See the connections. Build the understanding.

Unit conversion

Use units as part of the calculation, including powers, rates and experimental scales.

3 practice problems

Significant figures

What the digits in a measurement are allowed to claim

1 practice problem

Vector components

Turn directions into equations without losing the geometry

7 practice problems

Cross product

Build the geometry, signs and component method behind torque and magnetic force.

1 practice problem

Measurement uncertainty

What a reading tells you—and what it leaves unresolved

7 practice problems

Absolute and relative error

What a reading tells you—and what it leaves unresolved

1 practice problem

Error propagation

Follow the measurement model before choosing a formula

7 practice problems

Vernier calipers

Derive the fine reading from two scales, correct the zero, and judge what the instrument can actually establish.

1 practice problem

Micrometer screw gauge

Turn rotation into length, then turn a reading into a defensible measurement.

4 practice problems

Experimental graphs

Read slopes, intercepts and uncertainty as physical information rather than as a line-drawing exercise.

6 practice problems

Young modulus experiment

Separate material stiffness from specimen geometry, then infer a modulus from a controlled extension experiment.

1 practice problem

Resonance tube experiment

Use boundary conditions to find nodes, harmonics and the information hidden in resonance spacings.

1 practice problem

Focal length experiment

Trace the intermediate image, define the viewing condition and connect optical models to a bench experiment.

1 practice problem

Post office box experiment

Design a shunt or multiplier, quantify loading and infer an unknown resistance from a reproducible null.

1 practice problem

Derivatives as physical rates

Connect tangents, areas and initial conditions so that derivatives and integrals describe real changes.

3 practice problems

Integrals and accumulated change

Connect tangents, areas and initial conditions so that derivatives and integrals describe real changes.

2 practice problems

Exponential change and logarithms

Recognise fractional change, solve for time and decide when a small-angle model is accurate enough.

7 practice problems

Small-angle approximations

Recognise fractional change, solve for time and decide when a small-angle model is accurate enough.

2 practice problems

Motion & forces

10 concepts

Velocity and acceleration

Read motion as changing position—and changing velocity

5 practice problems

Constant acceleration

Derive the equations, choose an interval, and know when a calculated answer stops describing the motion.

7 practice problems

Projectile motion

Use one clock for both axes, then simplify encounters by comparing relative positions and velocities.

6 practice problems

Relative motion

Use one clock for both axes, then simplify encounters by comparing relative positions and velocities.

5 practice problems

Newton laws

Learn to choose a body, draw its forces, and explain a change of motion before calculating it.

1 practice problem

Connected bodies

Build force equations from the system, the contact state and the geometry of each connection.

3 practice problems

Static friction

Replace “friction equals μN” with a method that tests whether surfaces can remain at rest relative to each other.

3 practice problems

Kinetic friction

Build force equations from the system, the contact state and the geometry of each connection.

4 practice problems

Circular force balance

Derive inward acceleration, resolve real forces and test the limits of circular motion.

4 practice problems

Uniformly accelerated reference frames

Build force equations from the system, the contact state and the geometry of each connection.

1 practice problem

Energy & momentum

9 concepts

Work-energy theorem

Choose a system, account for each transfer and read possible motion from an energy balance.

2 practice problems

Elastic potential energy

Choose a system, account for each transfer and read possible motion from an energy balance.

6 practice problems

Power

Choose a system, account for each transfer and read possible motion from an energy balance.

4 practice problems

Potential-energy diagrams

Choose a system, account for each transfer and read possible motion from an energy balance.

1 practice problem

Mechanical energy conservation

Choose a system, account for each transfer and read possible motion from an energy balance.

6 practice problems

Motion of the center of mass

Choose the system and interval, then connect momentum exchange to centre-of-mass motion and impact outcomes.

1 practice problem

Impulse

Choose the system and interval, then connect momentum exchange to centre-of-mass motion and impact outcomes.

1 practice problem

Momentum conservation

Choose the system and interval, then connect momentum exchange to centre-of-mass motion and impact outcomes.

