A child presses a toy car away from their hand. Is this a push or a pull?
- Neither
- A push
- A pull
Answer and explanation
A push
The hand exerts a force away from itself on the toy.
Subjects
Physics
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Sample exercises
A child brings a drawer toward their body using its handle. What action is this?
- A pull
- A push
- A shadow
Answer and explanation
A pull
The handle is drawn toward the child.
A ball rolls toward a wall and then away. What changed?
- Its name
- Its direction
- Its material must have changed
Answer and explanation
Its direction
The observed path reverses direction; no material change is implied.
Which observation describes motion rather than colour?
- The toy moved toward the door.
- The toy has a red stripe.
- The toy is blue.
Answer and explanation
The toy moved toward the door.
Motion describes a change in position relative to something.
Describe one safe example of a push in a classroom.
Answer and explanation
For example, gently pushing a toy across an empty table.
Accept a specific safe object and action; do not require this wording.
Two toy cars are different sizes and roll on different floors. Why is that not a fair test of push strength?
Answer and explanation
More than push strength changed, so the cause of any difference is unclear.
Look for recognition of at least one other changed variable.
Study notes
Pushes, pulls and changes in motion
Describe familiar motions using an object, an action and a direction.
Grades K–2Pushes, pulls and changes in motion · Revision sheet
Describe familiar motions using an object, an action and a direction.
Grades K–2Light, seeing and shadows
Follow light from a source to an object and understand blocked light.
Grades 1–3Light, seeing and shadows · Revision sheet
Follow light from a source to an object and understand blocked light.
Grades 1–3Sound starts with vibration
Connect observable vibration with sound without confusing loudness and pitch.
Grades 1–4Sound starts with vibration · Revision sheet
Connect observable vibration with sound without confusing loudness and pitch.
Grades 1–4Magnets: test rather than guess
Distinguish attraction, repulsion and the limits of material generalizations.
Grades 2–5Magnets: test rather than guess · Revision sheet
Distinguish attraction, repulsion and the limits of material generalizations.
Grades 2–5Measurements, units and sensible precision
Read scales, record units and separate measurements from assumptions.
Grades 5–8Measurements, units and sensible precision · Revision sheet
Read scales, record units and separate measurements from assumptions.
Grades 5–8Distance is not displacement
Use paths and signed positions to explain round trips.
Grades 6–9Distance is not displacement · Revision sheet
Use paths and signed positions to explain round trips.
Grades 6–9Average speed and average velocity
Choose the correct numerator and include stops in elapsed time.
Grades 7–10Average speed and average velocity · Revision sheet
Choose the correct numerator and include stops in elapsed time.
Grades 7–10Reading position–time information
Interpret slopes without confusing the graph with a picture of a path.
Grades 7–10Reading position–time information · Revision sheet
Interpret slopes without confusing the graph with a picture of a path.
Grades 7–10Velocity–time graphs: slope and area
Separate acceleration from displacement when interpreting a graph.
Grades 9–12Velocity–time graphs: slope and area · Revision sheet
Separate acceleration from displacement when interpreting a graph.
Grades 9–12Balanced forces and inertia
Recognize that zero net force does not require zero velocity.
Grades 7–10Balanced forces and inertia · Revision sheet
Recognize that zero net force does not require zero velocity.
Grades 7–10Force, mass and acceleration
Apply the resultant force rule, including its sign and units.
Grades 8–11Force, mass and acceleration · Revision sheet
Apply the resultant force rule, including its sign and units.
Grades 8–11Interaction pairs act on different objects
Identify equal-and-opposite pairs without cancelling the wrong forces.
Grades 8–11Interaction pairs act on different objects · Revision sheet
Identify equal-and-opposite pairs without cancelling the wrong forces.
Grades 8–11Friction, resistance and terminal motion
Use force direction and model limitations instead of memorized slogans.
Grades 8–11Friction, resistance and terminal motion · Revision sheet
Use force direction and model limitations instead of memorized slogans.
Grades 8–11Mass, weight and gravitational field
Separate an object's mass from the local gravitational force.
Grades 6–10Mass, weight and gravitational field · Revision sheet
Separate an object's mass from the local gravitational force.
Grades 6–10Work, transfer and energy accounting
Track work by each force and distinguish energy from power.
Grades 8–11Work, transfer and energy accounting · Revision sheet
Track work by each force and distinguish energy from power.
