Whizmath

Physics Lessons

Dive deep into the fundamental laws governing our universe. Explore concepts from beginner to advanced levels.

Beginner Level

Heat and Thermodynamics

Explore the fundamental concepts of heat, temperature scales (Celsius, Fahrenheit, Kelvin), and the basic principles of heat transfer: conduction, convection, and radiation. Understand the initial laws governing energy flow.

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Mechanics

An introduction to the study of motion. Learn about displacement, velocity, acceleration, and the three fundamental Laws of Motion proposed by Newton: $F=ma$. Covers one-dimensional kinematic equations like $v = u + at$ and $s = ut + \frac{1}{2}at^2$.

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Projectile Motion

Analyze the two-dimensional motion of objects solely under the influence of gravity ($g \approx 9.8 \text{ m/s}^2$). Understand concepts like parabolic trajectories, horizontal range, maximum height, and time of flight without air resistance.

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Momentum

Introduces the concept of linear momentum ($p = mv$) and impulse ($\Delta p = F\Delta t$). Learn the law of conservation of momentum for isolated systems and its application in simple collision scenarios, where total momentum $\sum p_{initial} = \sum p_{final}$.

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Work, Energy, & Power

Learn about different forms of energy (kinetic energy $KE = \frac{1}{2}mv^2$, gravitational potential energy $PE = mgh$), how work ($W = Fd \cos \theta$) is done by forces, and the rate at which work is done (power $P = W/t$). Covers the work-energy theorem and the principle of conservation of mechanical energy.

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Waves and Optics

Understand the fundamental characteristics of waves (amplitude, wavelength $\lambda$, frequency $f$, speed $v = f\lambda$). Explore the basic properties of light, including reflection (mirrors) and refraction (lenses), and Snell's Law ($n_1 \sin \theta_1 = n_2 \sin \theta_2$).

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Electricity

Introduction to electric charge ($q$), Coulomb's Law ($F = k \frac{|q_1 q_2|}{r^2}$), electric fields, and electric potential. Learn about current ($I = \Delta q / \Delta t$), voltage ($V$), resistance ($R$), and Ohm's Law ($V = IR$). Analyze simple series and parallel circuits.

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Sound

Explore the nature of sound as a longitudinal wave. Covers properties like pitch (frequency), loudness (amplitude), and quality (timbre). Discuss resonance and basic acoustics.

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Gravitation

Understand Newton's Law of Universal Gravitation ($F = G \frac{m_1 m_2}{r^2}$), which describes the attractive force between any two masses. Learn about gravitational fields, weight, and the basics of planetary motion.

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Atomic Structure

Basic models of the atom, including early historical models (Rutherford, Bohr). Learn about the constituents of an atom: electrons, protons, and neutrons, and their properties.

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States of Matter

Explore the macroscopic properties of solids, liquids, and gases, including their molecular arrangements, intermolecular forces, and phase transitions (melting, boiling, sublimation).

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Simple Harmonic Motion

Introduction to oscillatory motion characterized by a restoring force proportional to displacement ($F = -kx$). Study simple pendulums ($T = 2\pi\sqrt{L/g}$) and mass-spring systems ($T = 2\pi\sqrt{m/k}$), and define period and frequency.

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Units and Measurements

Master the International System of Units (SI), understand significant figures, scientific notation ($A \times 10^n$), and the importance of precision and accuracy in physical measurements. Covers basic error analysis.

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Scalars and Vectors

Learn to distinguish between quantities that have only magnitude (scalars like mass, time) and those with both magnitude and direction (vectors like force, velocity). Covers graphical and analytical methods for vector addition and subtraction ($\vec{A} + \vec{B}$).

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Pressure & Buoyancy

Understand the concept of pressure ($P=F/A$) in fluids, including atmospheric pressure and hydrostatic pressure ($P=\rho gh$). Explore Archimedes' Principle and the concept of buoyancy, explaining why objects float or sink.

