Read position, displacement and distance
Calculate displacement, distance, average velocity and average speed, and interpret graph slope without mistaking the graph for a track.
Physics and physical systems
Connect observations, diagrams and calculations to explain physical change.
This is the course outline. Open a unit to choose a lesson; every lesson opens on its own page. Explanations and experiments live inside those lesson pages.
Course scope and preparation
The 123 lessons use bounded physical investigations with saved predictions, captures, reflections and public practice. They introduce signed position, graph slopes, distance, displacement, constant-velocity reference frames, acceleration, direction reversal, free-body diagrams, Newton’s laws, friction, inclined forces, uniform circular motion, work, kinetic energy, gravitational energy conservation, elastic energy, ideal spring oscillation, dissipative energy accounting, momentum, impulse, two-object collisions, torque, static equilibrium, rotational inertia, work, power, angular momentum and energy during mass redistribution, rolling energy, no-slip friction conditions, hydrostatic pressure, pressure forces, buoyancy, floating equilibrium, flow continuity, ideal pressure-work accounting, viscous resistance, velocity profiles, regime screening, dissipation, temperature, heat capacity, thermal equilibrium, phase-change energy, steady conduction, series thermal resistance, radiation, surface convection balances, ideal-gas states, molecular motion, gas mixtures, pressure-volume work, the first law, isothermal work, reversible adiabatic change, complete gas cycles, thermal efficiency, reservoir entropy balances, the Carnot limit, refrigeration, heat-pump performance, full harmonic motion, mass-dependent oscillation periods, pendulum timing, small-angle approximation limits, a physical timing protocol with a labeled synthetic practice alternative, traveling-wave snapshots, point histories, wavelength-frequency relationships, linear superposition, standing-wave nodes, tension-dependent wave speed, fixed-end harmonics, longitudinal sound, pressure-displacement relationships open/closed air-column modes sound Doppler shifts from source and observer motion, reflection, refraction, total internal reflection, thin-lens images, a focal-length measurement protocol, two-slit interference, single-slit diffraction, Coulomb forces, electric fields, point-charge potential, current, resistance, series and parallel circuits, electrical power, and a circuit measurement and fault-diagnosis protocol, nonideal source voltage and power, source parameter estimation, capacitor geometry and energy under fixed-voltage and fixed-charge constraints, and RC charging, discharge and energy accounting, and a discharge measurement protocol with uncertainty and meter-loading analysis, magnetic force directions, magnetic power and conditional circular motion, current-produced fields and forces between parallel currents, magnetic flux, Faraday induction, Lenz direction reasoning, motional emf and magnetic braking energy balances, self-inductance, RL current transients and magnetic-energy accounting. The heating, calorimetry and gas investigations reuse the chemistry models with separate physics notebooks. Arithmetic and graph reading are sufficient; programming and calculus are not required for these lessons.
The authored foundation now includes modern photon, matter-wave and nuclear evidence. A model notebook does not establish physical measurement skills or mastery. The cumulative project preserves design predictions, model trials, a first report, critique, revision and changed-condition evidence; practical skills and independently reviewed reasoning remain separate gates.
Position, motion and reference frames
Describe motion from a moving observer
Transform positions and velocities between constant-velocity frames and identify which claims depend on the observer.
Connect acceleration, velocity and position
Calculate velocity and displacement under constant acceleration, interpret units and distinguish negative acceleration from slowing down.
Distinguish stopping from reversing
Compute a stopping instant and distance before reversal, distinguish distance from displacement across a turn, and reject an invalid braking extrapolation.
Explain acceleration at constant speed
Identify tangent velocity and inward acceleration, calculate period and angular rate, and distinguish a stationary point from a completed orbit.
Forces, systems and Newton’s laws
Draw forces on one selected object
Construct a force ledger, distinguish weight from mass and identify why balanced forces are not necessarily a third-law pair.
Predict acceleration from net force and mass
Use net force divided by mass, test proportional changes, and explain constant velocity when net force is zero.
Distinguish static and sliding friction
Use a static-friction bound, determine sliding-friction direction from relative motion, and identify when a motion prediction must change regimes.
