MCAT Physics and Math Review

This guide provides a comprehensive review for the MCAT physics and math sections, offering key concepts, definitions, and calculations essential for understanding and scoring well.

Introduction to Vectors and Scalars

• Vectors: Quantities with magnitude and direction (e.g., velocity, acceleration, force).
• Scalars: Quantities with only magnitude (e.g., speed, coefficient of friction).
• Vector Addition: Combine vectors by adding head-to-tail.
• Vector Subtraction: Reverse the vector being subtracted and then add.
• Dot Product: Results in a scalar; calculated as ( \vec{A} \cdot \vec{B} = |A| |B| \cos \theta ).
• Cross Product: Results in a vector; calculated as ( \vec{A} \times \vec{B} = |A| |B| \sin \theta ) and uses the right-hand rule for direction.

Mechanical Equilibrium and Free Body Diagrams

• Translational Equilibrium: No net force; no acceleration, might be at rest or constant speed.
• Rotational Equilibrium: No net torque; object is not accelerating rotationally.

Motion

• Displacement: Change in position, path-independent.
• Velocity: Change in displacement over time.
• Instantaneous Velocity: Velocity at a specific instant.
• Force and Acceleration: Force results in acceleration if not zero.
• Newton’s Laws:
  1. An object at rest stays at rest/constant velocity if no net force is applied.
  2. ( F = ma ) (net force = mass × acceleration).
  3. For every action, there is an equal and opposite reaction.
• Motion Equations: Essential for calculating projectile motion and other dynamics.

Energy

• Kinetic Energy (KE): ( KE = \frac{1}{2} mv^2 ).
• Potential Energy (PE): Gravitational (( mgh )), Elastic.
• Conservation of Energy: Total energy (kinetic + potential) in a closed system remains constant.
• Work and Power:
  • Work: ( W = Fd \cos \theta ).
  • Power: Rate of doing work, ( P = \frac{W}{t} ).

Thermodynamics

• Laws:
  • Zeroth: Thermal equilibrium implies same temperature.
  • First: Energy conservation in systems.
  • Second: Entropy of any isolated system always increases.
• Processes:
  • Isothermal, adiabatic, isobaric, isochoric processes based on constant variable during the process.

Fluids

• Characteristics:
  • Density ( \rho = \frac{m}{V} ).
  • Pressure ( P = \frac{F}{A} ).
• Pascal’s Principle: Pressure applied to an enclosed fluid is transmitted undiminished.
• Archimedes’ Principle: Buoyant force is equal to the weight of the displaced fluid.
• Continuity Equation: ( A_1v_1 = A_2v_2 ) for incompressible fluids.
• Bernoulli’s Equation: Relates pressure, velocity, and height in a moving fluid.

Waves and Sound

• Wave Properties:
  • Transverse (light) vs Longitudinal (sound) waves.
  • Frequency, wavelength, speed relationship: ( v = f\lambda ).
• Sound: Travels fastest in solids, slowest in gases.
• Doppler Effect: Change in frequency or wavelength due to relative motion.

Electrostatics and Magnetism

• Electric Charge and Field:
  • Coulomb's Law: Force between two charges.
  • Electric Field: ( E = \frac{F}{q} ).
• Potential Energy and Voltage:
  • Voltage ( V = \frac{W}{q} ).
  • Capacitors store energy as electric field.
• Magnetism:
  • Moving charges create magnetic fields.
  • Right-hand rule for direction of magnetic force.

Circuits

• Ohm’s Law: ( V = IR ).
• Series and Parallel Circuits:
  • Series: Resistances add up.
  • Parallel: Inverses of resistances add up.
• Capacitors: Store electrical energy, different rules for series and parallel combinations.

Light and Optics

• Reflection: Angle of incidence equals angle of reflection.
• Refraction: Bending of light as it passes between media, governed by Snell's law.
• Mirrors and Lenses: Forms images based on focal point and curvature.

Modern Physics

• Photoelectric Effect: Light can eject electrons from metal surfaces.
• Bohr's Model: Electrons exist in quantized orbits.
• Nuclear Physics:
  • Fusion and Fission: Processes that release energy.
  • Radioactive Decay: Types include alpha, beta, gamma decay.

Mathematical Concepts

• Scientific Notation and Significant Figures.
• Trigonometry and Logarithms.
• Probability and Statistics:
  • Distributions (normal, skewed).
  • Statistical Significance and Hypothesis Testing.

Research Methods

• Scientific Method.
• Ethics in Research: Importance of confidentiality, informed consent.
• Study Designs: Cohort, case-control, cross-sectional.

Ensure you are comfortable with these concepts, as they form the foundation for solving physics and math problems on the MCAT. Practice problems and apply concepts to reinforce your understanding.