Grades 8–11Kinetic and gravitational potential energy
Check squared speed, vertical height and energy reference levels.
Grades 8–11Kinetic and gravitational potential energy · Revision sheet
Check squared speed, vertical height and energy reference levels.
Grades 8–11Power and efficiency without unit confusion
Compare rates and fractions rather than mixing energy and power.
Grades 8–11Power and efficiency without unit confusion · Revision sheet
Compare rates and fractions rather than mixing energy and power.
Grades 8–11Momentum in one-dimensional collisions
Use signed velocities and a clearly chosen isolated system.
Grades 9–12Momentum in one-dimensional collisions · Revision sheet
Use signed velocities and a clearly chosen isolated system.
Grades 9–12Impulse and stopping time
Relate changes in momentum to average forces over a time interval.
Grades 9–12Impulse and stopping time · Revision sheet
Relate changes in momentum to average forces over a time interval.
Grades 9–12Moments, pivots and equilibrium
Use perpendicular distances and check both force and turning balance.
Grades 8–11Moments, pivots and equilibrium · Revision sheet
Use perpendicular distances and check both force and turning balance.
Grades 8–11Springs and the linear elastic limit
Use extension, not total length, and distinguish force from stored energy.
Grades 9–12Springs and the linear elastic limit · Revision sheet
Use extension, not total length, and distinguish force from stored energy.
Grades 9–12Pressure, area and depth
Do not confuse pressure with force or absolute with additional pressure.
Grades 7–10Pressure, area and depth · Revision sheet
Do not confuse pressure with force or absolute with additional pressure.
Grades 7–10Displacement, density and buoyancy
Use displaced fluid weight and avoid shape-only explanations of floating.
Grades 8–11Displacement, density and buoyancy · Revision sheet
Use displaced fluid weight and avoid shape-only explanations of floating.
Grades 8–11Temperature is not total thermal energy
Separate a temperature reading from energy transfer and system size.
Grades 7–10Temperature is not total thermal energy · Revision sheet
Separate a temperature reading from energy transfer and system size.
Grades 7–10Conduction, convection and radiation
Identify transfer mechanisms and explain insulation as slowing transfer.
Grades 7–10Conduction, convection and radiation · Revision sheet
Identify transfer mechanisms and explain insulation as slowing transfer.
Grades 7–10Heating versus changing state
Choose between mcΔT and mL using the physical process.
Grades 9–12Heating versus changing state · Revision sheet
Choose between mcΔT and mL using the physical process.
Grades 9–12Wave vocabulary and energy transfer
Distinguish amplitude, wavelength, frequency and particle motion.
Grades 7–10Wave vocabulary and energy transfer · Revision sheet
Distinguish amplitude, wavelength, frequency and particle motion.
Grades 7–10Sound, echoes and travel time
Use round-trip reasoning and distinguish medium effects from source pitch.
Grades 8–11Sound, echoes and travel time · Revision sheet
Use round-trip reasoning and distinguish medium effects from source pitch.
Grades 8–11Reflection and the normal
Measure angles from a perpendicular reference line, not from the mirror.
Grades 7–10Reflection and the normal · Revision sheet
Measure angles from a perpendicular reference line, not from the mirror.
Grades 7–10Refraction and critical conditions
Track speed, wavelength and angle while frequency stays tied to the source.
Grades 9–12Refraction and critical conditions · Revision sheet
Track speed, wavelength and angle while frequency stays tied to the source.
Grades 9–12Thin lenses and image conventions
Use one sign convention and avoid claims that every convex lens image is real.
Grades 10–12Thin lenses and image conventions · Revision sheet
Use one sign convention and avoid claims that every convex lens image is real.
Grades 10–12Charge, current and complete circuits
Describe a steady circuit without saying that current is consumed.
Grades 7–10Charge, current and complete circuits · Revision sheet
Describe a steady circuit without saying that current is consumed.
Grades 7–10Series and parallel: what stays the same
Use topology before choosing voltage and current rules.
Grades 9–12Series and parallel: what stays the same · Revision sheet
Use topology before choosing voltage and current rules.
Grades 9–12Electrical energy and power
Combine voltage, current, resistance and time without mixing units.
Grades 9–12Electrical energy and power · Revision sheet
Combine voltage, current, resistance and time without mixing units.
Grades 9–12Fields, motors and induced effects
Connect magnetic fields with currents without treating field lines as wires.
