Law of Thermodynamics and Entropy 30 Day MCAT CHAPTER 3- THERMODYNAMICS SECOND LAW OF THERMODYNAMICS AND ENTROPY In a closed system, up to and including the universe, energy will spontaneously and irreversibly go from being localized to being spread out. every natural process is ultimately irreversible; under highly controlled conditions, certain equilibrium processes such as phase changes can be treated as essentially reversible Entropy: A measure of how much energy has spread out or how spread out energy has become.  4.1 Characteristics of Fluids and Solids 30 Day MCAT CHAPTER 4-FLUIDS Fluids: Pressure: Substances that flow and conform to the shape of their A measure of force per unit area; it is exerted by containers, includes liquids and gases. a fluid on the walls of its container and on objects They can exert perpendicular forces but not shear placed in the fluid. forces. Scalar quantity. The pressure exerted by a gas on its container Solids: will always be perpendicular to the container Do not flow. walls. They maintain their shape regardless of their container Absolute Pressure: The sum of all pressures at a certain point within a fluid; it is equal to the pressure at the surface of the fluid plus the pressure due to the fluid itself. Gauge Pressure: The difference between absolute pressure and atmospheric pressure. Density: In liquids, gauge pressure is caused by the Mass per unit volume of substance. weight of the liquid above the point of measurement.  4.2 Hydrostatics 30 Day MCAT CHAPTER 4-FLUIDS Pascal’s Principle: Archimedes’ Principle: A pressure applied to an incompressible fluid will be When an object is placed in a fluid, the fluid distributed undiminished throughout the entire generates a buoyant force against the object that volume of the fluid. is equal to the weight of the fluid displaced by the object. Hydraulic Machines: If the max buoyant force is larger than the force of Operate based on the application of Pascal’s principle gravity on the object, the object will float. If the to generate mechanical advantage. max buoyant force is smaller than the force of gravity on the object, the object will sink. Surface Tension: Specific Gravity: Cohesive forces give rise to surface tension. Ratio of density of an object to density of water. Cohesive vs. Adhesive: Fluids experience cohesive forces with other molecules of the same fluid and adhesive forces with other materials.  4.3 Fluid Dynamics 30 Day MCAT CHAPTER 4-FLUIDS Viscosity: Continuity Equation: A measure of a fluid’s internal friction. Fluids will flow more quickly through narrow Viscous Drag is a nonconservative force generated by passages and more slowly through wider ones. viscosity. Bernoulli’s Equation: The sum of the static pressure and the dynamic pressure will be constant between any two points in a closed system. Laminar Flow: Smooth and orderly. Venturi Effect: The velocity of a fluid passing through a Turbulent Flow: constricted area will INCREASE and its Rough and disorderly. static pressure will DECREASE Poiseuille’s Law: Determines the rate of laminar flow. Venturi Tube: The average height of the horizontal tube remains The relationship between radius and pressure gradient constant, so pgh remains constant at points 1 and 2. is inverse exponential to the fourth power. As cross-sectional area decreases from point 1 to point 2, the linear speed must increase. Flow Rate: As the dynamic pressure increases, the absolute pressure must decrease at point 2, causing the A = cross sectional area column of fluid sticking up from the Venturi tube be v = velocity to be lower at point 2.  4.4 Fluids in Physiology 30 Day MCAT CHAPTER 4-FLUIDS Circulatory System: Breathing: The circulatory system behaves as a closed system Inspiration and expiration create a pressure with nonconstant flow. gradient not only for the respiration system, The nonconstant flow = our pulse. but for the circulatory system too. Alveoli: Air at the alveoli has essentially zero speed. venous circulation has three times the arterial circulation volume of arterial Pressure is directly related to velocity, area, and is primarily circulation and is resistance. motivated by the motivated by the Area is inversely related to resistance and velocity. heart skeletal musculature ⬆️➡️ ⬇️ Cross-sectional area ­ Resistance and/or and expansion of the ⬇️ velocity ̄ resistance decreases as the total heart cross-sectional area increases inspiration and expiration create a pressure gradient not only for the respiratory system, but for the circulatory system as well  5.1 Charges 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Coulomb: Conductors: The SI unit of charge Allow the free and uniform passage