6 practice problems

Two-dimensional collisions

Choose the system and interval, then connect momentum exchange to centre-of-mass motion and impact outcomes.

1 practice problem

Rotation & gravitation

17 concepts

Moment of inertia

Derive the axis-dependent quantities that connect turning forces to angular motion.

5 practice problems

Parallel-axis theorem

Derive the axis-dependent quantities that connect turning forces to angular motion.

4 practice problems

Torque

Derive the axis-dependent quantities that connect turning forces to angular motion.

7 practice problems

Rotational dynamics

Derive the axis-dependent quantities that connect turning forces to angular motion.

6 practice problems

Rolling without slipping

Connect the contact constraint to rotation, then choose when angular momentum is the conserved quantity.

4 practice problems

Rolling energy

Connect the contact constraint to rotation, then choose when angular momentum is the conserved quantity.

2 practice problems

Angular momentum

Connect the contact constraint to rotation, then choose when angular momentum is the conserved quantity.

3 practice problems

Angular momentum conservation

Connect the contact constraint to rotation, then choose when angular momentum is the conserved quantity.

2 practice problems

Static equilibrium

Derive the axis-dependent quantities that connect turning forces to angular motion.

4 practice problems

Gravitational superposition

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

1 practice problem

Gravity inside a sphere

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

1 practice problem

Escape speed

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

1 practice problem

Kepler laws

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

3 practice problems

Circular satellites

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

3 practice problems

Perpendicular-axis theorem

Derive the axis-dependent quantities that connect turning forces to angular motion.

1 practice problem

Radius of gyration

Derive the axis-dependent quantities that connect turning forces to angular motion.

1 practice problem

Geostationary and synchronous orbits

Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.

1 practice problem

Matter & fluids

12 concepts

Stress and strain

Separate material stiffness from specimen geometry, then infer a modulus from a controlled extension experiment.

5 practice problems

Hydrostatic pressure

Derive pressure from equilibrium, then use it to explain buoyancy and support readings.

4 practice problems

Buoyancy

Derive pressure from equilibrium, then use it to explain buoyancy and support readings.

2 practice problems

Floating equilibrium

Derive pressure from equilibrium, then use it to explain buoyancy and support readings.

7 practice problems

Continuity equation

Track mass first, then connect pressure, speed and height along a valid flow model.

2 practice problems

Bernoulli equation

Track mass first, then connect pressure, speed and height along a valid flow model.

3 practice problems

Viscosity

Derive the velocity profile, track pressure losses and test what a change in radius really means.

7 practice problems

Stokes law

Choose the drag model, balance forces and test the Reynolds number before trusting a speed.

1 practice problem

Surface tension

Count interfaces and connect boundary forces, surface work, pressure jumps and wetting.

3 practice problems

Capillarity

Read the meniscus, count the interfaces and connect pressure, height and surface energy.

4 practice problems

Excess pressure in drops and bubbles

Read the meniscus, count the interfaces and connect pressure, height and surface energy.

4 practice problems

Critical speed and flow regimes

Choose the drag model, balance forces and test the Reynolds number before trusting a speed.

1 practice problem

Oscillations & waves

16 concepts

Simple harmonic motion

Build spring and pendulum models from equilibrium, then connect their motion to energy and initial conditions.

5 practice problems

Spring-mass oscillators

Build spring and pendulum models from equilibrium, then connect their motion to energy and initial conditions.

2 practice problems

Physical pendulum

Build spring and pendulum models from equilibrium, then connect their motion to energy and initial conditions.

1 practice problem

Damped oscillations

Follow the energy, impose the initial conditions, and say which response is being measured.

2 practice problems

Forced oscillations and resonance

Follow the energy, impose the initial conditions, and say which response is being measured.

1 practice problem

Wave description

Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.

2 practice problems

Wave phase

Predict what a detector reads by connecting path, phase and field addition.

3 practice problems

Wave power and intensity

Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.

1 practice problem

Wave superposition

Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.

1 practice problem

Standing waves

Use boundary conditions to find nodes, harmonics and the information hidden in resonance spacings.

1 practice problem

Sound speed

Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.