Grades 9–12Fields, motors and induced effects · Revision sheet
Connect magnetic fields with currents without treating field lines as wires.
Grades 9–12Ideal transformers and conservation
Use turns ratios and distinguish the ideal AC model from real losses.
Grades 10–12Ideal transformers and conservation · Revision sheet
Use turns ratios and distinguish the ideal AC model from real losses.
Grades 10–12Atomic models and photon energy
Distinguish nuclei, electron energy levels and the scope of simple models.
Grades 10–12Atomic models and photon energy · Revision sheet
Distinguish nuclei, electron energy levels and the scope of simple models.
Grades 10–12Half-life: a statistical model
Apply repeated halving without predicting an individual decay time.
Grades 9–12Half-life: a statistical model · Revision sheet
Apply repeated halving without predicting an individual decay time.
Grades 9–12Circular motion: changing velocity at constant speed
Keep centripetal acceleration and actual force sources distinct.
Grades 10–12Circular motion: changing velocity at constant speed · Revision sheet
Keep centripetal acceleration and actual force sources distinct.
Grades 10–12Projectile components and model limits
Treat horizontal and vertical motion together without inventing horizontal gravity.
Grades 10–12Projectile components and model limits · Revision sheet
Treat horizontal and vertical motion together without inventing horizontal gravity.
Grades 10–12Physics evidence: uncertainty and proportionality
Interpret patterns without turning a short dataset into proof.
Grades 9–12Physics evidence: uncertainty and proportionality · Revision sheet
Interpret patterns without turning a short dataset into proof.
Grades 9–12Average speed over two stages
Add all distances and all elapsed times before dividing.
Grades 6–9Displacement and average velocity
Use consistent SI units and keep the stated direction convention.
Grades 7–10Distance on a return journey
Distance adds path lengths; displacement uses the change in position.
Grades 6–9Acceleration from two readings
Use consistent SI units and keep the stated direction convention.
Grades 8–11Velocity with constant acceleration
This equation requires constant acceleration over the interval.
Grades 9–12Displacement with constant acceleration
Displacement may be negative; do not automatically take its absolute value.
Grades 9–12Idealized stopping time
b is the positive magnitude of constant deceleration; reaction time is excluded.
Grades 9–12Idealized braking distance
Assume straight-line motion and constant deceleration up to rest.
Grades 10–12Closing speed
Add speeds only here because the objects move directly toward each other.
Grades 8–11Time to maximum height
At the highest point velocity is zero, but gravitational acceleration is not.
Grades 10–12Free fall from rest
Treat g as constant, ignore air resistance, and start from rest.
Grades 9–12Horizontal projectile range
Initial vertical velocity is zero; ignore air resistance and use level ground below.
Grades 10–12Perpendicular force resultant
Use this rule only for perpendicular components.
Grades 9–12Acceleration with opposing forces
Use consistent SI units and keep the stated direction convention.
Grades 7–10Weight in a given field
Mass is measured in kg; weight is a force measured in N.
Grades 6–10Kinetic friction model
This is sliding friction with the stated coefficient, not a universal rule for static friction.
Grades 10–12Signed linear momentum
Use consistent SI units and keep the stated direction convention.
Grades 9–12Objects stick together
For this isolated collision momentum is conserved; kinetic energy generally is not.
Grades 10–12Impulse from velocity change
Use consistent SI units and keep the stated direction convention.
Grades 9–12Average force during contact
Convert milliseconds to seconds before dividing.
Grades 10–12Work by an angled force
θ is the angle between the force and displacement, not an arbitrary drawing angle.
Grades 10–12Change in kinetic energy
Square each speed before subtracting; a loss gives a negative change.
Grades 9–12Gravitational energy gain
Use the vertical height change and the specified constant field strength.
Grades 7–10Useful output energy
Convert the efficiency percentage to a fraction; wasted energy remains part of the energy account.
Grades 8–11Energy from constant power
Power is an energy-transfer rate; watts times seconds gives joules.
Grades 7–10Extension of an ideal spring
Stay in the linear elastic range; extension is not total spring length.
Grades 9–12Elastic energy in a spring
Convert extension to metres, then square it; the spring is ideal and linear.
Grades 10–12Balance moments about a pivot
Use perpendicular lever arms; neglect the beam’s own weight in this model.