of electrons when charged Protons & Electrons: Protons have a positive charge and electrons have a Insulators: negative charge. Resist the movement of charge and will have Both protons and electrons possess the fundamental localized areas of charge that do not distribute over unit of charge the surface of the material Protons and electrons have different masses. Attraction & Repulsion: Opposite charges exert attractive forces, and like charges exert repulsive forces  5.2 Coulomb’s Law 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Coulomb’s Law: Field Lines: Gives the magnitude of the electrostatic force vector Used to represent the electric field vectors for a between two charges. charge. The force vector points along the line connecting the They show the activity of a positive test charge, centers of the two charges. which would move away from a positive charge and move toward a negative charge (north to south). The field is stronger where the field lines are closer together. Electric Field: Every charge generates an electric field, which can exert forces on other charges  5.3 Electrical Potential Energy 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Electrical potential energy Increases: is the amount of work required to bring the test charge Like charges move toward each other. from infinitely far away to a given position in the vicinity Opp charges move apart of a source charge. Decreases: Opp charges move toward each other. Like charges move apart Electrical Potential Energy: the electrical potential energy of a system will increase when two like charges move toward each other or when two opposite charges move further apart the electrical potential energy of a system will decrease when two opposite charges move toward each other or when two like charges move further apart  5.4 Electrical Potential 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Electrical potential Voltage: is the electrical potential energy per unit charge. Potential difference. Different points in the space of an electric field The change in electrical potential that accompanies surrounding a source charge will have different the mvmt of a test charge from one position to electrical potential values. another. Test Charges: Will move spontaneously in whichever direction results in a decrease in their electrical potential energy. POS Test Charges: ➡️ High potential Low potential NEG Test Charges: ➡️ Low potential High potential positive test charges will move spontaneously from high potential to low potential negative test charges will move spontaneously from low potential to high potential Electrical Potential: From electrical potential energy  5.5 Special Cases in Electrostatics 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Equipotential Lines: Electric Dipole: Generated by two charges of opposite sign A line on which the potential at every point is the same. separated by a fixed distance d. Equipotential lines are always perpendicular to electrical field lines. In an external electric field, an electric dipole Work will be done when a charge is moved from one will experience a net torque until it is aligned equipotential line to another. with the electric field vector. No work is done when a charge moves from a point on an equipotential line to another point on the same line. An electric field will not induce any translational motion in the dipole regardless of its orientation with respect to the electric field vector. Net Torque: Dipole Moment: The product of charge and separation distance  5.6 Magnetism 30 Day MCAT CHAPTER 5-ELECTROSTATICS AND MAGNETISM Magnetic Field: Ferromagnetic Materials: Created by magnets and moving charges. Possess SOME unpaired electrons and become SI unit is the tesla (T). 1 T = 10,000 gauss STRONGLY MAGNETIC in an external magnetic field Diamagnetic Materials: Possess NO unpaired electrons and are slightly REPELLED by a magnet Characteristics of Magnetic Fields: Current-carrying wires create magnetic fields that are concentric circles surrounding the wire. External magnetic fields exert forces on charges moving in any direction except parallel or antiparallel to the field. Paramagnetic Materials: Point charges may undergo uniform circular motion in a Possess SOME unpaired electrons and become uniform magnetic field wherein the centripetal force is WEAKLY MAGNETIC in an external magnetic field the magnetic force acting on the point charge. Determine direction using the right-hand rule. Lorentz Force: Sum of the electrostatic and magnetic forces acting on a body  6.1 Current 30 Day MCAT CHAPTER 6- CIRCUITS Current: Conductive Materials: The movement of charge that occurs between two Metallic Conduction: points that have different electrical potentials. The flow of current due to movement of By convention, current is defined as the mvmt of electrons positive charge from the high-potential end of a voltage Electrolytic Conduction: source to the low-potential end. The movement of free ions under electric field In reality, it is negatively-charged particles (electrons) Insulators: that move in a circuit, from low potential to high Materials that do not conduct a current potential Kirchhoff’s Laws: Express conservation of charge and energy. Junction Rule: The sum of the currents flowing into a junction is equal to the sum of the currents flowing out of that junction. Loop Rule: In a closed loop, the sum of voltage sources is always equal to the sum of voltage drops.  6.2 Resistance 30 Day MCAT CHAPTER 6- CIRCUITS Resistance: Ohm’s Law: Capacitors in Series: The opposition that a substance For a given resistance, the magnitude The total capacitance of offers to the flow of e- of the current through a resistor is capacitors in series is proportional to the voltage drop across equal to the reciprocal of the resistor. the sum of the reciprocals Resistors in Series: of their individual Additive. Sum together to create the capacitances. total resistance of a circuit. Total capacitance will Resistors in Parallel: always be less than the Resistors: Conductive materials with a ⬇️equivalent resistance of a circuit. value of the smallest capacitor. moderate amount of resistance that slow down electrons without stopping them. Resistors in Series: Total resistance is equal to the sum of all the individual resistors. Capacitors in Parallel: Total capacitance is p = resistivity, L = length of resistor, equal to the sum of all A = cross sectional area the individual capacitances. Resistors in Parallel: To get the total resistance, add the reciprocals of the resistances of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance.  6.3 Capacitance and Capacitors 30 Day MCAT CHAPTER 6- CIRCUITS Capacitors: Series /Parallel: Have the ability to store and discharge electrical Series: potential energy. ⬇️equivalent capacitance of a circuit Parallel: Sum together to create a large equivalent capacitance Dielectric Materials: Insulators placed between the plates of a Capacitance: capacitor that increase capacitance by a factor In parallel plate capacitors, it is determined by the area equal to the material’s dielectric constant, k of the plates and the distance between the plates. Capacitance based on parallel plate geometry: Electric field in a capacitor: Potential energy of a capacitor:  6.4 Meters 30 Day MCAT CHAPTER 6- CIRCUITS Ammeters: Inserted in SERIES in a circuit to measure current; they have negligible resistance Sample VU Meter Voltmeters: Inserted in PARALLEL in a circuit to measure a voltage drop; they have very large resistances Ohmmeters: Electrical Meters Inserted around a resistive element to measure resistance; they are self- powered and have negligible resistance Safe Meter Usage  7.1 General Wave Characteristics 30 Day MCAT CHAPTER 7- WAVES AND SOUND Transverse Waves: Angular Frequency (w): Partially Constructive / Have oscillations of wave particles Also known as radial or circular Destructive Interference: perpendicular to the direction of frequency, measures angular Occurs when two waves are not wave propagation. LIGHT displacement per unit time. quite perfectly in or out of phase Longitudinal Waves: Expressed in radians per with each other. The displacement Have oscillations of wave particles second. of the resultant wave is equal to parallel to the direction of wave the sum of the displacements of propagation. SOUND Period (T): the two interfering waves. The number of seconds it takes Traveling Waves: to complete a cycle. It is the Have continuously shifting points Displacement (x): inverse of frequency. of maximum and minimum Interference: displacement. Refers to how far a point is from Describes the ways in which Standing Waves: the equilibrium position, expressed waves interact in space to form Produced by the constructive and as a vector quantity. a resultant wave. destructive interference of two Amplitude (A): The magnitude of its maximal Constructive Interference: waves of the same frequency displacement. The maximum point Occurs when waves are exactly traveling in opposite directions in is called a crest. The minimum in phase with each other. The the same space. point is called a trough. amplitude of the resultant wave Antinodes: Wavelength (l): is equal to the sum of the Points of maximum oscillation. The distance between two crests amplitudes of the two Nodes: or two troughs. interfering waves. Points where there is no Frequency (f): Destructive Interference: oscillation. The number of cycles it makes per Occurs when waves are exactly Resonance: second. out of phase with each other. The increase in amplitude that Expressed in Hz. The amplitude of the resultant occurs when a periodic force is Damping: wave is equal to the difference applied at the natural (resonant) A decrease in amplitude caused by in amplitude between the two frequency. an applied or nonconservative force. interfering waves.  