1 practice problem

Longitudinal waves

Read a wave equation, distinguish particle motion from propagation and connect phase to energy transport.

1 practice problem

Sound intensity and decibels

Count arriving wavefronts, track a changing phase difference and use decibels as logarithmic ratios.

1 practice problem

Open and closed pipes

Use boundary conditions to find nodes, harmonics and the information hidden in resonance spacings.

2 practice problems

Beats

Count arriving wavefronts, track a changing phase difference and use decibels as logarithmic ratios.

1 practice problem

Doppler effect

Count arriving wavefronts, track a changing phase difference and use decibels as logarithmic ratios.

1 practice problem

Thermal physics

32 concepts

Thermal equilibrium

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

1 practice problem

Temperature scales

Use units as part of the calculation, including powers, rates and experimental scales.

1 practice problem

Thermal expansion

Follow what can move, what the ruler measures and when heating produces stress.

7 practice problems

Heat capacity

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

2 practice problems

Calorimetry

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

7 practice problems

Latent heat

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

5 practice problems

Phase changes

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

4 practice problems

First law of thermodynamics

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

5 practice problems

Pressure-volume work

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

5 practice problems

Isochoric processes

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

3 practice problems

Isobaric processes

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

1 practice problem

Cyclic processes

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

2 practice problems

Conduction

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

3 practice problems

Convection

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

1 practice problem

Thermal radiation

Separate emission from net exchange, count the relevant areas and connect temperature to a broad spectrum.

3 practice problems

Ideal gas equation

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

3 practice problems

Molecular rms speed

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

2 practice problems

Kinetic interpretation of pressure

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

1 practice problem

Molecular speed distribution

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

1 practice problem

Gas heat capacities

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

6 practice problems

Equipartition

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

4 practice problems

Adiabatic processes

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

3 practice problems

Isothermal processes

Use energy conservation with an explicit system and sign convention, then audit every leg of a gas cycle.

3 practice problems

Entropy

Use energy and entropy as separate checks on a complete thermal cycle.

1 practice problem

Second law

Use energy and entropy as separate checks on a complete thermal cycle.

2 practice problems

Heat engines

Use energy and entropy as separate checks on a complete thermal cycle.

2 practice problems

Carnot efficiency

Use energy and entropy as separate checks on a complete thermal cycle.

2 practice problems

Refrigerators

Use energy and entropy as separate checks on a complete thermal cycle.

1 practice problem

Newton’s law of cooling

Track energy through mixing and phase changes, then distinguish steady heat flow from a changing temperature.

2 practice problems

Wien’s displacement law

Separate emission from net exchange, count the relevant areas and connect temperature to a broad spectrum.

2 practice problems

Stefan–Boltzmann law

Separate emission from net exchange, count the relevant areas and connect temperature to a broad spectrum.

2 practice problems

Molecular mean free path

Connect pressure and temperature to particle motion, then distinguish collision distance from collision time.

1 practice problem

Electricity & circuits

25 concepts

Coulomb law

Use vectors, integration and symmetry to choose the right method for an electrostatic field.

2 practice problems

Charge conservation

Read the connections, solve a shared voltage and audit the energy.

1 practice problem

Electric field

Use vectors, integration and symmetry to choose the right method for an electrostatic field.

3 practice problems

Fields of continuous charge distributions

Use vectors, integration and symmetry to choose the right method for an electrostatic field.

1 practice problem

Dipole torque and energy

Connect energy to field gradients, then track charge, voltage and mechanical constraints in electrostatic systems.

1 practice problem

Gauss law

Use vectors, integration and symmetry to choose the right method for an electrostatic field.

3 practice problems

Electrostatic conductors

Read a voltage map, track signed work and choose between fields and energy.

1 practice problem

Electric potential

Read a voltage map, track signed work and choose between fields and energy.

9 practice problems

Equipotential surfaces

Read a voltage map, track signed work and choose between fields and energy.

2 practice problems

Potential difference

Read a voltage map, track signed work and choose between fields and energy.

1 practice problem

Electric field from potential

Connect energy to field gradients, then track charge, voltage and mechanical constraints in electrostatic systems.