Grades 8–11Pressure on a surface
Use the normal force and contact area in square metres.
Grades 7–10Liquid pressure increase
This is pressure above the surface pressure, not absolute pressure.
Grades 9–12Buoyancy from displaced volume
Use the density of the fluid and displaced fluid volume, not the object’s density.
Grades 9–12Energy for a temperature rise
Assume constant specific heat, no phase change and no energy loss.
Grades 9–12Energy for a phase change
At the phase-change temperature, use latent heat rather than a temperature-rise formula.
Grades 10–12Ideal mixing temperature
Both portions have the same constant specific heat; no phase change, container heating or loss.
Grades 10–12Steady conduction through a slab
Use a uniform slab, steady temperatures and one-dimensional conduction.
Grades 11–12Wave speed from frequency and wavelength
Use wavelength in metres and frequency in hertz.
Grades 7–11Period from many oscillations
A period is the duration of one complete oscillation, not its frequency.
Grades 8–11Distance from an echo
The recorded time includes travel to the reflector and back.
Grades 8–11Refraction using given sine values
Angles are measured from the normal. Find the sine requested, not an angle in degrees.
Grades 10–12Light speed in a medium
The refractive index is dimensionless; use the given vacuum speed.
Grades 10–12Image distance for a converging lens
This model uses a thin lens, a real object beyond the focal point, and positive real-image distances.
Grades 11–12Image-size magnification
This question asks for size, not orientation; the magnification magnitude is given.
Grades 10–12Charge transferred by current
Current is a rate of charge transfer; use seconds, not minutes, here.
Grades 8–11Current in an ohmic resistor
Assume an ohmic resistor at constant temperature; circuit values are theoretical.
Grades 8–11Power in a series resistor network
Ideal source and wires; resistors are ohmic and connected in series.
Grades 10–12Total current in parallel branches
Each parallel branch has the same potential difference; branch currents add.
Grades 10–12Energy in kilowatt-hours
A kilowatt-hour is energy, not power.
Grades 8–11Ideal transformer voltage ratio
This ideal transformer model uses alternating voltage; it is not a mains-wiring activity.
Grades 10–12Force on a perpendicular current-carrying wire
The straight active wire length is perpendicular to the uniform magnetic field.
Grades 11–12Average induced emf
Use flux change per turn; the question asks magnitude, not the direction set by Lenz’s law.
Grades 11–12Expected amount after half-lives
This predicts the expected remaining amount for a large ensemble; individual decays are random.
Grades 9–12Photon energy in a scaled unit
Track powers of ten; the answer is a coefficient in units of 10⁻¹⁹ J.
Grades 11–12Motion & graphs · Formula reference 1
Formula reference
Grades 6–12Motion & graphs · Formula reference 2
Formula reference
Grades 8–12Motion & graphs · Formula reference 3
Formula reference
Grades 9–12Forces & equilibrium · Formula reference 1
Formula reference
Grades 6–12Forces & equilibrium · Formula reference 2
Formula reference
Grades 8–11Momentum & collisions · Formula reference
Formula reference
Grades 9–12Energy, work & power · Formula reference 1
Formula reference
Grades 7–12Energy, work & power · Formula reference 2
Formula reference
Grades 10–12Pressure & fluids · Formula reference
Formula reference
Grades 7–12Thermal physics · Formula reference
Formula reference
Grades 9–12Waves & sound · Formula reference
Formula reference
Grades 7–11Light & optics · Formula reference
Formula reference
Grades 10–12Electricity & circuits · Formula reference
Formula reference
Grades 8–12Magnetism & induction · Formula reference
Formula reference
Grades 10–12Atomic & nuclear models · Formula reference
Formula reference
Grades 9–12Rotational dynamics and rolling constraints
Angular velocity is the time derivative of angular displacement. For a fixed axis and constant moment of inertia, net torque equals I times angular acceleration.
UniversityRotational dynamics and rolling constraints · revision notes
Angular velocity is the time derivative of angular displacement. For a fixed axis and constant moment of inertia, net torque equals I times angular acceleration.
UniversityDriven oscillations, damping and resonance
A linear mass-spring oscillator obeys mx″+kx=0. Its natural angular frequency is sqrt(k/m), not k/m.
UniversityDriven oscillations, damping and resonance · revision notes
A linear mass-spring oscillator obeys mx″+kx=0. Its natural angular frequency is sqrt(k/m), not k/m.