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Elasticity of Materials

Introduction to how materials deform under stress ($\sigma = F/A$) and strain ($\epsilon = \Delta L / L_0$). Covers Hooke's Law ($F = kx$), Young's Modulus ($E = \sigma / \epsilon$), and basic concepts of elastic and plastic deformation for solids.

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Magnetism Basics

Discover the fundamental principles of magnetism, including magnetic poles, magnetic fields produced by permanent magnets, and the simple interaction between magnets.

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Light & Color

Explore the nature of light as an electromagnetic wave. Understand the visible spectrum, primary and secondary colors, and how objects absorb and reflect light to appear colored.

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Fluid Dynamics Basics

Introduction to the principles governing fluid flow. Covers the continuity equation ($A_1v_1 = A_2v_2$) for incompressible fluids and basic applications of Bernoulli's principle for steady flow.

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Thermal Properties of Matter

Examine how materials respond to heat, including concepts like specific heat capacity, thermal expansion (linear, area, volume), and thermal conductivity ($Q/t = kA\Delta T/L$).

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Electrical Power & Energy

Calculate electrical power ($P = IV = I^2R = V^2/R$) and energy consumed by electrical devices. Discuss kilowatt-hours and basic household electricity safety.

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Wave Superposition

Understand how two or more waves interact when they overlap, leading to phenomena like interference (constructive and destructive) and standing waves.

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Simple Machines

Discover the six classical simple machines: lever, wheel and axle, pulley, inclined plane, wedge, and screw. Understand their mechanical advantage ($MA = \text{output force}/\text{input force}$) and efficiency.

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Energy Transformations

Explore the conversion of energy from one form to another (e.g., potential to kinetic, chemical to electrical) and the law of conservation of energy in various systems.

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Circuits: Parallel & Series

Deepen your understanding of how resistors behave in series ($R_{eq} = \sum R_i$) and parallel ($\frac{1}{R_{eq}} = \sum \frac{1}{R_i}$) circuits. Analyze voltage, current, and power distribution in basic circuit configurations.

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Optics: Mirrors

Focus on the principles of reflection from plane mirrors, concave mirrors, and convex mirrors. Learn to construct ray diagrams and apply the mirror equation to find image characteristics (real/virtual, inverted/upright, magnified/diminished).

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Intermediate Level

Heat and Thermodynamics

A deeper dive into the First Law of Thermodynamics ($\Delta U = Q - W$), specific heat capacity, latent heat ($Q = mL$), and phase changes. Analyze pressure-volume diagrams and different thermodynamic processes (isothermal, adiabatic).

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Mechanics

Expands on Newton's Laws, including non-inertial frames and forces like friction and drag. Introduces rotational kinematics and dynamics, covering concepts like torque ($\tau = rF \sin \theta$), moment of inertia ($I$), and angular momentum ($L = I\omega$).

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Projectile Motion

Advanced analysis including the effects of air resistance on trajectory. Explore projectile motion on inclined planes and consider varying initial conditions for maximum range or height. Involves solving coupled differential equations.

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Momentum

Detailed study of elastic and inelastic collisions in one and two dimensions. Apply the conservation of momentum and energy principles to solve complex collision problems involving multiple objects. Understand the coefficient of restitution.

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Fluids

Explore static fluids (fluid pressure variation with depth, Pascal's principle) and dynamic fluids. Covers continuity equation ($A_1v_1 = A_2v_2$), Bernoulli's principle ($P + \rho gh + \frac{1}{2}\rho v^2 = \text{constant}$) for fluid flow, and an introduction to viscosity and surface tension.

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Magnetism

Detailed study of magnetic fields produced by currents (Biot-Savart Law, Ampere's Law $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$). Learn about the Lorentz force ($\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$) on moving charges and current-carrying wires in magnetic fields, and applications like motors.

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Circular Motion

Analyze uniform and non-uniform circular motion. Covers centripetal force ($F_c = mv^2/r$) and acceleration ($a_c = v^2/r$), angular velocity ($\omega$), and applications in real-world scenarios like banked curves and roller coasters.