7.2 Sound 30 Day MCAT CHAPTER 7- WAVES AND SOUND Sound: Doppler Effect: Produced by mechanical disturbance of a material A shift in the perceived frequency of a sound that creates an oscillation of the molecules in the compared to the actual frequency of the emitted material. sound when the source of the sound and its detector are moving relative to one another. Propagation: The apparent frequency will be higher than the emitted Sound propagates through all forms of matter but frequency when the source and detector are moving not through a vacuum. Fastest through solids, toward each other. followed by liquids, and slowest through gases. The apparent frequency will be lower than the emitted Within a medium, as density increases, speed of frequency when the source and detector are moving sound decreases. away from each other. Pitch: The apparent frequency can be higher, lower, or equal Our perception of frequency. to the emitted frequency when the two objects are moving in the same direction, depending on their Intensity: relative speeds. Intensity is related to a wave’s amplitude. Intensity decreases over distance and some energy is lost to attenuation from frictional forces. Use the Top sign for “toward”, bottom sign for “away” Ultrasound: Strings and Open Pipes: Uses high frequency sound waves to compare the Support standing waves and the length of the relative densities of tissues in the body. Doppler string or pipe is equal to some multiple of half- Ultrasound is used to determine the flow of blood wavelengths. within the body. 1st, 2nd, and 3rd Harmonics of a Closed Pipes: String: N = node, A = antinode. Closed at one end. Support standing waves, and As a shortcut, for strings the length of the pipe is equal to some odd attached at both ends, the number of antinodes present will multiple of quarter-wavelengths. tell you which harmonic it is  8.1 Electromagnetic Spectrum 30 Day MCAT CHAPTER 8- LIGHT AND OPTICS Electromagnetic Waves: Visible Spectrum: Transverse waves that consist of an oscillating electric field and an oscillating magnetic field. The two fields are perpendicular to each other and to the direction of propagation of the wave. Electromagnetic Spectrum: Hydrogen Spectral Series: The range of frequencies and wavelengths found in Lyman: Ultraviolet, n = 1 EM waves. Balmer: Visible, n = 2 Paschen: Infrared, n = 3 Acrostic “Loves Beer Pong”, then n = 1, n = 2, n = 3 Rydberg Formula: EM Spectrum:  8.2 Geometrical Optics 30 Day MCAT CHAPTER 8- LIGHT AND OPTICS Dispersion: Reflection: When various wavelengths of light separate from Rebounding of incident light waves at a medium’s each other. boundary Law of Reflection: Snell’s Law: The law of refraction. There is an inverse relationship between the index of refraction and the sine of the Spherical Mirrors: angle of refraction (measured from the normal) Total Internal Reflection: When light cannot be refracted out of a medium and is instead reflected back inside the medium. Occurs when light moves from a medium with a HIGHER index of refraction to a medium with a LOWER index of refraction with a high incident q. Critical Angle: Refraction: The minimum incident angle at which total reflection The bending of light as it passes from one medium to occurs. another. The speed of light changes depending on Lenses: index of refraction of the medium. This speed Refract light to form images of objects. Thin change causes refraction. The amount of refraction symmetrical lenses have focal points on each side. depends on the wavelengths involved. Lensmaker’s Equation: Lenses with non-negligible thickness require the lensmaker’s eq.  8.3 Diffraction 30 Day MCAT CHAPTER 8- LIGHT AND OPTICS Diffraction: Interference: The bending and spreading out of light waves as they When waves interact with each other, the pass through a narrow slit. displacements add together in a process called Diffraction may produce a large central light fringe interference. surrounded by alternating light and dark fringes with the addition of a lens. Young’s Double-Slit Experiment: Shows the constructive and destructive interference of waves that occur as light passes through parallel slits, resulting in minima (dark fringes) and maxima (bright fringes) of intensity.  