1 practice problem

Electrostatic potential energy

Read a voltage map, track signed work and choose between fields and energy.

4 practice problems

Capacitance

Connect energy to field gradients, then track charge, voltage and mechanical constraints in electrostatic systems.

5 practice problems

Capacitors in series and parallel

Connect energy to field gradients, then track charge, voltage and mechanical constraints in electrostatic systems.

2 practice problems

Drift velocity

Connect microscopic drift to wire geometry, circuit topology and temperature-dependent power.

1 practice problem

Resistance and resistivity

Connect microscopic drift to wire geometry, circuit topology and temperature-dependent power.

2 practice problems

Temperature dependence of resistance

Connect microscopic drift to wire geometry, circuit topology and temperature-dependent power.

1 practice problem

Ohm law

Read the connections, solve a shared voltage and audit the energy.

6 practice problems

Electrical power

Read the connections, solve a shared voltage and audit the energy.

6 practice problems

EMF and internal resistance

Distinguish emf from terminal voltage, infer source models and track energy in both directions.

9 practice problems

Resistors in series and parallel

Connect microscopic drift to wire geometry, circuit topology and temperature-dependent power.

2 practice problems

Kirchhoff laws

Read the connections, solve a shared voltage and audit the energy.

10 practice problems

RC transients

Derive the exponential response and carry capacitor voltage correctly through a sequence of circuit changes.

4 practice problems

Galvanometer conversion and sensitivity

Design a shunt or multiplier, quantify loading and infer an unknown resistance from a reproducible null.

1 practice problem

Galvanometer half-deflection experiment

Use a controlled current split to measure coil resistance and current per scale division.

3 practice problems

Magnetism & induction

27 concepts

Magnetic force on a charge

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

5 practice problems

Lorentz force

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

2 practice problems

Crossed fields

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

3 practice problems

Velocity selector

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

2 practice problems

Charged-particle circular motion

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

5 practice problems

Magnetic dipole moment

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

2 practice problems

Biot-Savart law

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

3 practice problems

Field of a current loop

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

2 practice problems

Magnetic flux

Follow the changing flux, establish the sign, and close the energy account.

4 practice problems

Faraday law

Follow the changing flux, establish the sign, and close the energy account.

3 practice problems

Lenz law

Follow the changing flux, establish the sign, and close the energy account.

3 practice problems

Motional EMF

Follow the changing flux, establish the sign, and close the energy account.

2 practice problems

Induced electric fields

Follow the changing flux, establish the sign, and close the energy account.

2 practice problems

Self-inductance

Follow the changing flux, establish the sign, and close the energy account.

2 practice problems

Mutual inductance

Track shared flux, winding polarity, stored energy and the load seen by the source.

2 practice problems

Inductor energy

Follow the changing flux, establish the sign, and close the energy account.

3 practice problems

LC oscillations

Connect charge, current, phase and loss without confusing three different frequencies.

1 practice problem

RMS quantities

Build the circuit response from derivatives, then use phasors and energy to check it.

1 practice problem

Reactance

Build the circuit response from derivatives, then use phasors and energy to check it.

2 practice problems

RLC circuits

Connect charge, current, phase and loss without confusing three different frequencies.

2 practice problems

Electrical resonance

Connect charge, current, phase and loss without confusing three different frequencies.

2 practice problems

AC power and power factor

Build the circuit response from derivatives, then use phasors and energy to check it.

1 practice problem

Transformers

Track shared flux, winding polarity, stored energy and the load seen by the source.

2 practice problems

Displacement current

Resolve the capacitor-gap puzzle, derive the wave speed and follow energy through the fields.

1 practice problem

Magnetic materials

Connect microscopic alignment to measurable fields, sample geometry and energy loss.

2 practice problems

Eddy currents

Follow the changing flux, establish the sign, and close the energy account.

1 practice problem

Magnetic field of a dipole

Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.

2 practice problems

Optics

21 concepts

Electromagnetic wave speed

Resolve the capacitor-gap puzzle, derive the wave speed and follow energy through the fields.