Resolve forces on an incline
Resolve gravity into slope-aligned components, calculate normal force and acceleration, and explain mass cancellation under frictionless assumptions.
Identify the force that bends a path
Calculate inward force, distinguish fixed-speed from fixed-angular-rate comparisons, and predict tangent motion after ideal release.
Work, energy and conservation
Connect work to kinetic energy
Calculate constant-force work with signs, relate net work to the change in kinetic energy, and distinguish force-position area from force-time area.
Use energy to test a stopping target
Determine stopping displacement from negative work, distinguish reachable targets from invalid extrapolations, and recognize that energy alone does not identify velocity direction.
Choose a gravitational energy reference
Calculate gravitational potential-energy differences, explain an arbitrary zero reference, and distinguish negative potential energy from impossible negative kinetic energy.
Track mechanical energy during a descent
Use K+U conservation for a frictionless descent, reconcile gravitational work with potential-energy accounting, and identify conditions that require additional energy terms.
Store energy in an ideal spring
Use F = −kx and U = ½kx² with explicit units, explain the energy parabola, and distinguish force direction from stored energy.
Explain spring turning points and fastest motion
Predict speed, force and acceleration at equilibrium and turns, distinguish velocity branches, and compare stiffness effects on period.
Account for energy when friction acts
Distinguish mechanical energy from total energy, calculate internal-energy increase, and keep the block and track system boundary explicit.
Test a friction-limited stopping prediction
Calculate stopping distance and time, distinguish sliding friction from a persistent reverse force, and test how resistance and initial speed affect stopping.
Momentum, impulse and collisions
Connect impulse to signed momentum
Calculate signed momentum and impulse, predict final velocity, and explain why a negative momentum is compatible with positive kinetic energy.
Compare force pulses with the same impulse
Read signed force-time area, compare rectangular and triangular pulses, and explain what equal impulse does and does not determine.
Conserve momentum across a two-object collision
Calculate total signed momentum, relate individual momentum changes to internal impulses, and determine a common final velocity for a sticking collision.
Distinguish elastic and inelastic collisions
Classify collision outcomes using kinetic energy, interpret restitution as a relative-speed ratio, and explain why bouncing does not guarantee an elastic collision.
Torque, rotation and angular momentum
Connect torque to force and lever arm
Calculate signed torque for perpendicular forces, identify the perpendicular lever arm, and explain why a force through the pivot has zero torque about it.
Require both force and torque balance
Apply separate net-force and net-torque conditions, calculate pivot reaction, and identify when a proposed balance is impossible within the available lever arm.
Relate mass distribution to angular acceleration
Calculate point-mass rotational inertia, apply net torque = Iα, and connect angular motion in radians to tangential speed and acceleration.
Connect torque, rotational work and power
Calculate rotational kinetic energy and constant-torque work, interpret power = torque × angular velocity, and compare fixed-time versus fixed-angle claims.
Conserve angular momentum when radius changes
Calculate fixed-axis angular momentum, justify its conservation and infer final angular velocity from endpoint inertias.
Find the energy source during a change of radius
Account for mechanism work between zero-radial-speed endpoints and explain how zero torque can coexist with energy transfer.
Combine translation and rotation in rolling
Use the no-slip relation v=Rω, account for translation and rotation about the center, and predict speed from the inertia factor.
Check whether rolling without slipping is possible
Find the required static friction, compare it with μsN, and distinguish zero contact-point speed from zero friction or zero torque.
Pressure, buoyancy and fluid motion
Relate liquid pressure to depth and density
Use p=p_surface+ρgh with defined units and assumptions, and distinguish pressure from total force and density from total mass.
Calculate pressure force from both sides
Distinguish absolute and gauge pressure, convert pressure and area to force, and add opposing pressure forces with a consistent direction.
Derive buoyancy from displaced liquid
Calculate buoyancy using liquid density and submerged volume, distinguish it from object weight and predict the sign of the submerged force imbalance.
Predict floating fraction and neutral buoyancy
Find the submerged volume fraction of a floating rigid object, identify when equilibrium is impossible and distinguish a neutral depth from a unique stable position.