8.4 Polarization 30 Day MCAT CHAPTER 8- LIGHT AND OPTICS Plane-Polarized Light: Circular Polarized Light: A polarizing filter only lets light through if the E field of All of the light rays have electric fields with equal the wave aligns with the openings in the filter. intensity but constantly rotating direction. The E fields of the exiting light oscillate along the Circularly polarized light is created by exposing same axis. unpolarized light to special pigments or filters. "Pretty Lights Make Optics Glow" "Pretty": Represents Polarization "Lights": Stands for Light "Make": Refers to Mechanism "Optics": Represents the study of optics "Glow": Stands for Geometric Optics  9.1 The Photoelectric Effect 30 Day MCAT CHAPTER 9- ATOMIC AND NUCLEAR PHENOMENA The Photoelectric Effect Threshold Frequency: The ejection of an electron from the surface of a metal The minimum light frequency necessary to in response to light eject an electron from a given metal. Energy of a photon of light: Work Function: To calculate l from λ use: The minimum energy necessary to eject an c = speed of light = electron from a given metal. Maximum kinetic energy in the photoelectric effect: Define threshold frequency. Threshold frequency and work function Work Functions  9.2 Absorption and Emission of Light 30 Day MCAT CHAPTER 9- ATOMIC AND NUCLEAR PHENOMENA Bohr Model: Fluorescence: States that electron energy levels are stable and Occurs when a species absorbs high-frequency light discrete, corresponding to specific orbits. and then returns to its ground state in multiple steps. Each step has less energy than the absorbed light and is within the visible range of the electromagnetic spectrum. Absorption: An electron can jump from a lower-energy to a higher- energy orbit by absorbing a photon of light of the same frequency as the energy difference between the orbits. Emission: When an electron falls from a higher-energy to a lower- energy orbit, it emits a photon of light of the same frequency as the energy difference between the orbits. Absorption Spectra: May be impacted by small changes in molecular structure.  9.3 Nuclear Binding Energy and Mass Effect 30 Day MCAT CHAPTER 9- ATOMIC AND NUCLEAR PHENOMENA Nuclear Binding Energy: 4 Fundamental Forces of Nature: Is the amount of energy that is released when Strong and weak nuclear force, electrostatic forces, nucleons (protons and neutrons) bind together. gravitation. the more binding energy per nucleon released, the more stable the nucleus Mass Defect: The difference between the mass of the unbonded nucleons and the mass of the bonded nucleons within the nucleus. "Energetic Nuclei Make Atoms Magnetically The unbonded constituents have more energy and, therefore, Entwined." more mass than the bonded constituents. Explanation: The mass defect is Energetic Nuclei: Refers to nuclear binding the amount of mass energy, the energy that holds nuclei converted to energy together. during nuclear Make Atoms: Represents the process of fusion. forming atoms from protons and neutrons. Magnetically Entwined: Illustrates the strong attractive forces (binding energy) that keep nucleons (protons and neutrons) together in the nucleus.  9.4 Nuclear Reactions 30 Day MCAT CHAPTER 9- ATOMIC AND NUCLEAR PHENOMENA Fusion: Gamma (y) Decay: Occurs when small nuclei combine into larger nuclei. The emission of a gamma ray, made up of photons, which converts a high-energy nucleus into a more Fission: stable nucleus. Occurs when a large nucleus splits into smaller Electron Capture: nuclei. Is the absorption of an electron from the inner shell Energy is released in both fusion and fission because that combines with a proton in the nucleus to form a the nuclei formed in both processes are more stable neutron. than the starting nuclei. Half-Life: Radioactive Decay: The amount of time required for half of a sample of The loss of small particles from the nucleus. radioactive nuclei to decay. Or, the time it takes to reduce the radioactivity of a substance by half. Exponential Decay: Alpha (a) Decay: The rate at which radioactive nuclei decay is The emission of an alpha particle proportional to the number of nuclei that remain. which is a helium nucleus. Beta-negative (b-) Decay: The decay of a neutron into a proton, with emission "Atoms Radiate, Transform, Emit Energy." of an electron and an antineutrino Explanation: Atoms Radiate: Refers to the emission of particles or radiation in nuclear reactions. Beta-positive (b+) Decay: Transform: Signifies the change in atomic nuclei “Positron emission”, the decay of a proton into a neutron, during nuclear reactions. with emission of a positron (e+, b+) and a neutrino Emit Energy: Highlights the release of energy as a result of nuclear reactions.  