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Electromagnetic Induction

Focuses on Faraday's Law of Induction ($\mathcal{E} = -N \frac{d\Phi_B}{dt}$), Lenz's Law, and motional EMF. Explores mutual and self-inductance ($L$) and their roles in electrical generators, transformers, and inductors.

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Ideal Gas Law

In-depth study of the Ideal Gas Law ($PV=nRT$) and its relationship to macroscopic properties like pressure, volume, and temperature. Discusses applications in various thermodynamic processes and introduces real gases.

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Kinetic Theory of Gases

Connects the microscopic behavior of gas particles to macroscopic properties. Derives the ideal gas law from molecular motion and discusses concepts like root-mean-square speed ($v_{rms} = \sqrt{3RT/M}$) and internal energy.

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Thermal Expansion

Quantify linear ($\Delta L = \alpha L_0 \Delta T$), area ($\Delta A = 2\alpha A_0 \Delta T$), and volume ($\Delta V = \beta V_0 \Delta T$) expansion of solids and liquids due to temperature changes. Understand applications in engineering and everyday phenomena.

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Optics

Deepen understanding of reflection and refraction through ray optics. Covers mirror and lens equations ($\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$), chromatic aberration, and introduces optical instruments like telescopes and microscopes.

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Electromagnetism

A unified study of electric and magnetic phenomena. Covers Maxwell's equations in their integral form, linking fundamental concepts of electric fields ($\vec{E}$), magnetic fields ($\vec{B}$), and electromagnetic waves ($c = 1/\sqrt{\mu_0 \epsilon_0}$).

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Wave Phenomena

Comprehensive study of interference (Young's double-slit experiment $d \sin \theta = m\lambda$), diffraction (single-slit, diffraction gratings), and polarization of light. Explore standing waves, beats, and the Doppler effect ($f' = f \frac{v \pm v_o}{v \mp v_s}$) for sound and light.

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Capacitance & Dielectrics

Detailed analysis of capacitors in series ($\frac{1}{C_{eq}} = \sum \frac{1}{C_i}$) and parallel ($C_{eq} = \sum C_i$). Understand how dielectric materials increase capacitance ($C = \kappa C_0$) and their role in energy storage ($U = \frac{1}{2}CV^2$). Explore RC circuits and time constants ($\tau = RC$).

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Nuclear Radiation

Study of different types of radioactive decay (alpha, beta, gamma), half-life calculations ($N = N_0 (1/2)^{t/T_{1/2}}$), and the biological effects of radiation. Introduces basic principles of nuclear stability and binding energy.

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DC Circuits Analysis

Advanced techniques for analyzing direct current circuits, including Kirchhoff's laws (junction rule $\sum I_{in} = \sum I_{out}$, loop rule $\sum \Delta V = 0$), node voltage method, mesh current method, and superposition theorem for complex networks.

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Sound Intensity & Decibels

Quantify sound intensity ($I = P/A$) and learn about the decibel scale ($\beta = 10 \log_{10}(I/I_0)$). Covers the inverse square law for sound propagation and explores concepts like resonance and standing waves in pipes and strings.

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Astrophysics Basics

An introductory overview of the cosmos, including the life cycles of stars, types of galaxies, and the large-scale structure of the universe. Touches on telescopes and astronomical observation methods, including luminosity ($L = 4\pi R^2 \sigma T^4$) and apparent brightness ($b = L / (4\pi d^2)$).

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Magnetic Force & Fields

Further delve into magnetic fields generated by current loops and solenoids ($\mu_0 n I$). Explore the magnetic force on current-carrying conductors ($F = ILB \sin \theta$) and torque on current loops in magnetic fields ($\tau = NIAB \sin \phi$).

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Resonance & Damping

Study the phenomenon of resonance in oscillating systems, where a driving force matches the natural frequency. Analyze the effects of damping on oscillations and their practical implications.

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Introduction to Modern Physics

A bridge to advanced topics, introducing the limitations of classical physics. Covers blackbody radiation, the ultraviolet catastrophe, and the beginnings of quantum theory and relativity.