Conserve mass through a changing pipe area
Convert flow and area units, apply Q=Av and mass conservation, and distinguish fixed-flow comparisons from fixed-pressure experiments.
Account for pressure work in ideal flow
Apply a horizontal ideal-flow energy balance, distinguish gauge and absolute pressure, and verify that pressure work supplies the change in kinetic-energy flow.
Connect pipe geometry to viscous flow
Use Poiseuille resistance with consistent units, distinguish mean and center speed, and explain what is held fixed in a comparison.
Check flow regimes and dissipative pressure work
Calculate a pipe Reynolds number from mean speed and diameter, reject unsupported predictions, and account for pressure-work dissipation.
Temperature, heat and thermal systems
Distinguish temperature, heat and heat capacity
Convert Celsius temperatures and temperature differences to kelvin, distinguish heat from internal energy, and use heat capacity within one phase.
Find thermal equilibrium with an energy balance
Construct a signed energy balance, use heat-capacity weighting and explain why an endpoint calculation does not predict a cooling time.
Track energy through a phase change
Partition supplied energy between temperature change and latent heat, calculate phase fractions, and distinguish an energy axis from a time axis.
Distinguish heat-transfer rate from stored energy
Apply the slab conduction relation, distinguish watts from joules and heat flux, and identify the maintained boundary conditions.
Combine thermal resistances in series
Add series resistances, solve an interface temperature, and test how thickness and conductivity affect the whole assembly.
Separate emitted radiation from net heat transfer
Use absolute temperature in the Stefan–Boltzmann relation, interpret gray emissivity and explain radiative equilibrium.
Combine convection and radiation at a surface
Apply an assigned convection coefficient, combine parallel surface transfers and distinguish thermal holding power from device electricity or a cooling trajectory.
Relate ideal-gas pressure, volume and temperature
Apply PV = nRT with absolute pressure and kelvin temperature, compare constrained state changes and identify limits of the ideal model.
Connect molecular motion to gas pressure
Relate pressure to molecular momentum transfer, temperature to mean translational kinetic energy and RMS speed to temperature and molar mass.
Account for pressure in an ideal-gas mixture
Add partial pressures, use mole fractions correctly and handle pure-component and empty-vessel limits without dividing by zero.
Calculate gas work along different paths
Calculate constant-pressure boundary work, identify zero work at constant volume and explain path dependence using equal-scale diagrams.
Close the first-law energy account
Use ΔU = Q − W with explicit signs, compute a monatomic ideal-gas energy change and reconcile each leg and whole path.
Keep a gas at constant temperature while it does work
Explain why an isothermal ideal-gas expansion requires heat, calculate signed work using a volume ratio and identify the assumptions behind a pressure-volume area.
Cool an expanding gas without removing heat
Use an adiabatic energy balance, compare pressure and temperature endpoints and state when the constant-gamma path relation applies.
Return a gas to its starting state and obtain net work
Distinguish zero cyclic internal-energy change from nonzero heat and work, include compression work and reconcile a complete cycle.
Audit a heat engine’s efficiency
Compute thermal efficiency from total positive heat input, diagnose misleading denominators and distinguish work per cycle from power.
Check entropy as well as energy
Calculate reservoir entropy changes, distinguish a subsystem decrease from a total decrease and screen a cyclic engine with explicit boundaries.
Use reservoir temperatures to bound engine efficiency
Apply eta ≤ 1 − Tc/Th using kelvin, connect the equality case to reversible operation and reject unsupported claims of attainable power.
Move heat from cold to warm with work
Distinguish work input from work output, calculate delivered heat and diagnose cooling proposals that require too little work.
Compare cooling and heating performance
Calculate cooling and heating COP, derive reversible bounds and distinguish per-cycle ratios from capacity and seasonal performance.
Oscillations and waves
Read a complete oscillation in three motion graphs
Predict turning-point and equilibrium behavior, distinguish acceleration from velocity direction and explain phase relationships across a full cycle.
Predict how mass changes the period
Apply T = 2π√(m/k), relate frequency to period and explain which changes affect timing versus energy in the ideal spring model.
Connect pendulum length, gravity and period
Apply the small-angle period relation, explain mass cancellation and connect release height to speed without confusing angle with length.