10.1 Arithmetic and Significant Figures 30 Day MCAT CHAPTER 10- MATHEMATICS Scientific Notation: Significant Figures: Improves the ease of calculation. It is usually helpful Include all nonzero digits and any trailing zeroes to convert a number to scientific notation in a number with a decimal point. LARS mnemonic when moving the decimal within scientific notation. Left ➡️ Add, Right➡️ Subtract Estimation: Multiplication: If one number is rounded up, the other should be rounded down in proportion. Division: If one number is rounded up, the other should also be rounded up in proportion.  10.2 Exponents and Logarithm 30 Day MCAT CHAPTER 10- MATHEMATICS Estimating Square Roots: Log and Ln: To calculate the square root of any number less than 400, you can approximate its value by determining which two perfect squares it falls between. For √ example, 180 is between 13 and 14. √ √ √ √ √ 180 = 4 × 9 × 5 = 2 × 3 × 5 = 6 5 √ √ ≈ 5 √ ≈ 2.2 so 6 5 13.2. Common Squares: Estimating Log: The Unit Circle  10.3 Trigonometry 30 Day MCAT CHAPTER 10- MATHEMATICS Trigonometric Common Values: relationships can be calculated based on the lengths of the sides of right triangles Inverse trigonometric functions use the calculated value from a ratio of side lengths to calculate the angle of interest  10.4 Problem-Solving 30 Day MCAT CHAPTER 10- MATHEMATICS Direct Proportion: a direct proportion, as one variable increases, the other variable also increases by a constant ratio, and vice versa. Inverse Proportion: an inverse proportion, as one variable increases, the other variable decreases by a constant ratio, and vice versa.  11.1 The Scientific Method 30 Day MCAT CHAPTER 11-REASONING ABOUT THE DESIGN AND EXECUTIONS OF RESEARCH The scientific method is a series of eight steps for the generation of new knowledge Initial steps: Focus on formulating a hypothesis. Intermediate steps: Focus on testing that hypothesis. Final steps: Provide results for further testing of the hypothesis. FINER Method: Assesses the value of a research question on the basis of whether or not it is feasible, interesting, novel, ethical, and relevant.  11.2 Basic Science Research 30 Day MCAT CHAPTER 11-REASONING ABOUT THE DESIGN AND EXECUTIONS OF RESEARCH Basic Science Research Controls: Occurs in the lab, not in human subjects. Positive Controls: Basic science research is often the best type Ensure that a change in the dependent variable for demonstrating causality because the occurs when expected. experimenter has the highest degree of control Negative Controls: over the experimental conditions. Ensure that no change in the dependent Variables: variable occurs when none is expected. Independent Variable: Manipulated Dependent Variable: Observe for change. Accuracy (Validity): The quality of approximating the true value. Precision (Reliability): The quality of being consistent in approximations.  11.3 Human Subjects Research 30 Day MCAT CHAPTER 11-REASONING ABOUT THE DESIGN AND EXECUTIONS OF RESEARCH Human subjects research Bias: is subject to ethical constraints that are Selection Bias: The sample differs from the generally absent in basic science research. population. Causal conclusions are harder to determine Detection Bias: Arises from educated professionals because circumstances are harder to using their knowledge in an inconsistent way by control. searching for an outcome disproportionately in certain Much of human subject research is populations. observational. Hawthorne Effect: Behavior of subjects is altered simply by knowing that they are being studied. Cohort Studies: Social Desirability Bias: A type of response bias that is Record exposures throughout time and the tendency of survey respondents to answer then assess the rate of a certain outcome. questions in a manner that will be viewed favorably by others. Cross-sectional Studies: Assess both exposure and outcome at the Placebo Effect: Results are influenced by the fact that the same point in time. subjects are aware they are or are not in the control group. Case-Control Studies: Assess outcome status and then assess for Confounding Variable: An extraneous variable that relates exposure history. to BOTH the dependent and independent variables. Hill’s Criteria: Mediating Variable: The means by which the IV affects Used to determine if causality can be the DV. It is the “middleman” between the IV and DV. supported. The criteria include temporality (necessary for causality), strength, dose- Moderating Variable: Influences the already established response, relationships, consistency, relationship between the IV and DV. Moderators affect the plausibility etc. strength of the relationship between the two variables.  