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AC Circuits Basics

Introduction to alternating current (AC) circuits, including concepts of AC voltage and current, reactance of inductors ($X_L = \omega L$) and capacitors ($X_C = 1/\omega C$), and simple RL, RC, and RLC series circuits.

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Wave-Particle Duality

Explore the concept that particles can exhibit wave-like properties (e.g., de Broglie wavelength $\lambda = h/p$) and waves can exhibit particle-like properties (photons), a foundational idea in quantum mechanics.

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Electromagnetic Spectrum

Categorize and understand the various forms of electromagnetic radiation (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays) based on their wavelength and frequency.

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Heat Engines & Refrigerators

Analyze the operation of heat engines (e.g., Stirling engine, Otto cycle) and refrigerators/heat pumps. Understand their efficiency (Carnot efficiency $\eta = 1 - T_C/T_H$) and the limitations imposed by the Second Law of Thermodynamics.

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Fluid Viscosity & Flow

Detailed study of fluid viscosity, internal friction within fluids, and its effect on fluid flow. Covers Poiseuille's Law for laminar flow and introduces concepts of turbulent flow and Reynolds number.

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Nuclear Fission & Fusion

Explore the processes of nuclear fission (splitting atoms) and nuclear fusion (combining atoms). Understand their applications in nuclear power generation, weapons, and stellar energy production ($E=mc^2$).

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Acoustics & Musical Instruments

Apply principles of sound waves to understand the physics of musical instruments. Covers topics like harmonics, overtones, resonance in strings and air columns, and the production of musical notes.

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Advanced Level

Heat and Thermodynamics

Explore the Second Law of Thermodynamics (entropy $\Delta S \ge 0$), Gibbs free energy ($G = H - TS$), and Carnot engines. Delve into statistical mechanics, connecting macroscopic properties to microscopic states using Boltzmann distribution ($P(E) \propto e^{-E/k_B T}$).

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Mechanics

Advanced classical mechanics using Lagrangian ($\mathcal{L} = T - V$) and Hamiltonian ($\mathcal{H} = T + V$) formulations. Study rigid body dynamics, coupled oscillations, and an introduction to continuum mechanics and elasticity theory.

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Projectile Motion

Examine projectile motion in more complex scenarios, including non-uniform gravitational fields and advanced air resistance models. Introduces orbital mechanics (Kepler's Laws) and the physics of spacecraft trajectories using conic sections.

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Momentum

Advanced treatment of momentum, including relativistic momentum ($\vec{p} = \gamma m \vec{v}$) and energy ($E = \sqrt{(pc)^2 + (m_0 c^2)^2}$), and momentum in continuous systems (e.g., rocket propulsion, fluid flow). Explores advanced collision theory and scattering processes.

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Nuclear Physics

In-depth study of nuclear structure, forces (strong nuclear force), and models (liquid drop, shell model). Covers radioactive decay rates, nuclear reactions (fission, fusion $E=mc^2$), and provides an introduction to particle accelerators and detectors.

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Quantum Mechanics

Deep dive into the Schrödinger equation (time-dependent $i\hbar \frac{\partial}{\partial t}\Psi = \hat{H}\Psi$, time-independent $\hat{H}\Psi = E\Psi$), wave functions, and operators. Explore quantum phenomena like tunneling, quantum entanglement, and the basics of quantum field theory and quantum computing.

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Relativity

Comprehensive study of Special Relativity (Lorentz transformations, time dilation $\Delta t' = \gamma \Delta t$, length contraction $L' = L/\gamma$, mass-energy equivalence $E=mc^2$) and an introduction to General Relativity (spacetime curvature, gravitational waves, black holes).

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Astrophysics

Advanced topics in stellar structure and evolution (H-R diagram), cosmology (Big Bang theory, cosmic microwave background, dark energy), and phenomena like supernovae, neutron stars, and active galactic nuclei.