Test where the small-angle approximation is useful
Quantify period underestimation, distinguish numerical from model error and explain why amplitude independence fails beyond the small-angle limit.
Measure pendulum periods and test a prediction
Define a full cycle, preserve raw timing data, estimate a period and explain uncertainty before judging agreement with a model.
Distinguish a wave snapshot from a point history
Track a material point separately from a moving crest and explain what each graph holds fixed.
Relate wavelength, frequency and wave speed
Apply speed = wavelength × frequency and distinguish pattern speed from transverse material velocity.
Add wave displacements and interpret cancellation
Apply linear superposition at the same position and time, distinguish displacement from velocity, and identify limits of the prescribed-wave model.
Locate standing-wave nodes and antinodes
Identify nodes through time, calculate their spacing, interpret an amplitude envelope and separate a prescribed standing pattern from a bounded resonance experiment.
Connect string tension and mass density to wave speed
Use wave speed = sqrt(tension / linear mass density), keep units consistent and explain the assumptions behind a tension comparison.
Build the harmonic series from fixed-end modes
Apply wavelength = 2L/n and frequency = n times the fundamental, while distinguishing mode shape from a driven response or a complete instrument sound.
Follow longitudinal motion in a sound wave
Identify sound as longitudinal bulk motion in this fluid model, interpret wavelength and period, and explain the displacement exaggeration.
Connect compression, displacement and sound pressure
Distinguish pressure perturbation from absolute pressure, relate compression to displacement gradient, and explain why pressure amplitude changes with frequency when displacement amplitude is held fixed.
Find pressure and displacement modes in an open tube
Identify open ends as pressure nodes and displacement antinodes, derive the open-open harmonic series and interpret normalized profiles.
Explain the odd harmonics of a closed-open tube
Derive quarter-wavelength boundary matching, identify odd harmonic frequencies and compare a closed-open column with an open-open column of the same length.
Explain how source motion changes wavefront spacing
Derive rightward wavefront spacing from source motion and predict frequency for a stationary observer.
Separate observer motion from source motion
Use signed velocities relative to air, distinguish encounters from spacing and test equal-closing-speed claims.
Light, rays and optical systems
Measure reflection angles from the normal
Draw a normal, convert surface angles to normal angles and predict a reflected direction.
Connect refraction to wave speed and wavelength
Apply Snell’s law and explain why frequency stays fixed while speed and wavelength change.
Find the threshold for total internal reflection
Find a critical angle and distinguish below-critical transmission, the critical limit and total internal reflection.
Locate real images with a converging lens
Use the thin-lens equation and ray intersections to locate an inverted real image.
Distinguish a virtual image from the focal-plane limit
Distinguish a virtual image from a parallel outgoing bundle and avoid assigning a finite image at focus.
Trace the upright virtual image of a diverging lens
Apply the sign convention to a diverging lens with a real object and interpret its ray extensions.
Estimate focal length from repeated image measurements
Estimate focal length from several real-image arrangements and distinguish repeatability, bounded uncertainty and systematic error.
Connect optical path difference to bright and dark fringes
Relate integer and half-integer path differences to interference and explain the model’s coherence assumptions.
Infer slit separation from a fringe pattern
Predict fringe spacing, invert the relationship and distinguish approximation error from measurement uncertainty.
Explain the broad central band from a single slit
Predict single-slit minima and central width while distinguishing width from two-slit separation.
Electric charge, fields and circuits
Predict attraction and repulsion between charges
Apply Coulomb’s law with units and distinguish third-law partners from net force on one object.
Separate electric field from force on a charge
Use F = qE, identify field direction by a positive test charge and explain nonzero field at zero probe charge.
Connect voltage, interaction energy and electric work
Calculate point-charge potential, pair energy and field work while keeping the reference and charge fixed.
Connect current, voltage and resistance
Calculate current and transported charge, distinguish current from voltage, and interpret current-versus-voltage slope.
Follow current and voltage through a series path
Calculate series equivalent resistance and voltage drops, and explain why current is equal throughout one steady path.
Account for current at a parallel junction
Calculate parallel equivalent resistance and branch currents and verify current conservation.