11.4 Ethics 30 Day MCAT CHAPTER 11-REASONING ABOUT THE DESIGN AND EXECUTIONS OF RESEARCH Medical Ethics: 4 tenets: beneficence, nonmaleficence, respect for patient autonomy, and justice Research Ethics: Respect for persons, justice, beneficence. Must have equipoise – a lack of knowledge about which arm of research study is better for the subject  11.5 Research in the Real World 30 Day MCAT CHAPTER 11-REASONING ABOUT THE DESIGN AND EXECUTIONS OF RESEARCH Populations: Within-Subject Design: All of the individuals who share a set of Controls for individual variations in a characteristics. measurement by comparing the scores of a Population data are called parameters. subject in one condition to the scores of the same subject in other conditions. Samples: So the subject serves as its own control. A subset of a population that are used to estimate population data. Sample data are Statistical Significance: called statistics. Refers to the low likelihood of the experimental findings being due to chance. Internal Validity: If the outcome of the research is that the DV Clinical Significance: has been affected as a result of Refers to the usefulness or importance of manipulating the IV. experimental findings to patient care or Any confounding variables have been patient outcomes. controlled for. External Validity: Refers to the ability of a study to be generalized to the population that it describes.  12.1 Measures of Central Tendency 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Measures of Central Tendency Mean: Provide a single value representation for the The average. middle of the data set. Median: The value that lies in the middle of the data set. Tends to be least susceptible to outliers, but may not be useful for data sets with large ranges. Mode: The data point that appears most often.  12.2 Distributions 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Normal Distribution: Symmetrical and the mean, median, and mode are equal. Standard Distribution: A normal distribution with a mean of 0 and a standard deviation of 1. It is used for most calculations. Skewed Distribution: Have differences in their mean, median, and mode. Skew direction is the direction of the tail. Bimodal Distribution: Multiple peaks, although not necessarily multiple modes.  12.3 Measures of Distribution 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Range: Standard Deviation (σ): Difference between largest and smallest value. A measurement of variability about the mean. Can be used to determine outliers. Interquartile Range: The difference between the value of the third quartile and first quartile. Can be used to Outliers: determine outliers. In general, any value that lies more than 3 standard deviations from the mean.  12.4 Probability 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Independent Events: The probability of independent events does not change based on the outcomes of other events. Dependent Events: The probability of a dependent event changes depending on the outcomes of other events. Terminology: Mutually Exclusive: Cannot occur simultaneously. When a set of outcomes is exhaustive, there are no other possible outcomes.  12.5 Statistical Testing 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Hypothesis Tests: p-value: Use a known distribution to determine whether Whether or not a finding is statistically the null hypothesis can be rejected. significant is determined by the comparison of a p-value to the selected significance level (a). A significance level of 0.05 is commonly used. Confidence Intervals: Are a range of values about a sample mean that are used to estimate the population mean. A wider interval is associated with a higher confidence level (95% is common).  12.6 Charts, Graphs and Tables 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Pie and Bar Charts: Histograms and Box Plots: Used to compare categorical data. Used to compare numerical data. Linear, Semilog, and Log-log Plots: Can be distinguished by the axes. Slope: Maps are used to compare up to two demographic indicators Tables may contain related or unrelated categorical data  12.7 Applying Data 30 Day MCAT CHAPTER 12-DATA BASED AND STATISTICAL REASONING Correlation and Causation Data are separate concepts that are linked by Hill’s must be interpreted in the context of the current criteria hypothesis and existing scientific knowledge Statistical significance Practical significance refers to whether the results observed in a study addresses whether the observed effect or are likely to have occurred by random chance difference is large enough to have practical alone. importance or real-world significance.