UniversityCentral forces, angular momentum and effective potential
A central force is directed along the line joining the particle to a fixed centre and has magnitude depending only on radial distance in the usual model.
UniversityCentral forces, angular momentum and effective potential · revision notes
A central force is directed along the line joining the particle to a fixed centre and has magnitude depending only on radial distance in the usual model.
UniversityWave equations, normal modes and boundary conditions
The ideal one-dimensional wave equation is ytt=c²yxx. The parameter c is propagation speed for this nondispersive model.
UniversityWave equations, normal modes and boundary conditions · revision notes
The ideal one-dimensional wave equation is ytt=c²yxx. The parameter c is propagation speed for this nondispersive model.
UniversityElectric flux and Gauss symmetry
Electric flux is the oriented surface integral of E·dA. A negative flux reflects direction relative to the chosen normal, not negative area.
UniversityElectric flux and Gauss symmetry · revision notes
Electric flux is the oriented surface integral of E·dA. A negative flux reflects direction relative to the chosen normal, not negative area.
UniversityCapacitors, RC transients and field energy
For a linear capacitor Q=CV, with stored energy CV²/2. Potential difference and capacitance must refer to the same device.
UniversityCapacitors, RC transients and field energy · revision notes
For a linear capacitor Q=CV, with stored energy CV²/2. Potential difference and capacitance must refer to the same device.
UniversityFirst law, ideal gases and entropy
Use ΔU=Q−W, where W is work done by the system. A different sign convention is possible only when used consistently.
UniversityFirst law, ideal gases and entropy · revision notes
Use ΔU=Q−W, where W is work done by the system. A different sign convention is possible only when used consistently.
UniversityElectromagnetic waves and energy flow
In vacuum, plane electromagnetic waves have transverse electric and magnetic fields with E0=cB0. Both fields are perpendicular to propagation.
UniversityElectromagnetic waves and energy flow · revision notes
In vacuum, plane electromagnetic waves have transverse electric and magnetic fields with E0=cB0. Both fields are perpendicular to propagation.
UniversitySpecial relativity and invariant intervals
Special relativity describes inertial-frame transformations with invariant vacuum light speed. It replaces Galilean transformations when relativistic effects matter.
UniversitySpecial relativity and invariant intervals · revision notes
Special relativity describes inertial-frame transformations with invariant vacuum light speed. It replaces Galilean transformations when relativistic effects matter.
UniversityQuantum states, amplitudes and measurement
A normalized state vector encodes probability amplitudes. Overall global phase leaves measurement probabilities unchanged.
UniversityQuantum states, amplitudes and measurement · revision notes
A normalized state vector encodes probability amplitudes. Overall global phase leaves measurement probabilities unchanged.
UniversitySchrodinger equations and a particle in a box
The time-dependent equation is iℏ ∂ψ/∂t=Hψ. A time-independent Hamiltonian permits stationary-state analysis.
UniversitySchrodinger equations and a particle in a box · revision notes
The time-dependent equation is iℏ ∂ψ/∂t=Hψ. A time-independent Hamiltonian permits stationary-state analysis.
UniversityOperators, commutators and uncertainty
Observables are represented by suitable self-adjoint operators. In finite dimensions they are Hermitian matrices with real eigenvalues.
UniversityOperators, commutators and uncertainty · revision notes
Observables are represented by suitable self-adjoint operators. In finite dimensions they are Hermitian matrices with real eigenvalues.
UniversityEuler-Lagrange equations and constraints
For L(q,qdot,t), stationarity of S=∫L dt with fixed endpoints yields d/dt(∂L/∂qdot)−∂L/∂q=0.
Advanced universityEuler-Lagrange equations and constraints · revision notes
For L(q,qdot,t), stationarity of S=∫L dt with fixed endpoints yields d/dt(∂L/∂qdot)−∂L/∂q=0.
Advanced universityHamilton equations, phase space and Poisson brackets
For a regular Lagrangian, p=∂L/∂qdot and H=p qdot−L after expressing qdot in terms of q,p,t.
Advanced universityHamilton equations, phase space and Poisson brackets · revision notes
For a regular Lagrangian, p=∂L/∂qdot and H=p qdot−L after expressing qdot in terms of q,p,t.
Advanced universityCanonical ensembles and partition functions
For a system at inverse temperature β=1/(kBT), the canonical probability of a microstate of energy E is exp(−βE)/Z.