Audit electrical power and energy
Use P = VI and energy = Pt with consistent units and reconcile resistor powers with source output.
Measure a circuit and diagnose a mismatch
Use a documented measurement procedure, bounded uncertainty and an additional discriminating observation to evaluate a circuit model.
Explain voltage sag inside a source
Calculate a loaded source operating point and reconcile delivered and internally dissipated power.
Estimate a source model from measurements
Infer a linear source characteristic with correct units and evaluate its uncertainty and predictive limits.
Relate capacitor geometry to charge and voltage
Use consistent area and distance units in C = epsilon A/d and compare fixed-voltage with fixed-charge conditions.
Account for capacitor energy under different constraints
Choose the appropriate energy expression and include source work in a quasistatic geometry-change balance.
Predict how a capacitor charges through resistance
Calculate and interpret capacitor voltage and current at a selected fraction of the charging time constant.
Interpret capacitor discharge and threshold times
Use exponential decay to predict discharge, interpret current sign, and infer a time constant from a threshold reading.
Account for energy during charging and discharge
Check time-dependent energy balances and distinguish power, energy and asymptotic totals.
Measure a discharge time constant and test the model
Infer a discharge time constant and conditional capacitance, evaluate an unused reading, and design a discriminating measurement.
Magnetic forces and induction
Predict magnetic force direction and charge reversals
Predict magnetic-force components and explain the effects of reversing charge, velocity or field.
Explain magnetic turning without an energy gain
Calculate conditional circular radius and period and explain why magnetic power is zero.
Predict the magnetic field produced by a current
Predict long-wire field strength and direction and explain the limits of the thin infinite-wire approximation.
Explain attraction and repulsion between currents
Predict the direction and magnitude of parallel-wire forces and distinguish force per length from force on a finite segment.
Interpret magnetic flux and coil orientation
Calculate signed flux and linkage and explain zero-flux and zero-emf cases.
Predict induced voltage from flux change
Use Faraday’s law with units and distinguish flux value from its rate of change.
Use Lenz’s law with a clear viewing direction
Explain induced-current direction and the limits of the displayed energy account.
Generate an emf by changing loop area
Calculate motional emf and current with a consistent loop reference and distinguish closed and open circuits.
Balance magnetic braking with mechanical work
Calculate braking force and reconcile mechanical power and circuit heating within explicit assumptions.
Explain self-inductance and voltage reference signs
Interpret inductor voltage and current slope and explain why a closed decay path matters.
Predict resistor–inductor current transients
Calculate RL time constants, current fractions and voltage drops with explicit preparation.
Track inductor energy and sustained resistor heating
Verify separate RL energy balances and distinguish finite storage from unbounded long-time source work.
Modern evidence and limits of classical models
Calculate photon energy without confusing it with power
Convert wavelength to frequency and photon energy, then calculate photon rate from beam power.
Infer a spectral line from an energy-level difference
Use differences between stipulated levels to predict line energies and challenge identification from one line.
Test a photoelectric threshold
Use photon energy and a supplied work function to distinguish no emission from positive maximum kinetic energy.
Separate emitted-electron rate from stopping voltage
Compare a supplied quantum yield with photon rate while holding maximum electron energy fixed.
Compare matter wavelength with an observational scale
Calculate de Broglie wavelength from nonrelativistic kinetic energy and test when a wave description matters.
Conserve nucleon number and charge in nuclear change
Complete nuclear reaction equations while distinguishing necessary conservation from energetic possibility.
Predict an ensemble without assigning a lifetime to one nucleus
Use exponential survival and distinguish an expected ensemble count from a deterministic decay schedule.
Distinguish activity from remaining inventory and dose
Calculate activity from survivor number and half-life and explain why activity alone does not determine dose.
Account for rest mass and released energy
Convert a consistent initial-minus-final rest-mass difference into Q and preserve total energy conservation.
Compare fission and fusion without confusing balance with feasibility
Compare selected fusion and fission reaction ledgers and distinguish conservation, energy release and rate.
Projects, practice and evidence
Scientific inquiry and measurement provides optional preparation. All lessons can be opened directly.
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