2 practice problems

Malus law

Project the electric field, keep an intensity ledger and identify the plane of incidence.

2 practice problems

Snell law

Draw the normal, trace each boundary and let the geometry decide which formula applies.

5 practice problems

Total internal reflection

Draw the normal, trace each boundary and let the geometry decide which formula applies.

1 practice problem

Spherical mirrors

Keep the incident-light axis fixed and use reflection geometry to check every image.

2 practice problems

Refraction at a spherical surface

Use one sign convention, construct the rays and carry intermediate images through the system.

1 practice problem

Thin lenses

Use one sign convention, construct the rays and carry intermediate images through the system.

2 practice problems

Lens power

Use one sign convention, construct the rays and carry intermediate images through the system.

2 practice problems

Microscopes

Trace the intermediate image, define the viewing condition and connect optical models to a bench experiment.

1 practice problem

Telescopes

Trace the intermediate image, define the viewing condition and connect optical models to a bench experiment.

1 practice problem

Young double-slit experiment

Turn path differences into phase, add fields and keep slit width distinct from slit separation.

3 practice problems

Path difference

Predict what a detector reads by connecting path, phase and field addition.

2 practice problems

Coherence

Predict what a detector reads by connecting path, phase and field addition.

1 practice problem

Interference intensity

Predict what a detector reads by connecting path, phase and field addition.

7 practice problems

Thin-film interference

Build a phase ledger, then use it for coatings, wedges and curved gaps.

6 practice problems

Single-slit diffraction

Turn path differences into phase, add fields and keep slit width distinct from slit separation.

3 practice problems

Optical resolution

Separate where a peak appears from how narrowly it can distinguish two signals.

4 practice problems

Diffraction gratings

Separate where a peak appears from how narrowly it can distinguish two signals.

4 practice problems

Dispersion of light

Draw the normal, trace each boundary and let the geometry decide which formula applies.

1 practice problem

Brewster’s law

Project the electric field, keep an intensity ledger and identify the plane of incidence.

1 practice problem

Lens maker’s formula

Use one sign convention, construct the rays and carry intermediate images through the system.

1 practice problem

Atomic & nuclear physics

20 concepts

Photon energy and momentum

Separate energy per event from event rate, then connect particle momentum to wavelength.

3 practice problems

Photoelectric effect

Separate energy per event from event rate, then connect particle momentum to wavelength.

2 practice problems

De Broglie wavelength

Separate energy per event from event rate, then connect particle momentum to wavelength.

2 practice problems

Hydrogen energy levels

Read negative bound energies correctly and distinguish a level gap, a threshold and a cascade.

1 practice problem

Energy bands

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

1 practice problem

Intrinsic and doped semiconductors

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

1 practice problem

PN junction

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

1 practice problem

Nuclear size

Balance the particles, match the mass convention and include recoil in the energy account.

2 practice problems

Binding energy

Balance the particles, match the mass convention and include recoil in the energy account.

2 practice problems

Radioactive decay

Connect survival probability to measured activity, then test the assumptions behind an inferred age.

4 practice problems

Half-life

Connect survival probability to measured activity, then test the assumptions behind an inferred age.

4 practice problems

Nuclear fission

Balance the particles, match the mass convention and include recoil in the energy account.

1 practice problem

Nuclear fusion

Balance the particles, match the mass convention and include recoil in the energy account.

1 practice problem

Logic gates and truth tables

Translate the condition, follow intermediate signals and verify every input combination.

3 practice problems

LEDs, photodiodes and solar cells

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

4 practice problems

Zener voltage regulation

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

3 practice problems

Diode rectification

Explain the carriers, choose a diode model and verify the operating state before trusting the output.

1 practice problem

Mean life of a radioactive population

Connect survival probability to measured activity, then test the assumptions behind an inferred age.

1 practice problem

Energy balance in nuclear reactions

Balance the particles, match the mass convention and include recoil in the energy account.

1 practice problem

Characteristic and continuous X-ray spectra

Separate energy per event from event rate, then connect particle momentum to wavelength.

1 practice problem