Advanced universityCanonical ensembles and partition functions · revision notes
For a system at inverse temperature β=1/(kBT), the canonical probability of a microstate of energy E is exp(−βE)/Z.
Advanced universityPerturbation theory and approximation checks
Write H=H0+λV and expand observables or states about a solvable reference problem. Small λ is useful only relative to relevant spectral scales.
Advanced universityPerturbation theory and approximation checks · revision notes
Write H=H0+λV and expand observables or states about a solvable reference problem. Small λ is useful only relative to relevant spectral scales.
Advanced universityScattering, currents and probability conservation
Scattering models compare incoming and outgoing waves far from a localized interaction. Boundary conditions identify which waves are physically incident.
Advanced universityScattering, currents and probability conservation · revision notes
Scattering models compare incoming and outgoing waves far from a localized interaction. Boundary conditions identify which waves are physically incident.
Advanced universityVariational bounds and trial states
For a normalized trial state in the Hamiltonian domain, the expectation of a Hamiltonian bounded below is at least its ground energy.
Advanced universityVariational bounds and trial states · revision notes
For a normalized trial state in the Hamiltonian domain, the expectation of a Hamiltonian bounded below is at least its ground energy.
Advanced universityCurved spacetime and the scope of general relativity
General relativity relates spacetime geometry to stress-energy. The metric determines spacetime intervals and causal structure.
Advanced universityCurved spacetime and the scope of general relativity · revision notes
General relativity relates spacetime geometry to stress-energy. The metric determines spacetime intervals and causal structure.
Advanced universityRotational kinetic energy
Use moment of inertia about the stated rotation axis. Angular speed is in radians per second.
UniversityRotational kinetic energy · formula reference
Use moment of inertia about the stated rotation axis. Angular speed is in radians per second.
UniversityRolling without slipping
A uniform solid cylinder rolls without slipping, so ω = v/R; both translation and rotation contribute.
UniversityRolling without slipping · formula reference
A uniform solid cylinder rolls without slipping, so ω = v/R; both translation and rotation contribute.
UniversityMass-spring oscillation period
Ideal linear spring; negligible damping. Small displacement is assumed where Hooke’s law is approximate.
UniversityMass-spring oscillation period · formula reference
Ideal linear spring; negligible damping. Small displacement is assumed where Hooke’s law is approximate.
UniversityUnderdamped envelope after a time
This is the amplitude envelope, not instantaneous signed displacement. The oscillator is specified as underdamped.
UniversityUnderdamped envelope after a time · formula reference
This is the amplitude envelope, not instantaneous signed displacement. The oscillator is specified as underdamped.
UniversityIntensity-level difference
The ratio is an intensity ratio. Pressure-amplitude ratios use 20 log₁₀ under matched impedance conditions.
UniversityIntensity-level difference · formula reference
The ratio is an intensity ratio. Pressure-amplitude ratios use 20 log₁₀ under matched impedance conditions.
UniversityStored energy in an ideal capacitor
Convert microfarads to farads before using SI units. This is a paper exercise, not hardware guidance.
UniversityStored energy in an ideal capacitor · formula reference
Convert microfarads to farads before using SI units. This is a paper exercise, not hardware guidance.
UniversityRC discharge voltage
Ideal RC discharge with no driving source. Convert kilohms and microfarads consistently.
UniversityRC discharge voltage · formula reference
Ideal RC discharge with no driving source. Convert kilohms and microfarads consistently.
UniversityGauss-law electric flux
Net flux through the entire closed surface depends on enclosed charge, not on external charges.
UniversityGauss-law electric flux · formula reference
Net flux through the entire closed surface depends on enclosed charge, not on external charges.
UniversityMagnetic force magnitude
The stated velocity is perpendicular to the magnetic field. Magnetic force does no work on the point charge.
UniversityMagnetic force magnitude · formula reference
The stated velocity is perpendicular to the magnetic field. Magnetic force does no work on the point charge.
UniversityReversible isothermal ideal-gas work
Work is positive for expansion; the process is reversible and isothermal for an ideal gas.
UniversityReversible isothermal ideal-gas work · formula reference
Work is positive for expansion; the process is reversible and isothermal for an ideal gas.
UniversityCarnot upper-bound efficiency
Temperatures must be absolute. This is the reversible upper bound between two reservoirs, not a claim about a real engine.