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Electrodynamics

Rigorous treatment of Maxwell's equations in differential form ($\nabla \cdot \vec{E} = \rho/\epsilon_0$, $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$, etc.), electromagnetic wave propagation in various media, Poynting vector ($\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})$), and the principles of classical field theory.

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Solid State Physics

Study of crystal structures, lattice vibrations (phonons), band theory of solids (conductors, insulators, semiconductors), and phenomena like superconductivity and magnetism in materials.

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Photonics

Advanced topics in laser physics (types of lasers, applications), optical fibers, waveguides, and the interaction of light with matter at a quantum level, including non-linear optics.

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Plasma Physics

Study of the fourth state of matter – ionized gas. Covers plasma properties, magnetic confinement (tokamaks), inertial confinement, and its applications in fusion energy and astrophysical phenomena.

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Statistical Mechanics

Bridge between microscopic and macroscopic physics. Explores ensembles (microcanonical, canonical, grand canonical), partition functions ($Z$), and their use in deriving thermodynamic properties from molecular behavior.

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Cosmology

Detailed study of the origin, evolution, and large-scale structure of the universe, including inflation theory, dark matter, dark energy ($\Lambda$), and the fate of the cosmos based on current observational data.

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General Relativity Applications

Explore the real-world implications and phenomena predicted by General Relativity, such as gravitational lensing, gravitational redshift, the physics of black holes (Schwarzschild radius $R_s = 2GM/c^2$), and neutron stars.

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Particle Physics

Delve into the Standard Model of particle physics: quarks, leptons, and fundamental forces. Discuss symmetry, conservation laws, Higgs boson, and introduce concepts beyond the Standard Model like supersymmetry.

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Quantum Field Theory (QFT)

An advanced framework unifying quantum mechanics with special relativity. Covers concepts like quantum fields, Feynman diagrams, renormalization, and their role in understanding particle interactions and fundamental forces.

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Astroparticle Physics

The intersection of particle physics and cosmology. Investigates cosmic rays, neutrinos from space, dark matter and dark energy detection experiments, and the early universe's particle content.

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Computational Physics

Learn numerical methods to solve complex physics problems, including finite difference, Monte Carlo simulations of physical systems, data analysis techniques, and the use of computational tools in research and engineering.

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Quantum Optics

Study the quantum nature of light and its interaction with matter. Covers concepts like photon statistics, quantum entanglement in optical systems, and applications in quantum communication and quantum cryptography.

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Condensed Matter Physics

Advanced study of the macroscopic and microscopic physical properties of matter, including crystal defects, electronic band structure, and exotic states like topological insulators and quantum Hall effect.

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Non-linear Dynamics & Chaos

Explore systems whose behavior is not directly proportional to their causes. Covers concepts like phase space, fractals, strange attractors, and the unpredictable nature of chaotic systems in physics.

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Cryogenics & Low Temperature Physics

Investigate physics at extremely low temperatures, including phenomena like superconductivity, superfluidity (Bose-Einstein condensates), and the techniques used to achieve and maintain cryogenic environments.

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Medical Physics

Application of physics principles to medicine, covering diagnostic imaging (X-rays, MRI, ultrasound), radiation therapy, nuclear medicine, and the physics of the human body.

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Acoustic Physics

Advanced study of sound and vibrations, including wave propagation in different media, psychoacoustics (perception of sound), architectural acoustics, and noise control.

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Nanophysics

Exploration of physical phenomena at the nanoscale ($10^{-9}$ meters). Covers quantum effects in nanomaterials, fabrication techniques, and applications in electronics, medicine, and energy.

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Gauge Theory

Introduces the concept of gauge invariance as a principle for constructing fundamental interactions in physics, central to the Standard Model of particle physics.

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Supersymmetry (SUSY)

Explores a proposed extension to the Standard Model, postulating a symmetry between bosons and fermions. Discusses its implications for dark matter and grand unification theories.

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String Theory Basics

An introduction to string theory, a theoretical framework that posits point-like particles are replaced by one-dimensional strings. Discusses its potential to unify all fundamental forces.

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