UniversityCarnot upper-bound efficiency · formula reference
Temperatures must be absolute. This is the reversible upper bound between two reservoirs, not a claim about a real engine.
UniversityClassical monatomic ideal-gas internal energy
Only translational degrees of freedom contribute in this classical ideal-gas model.
UniversityClassical monatomic ideal-gas internal energy · formula reference
Only translational degrees of freedom contribute in this classical ideal-gas model.
UniversityLorentz factor
The speed is subluminal; Newtonian approximations become inaccurate as β increases.
UniversityLorentz factor · formula reference
The speed is subluminal; Newtonian approximations become inaccurate as β increases.
UniversityProper time from coordinate time
The clock moves at a constant speed between the two events; proper time is measured by that clock.
UniversityProper time from coordinate time · formula reference
The clock moves at a constant speed between the two events; proper time is measured by that clock.
UniversityInfinite-well energy ratio
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
UniversityInfinite-well energy ratio · formula reference
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
UniversityPhoton energy from wavelength
Use hc = 1239.84 eV·nm for the stated numerical convention.
UniversityPhoton energy from wavelength · formula reference
Use hc = 1239.84 eV·nm for the stated numerical convention.
UniversityEuler-Lagrange equation for a quartic potential
For L=mẋ²/2−ax⁴, the force is −4ax³. This one-dimensional model is conservative.
Advanced universityEuler-Lagrange equation for a quartic potential · formula reference
For L=mẋ²/2−ax⁴, the force is −4ax³. This one-dimensional model is conservative.
Advanced universityHamilton equation for velocity
For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.
Advanced universityHamilton equation for velocity · formula reference
For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.
Advanced universityPoisson bracket of two monomials
Use the declared order; reversing f and g reverses the bracket sign.
Advanced universityPoisson bracket of two monomials · formula reference
Use the declared order; reversing f and g reverses the bracket sign.
Advanced universityPartition function of a two-level system
Ground energy is zero with degeneracy 1; the excited level has degeneracy g. Energies are measured from the ground state.
Advanced universityPartition function of a two-level system · formula reference
Ground energy is zero with degeneracy 1; the excited level has degeneracy g. Energies are measured from the ground state.
Advanced universityExcited-state population with degeneracy
The probability refers to the whole excited level, including all its degenerate states.
Advanced universityExcited-state population with degeneracy · formula reference
The probability refers to the whole excited level, including all its degenerate states.
Advanced universityEntropy difference from multiplicity ratio
Use the microcanonical equal-a-priori-probability model and a ratio of multiplicities.
Advanced universityEntropy difference from multiplicity ratio · formula reference
Use the microcanonical equal-a-priori-probability model and a ratio of multiplicities.
Advanced universityExpectation value in an orthogonal eigenbasis
The squared amplitudes are probabilities. Orthogonality and normalization are specified.
Advanced universityExpectation value in an orthogonal eigenbasis · formula reference
The squared amplitudes are probabilities. Orthogonality and normalization are specified.
Advanced universityVariance of a two-outcome observable
Compute the second moment before subtracting the square of the mean.
Advanced universityVariance of a two-outcome observable · formula reference
Compute the second moment before subtracting the square of the mean.
Advanced universityFirst-order stationary perturbation
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
Advanced universityFirst-order stationary perturbation · formula reference
Nondegenerate first-order perturbation theory; the perturbation is diagonal in the stated orthonormal basis.
Advanced universityMinkowski interval in one spatial dimension
Use the (+,−) sign convention. A negative result is spacelike, not an arithmetic error.
Advanced universityMinkowski interval in one spatial dimension · formula reference
Use the (+,−) sign convention. A negative result is spacelike, not an arithmetic error.
Advanced universityVacuum electric-field energy density
This asks for the electric contribution only. A magnetic field would add B²/(2μ₀).
Advanced universityVacuum electric-field energy density · formula reference
This asks for the electric contribution only. A magnetic field would add B²/(2μ₀).
Advanced universityGroup velocity from a dispersion relation
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
Advanced universityGroup velocity from a dispersion relation · formula reference
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
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24 quiz questions · Advanced university
Physics4 lessons
Advanced physics methods and spacetime
Explore perturbation theory, scattering, variational quantum estimates and a conceptual bridge to general relativity.
32 quiz questions · Advanced university