Basque PAU Physics key terms

Force per unit mass experienced by a small test mass at a point in space; a vector pointing toward the attracting body, measured in N/kg or m/s².

Two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = GMm/r².

Universal proportionality constant in Newton's gravitation law, approximately 6.67 × 10⁻¹¹ N·m²/kg², measured in the Cavendish experiment.

Work done per unit mass by an external agent to bring a test mass from infinity to a point, taken as zero at infinity; a scalar measured in J/kg, always negative near a mass.

Minimum launch speed needed for a projectile to move from a body's surface to infinity without further propulsion, v = √(2GM/R), independent of projectile mass.

Speed of a satellite in a circular orbit of radius r around a body of mass M, given by v = √(GM/r); larger orbits correspond to slower motion.

Three empirical rules for planetary motion: elliptical orbits with the Sun at one focus, equal areas swept in equal times, and T² proportional to a³ for all planets of a system.

Equatorial circular orbit with period equal to one sidereal day and the same sense of rotation as Earth, so the satellite appears fixed above one point on the surface.

Because gravity acts along the line joining the bodies, torque about the central mass is zero, so mvr stays constant and a satellite moves faster near periapsis.

The electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation: F = kq₁q₂/r², attractive for opposite signs.

Electric force per unit positive charge at a point, a vector measured in N/C or V/m; field lines leave positive charge and enter negative charge.

Work done per unit positive charge to bring a test charge from infinity to a point, a scalar measured in volts and zero at infinity; equals kq/r for a point charge.

A surface on which the electric potential has the same value everywhere; field lines cross it at right angles and no work is done moving charge along it.

Scalar product of the electric field and the area vector of a surface, counting field lines passing through it; measured in N·m²/C and central to Gauss's law.

The total electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space, ε₀; useful for highly symmetric charge distributions.

A pair of equal and opposite charges separated by a distance; its dipole moment p = qd points from negative to positive and it experiences torque pE sinθ in a uniform field.

Charge stored per unit potential difference across a conductor or capacitor, C = Q/V, measured in farads; for parallel plates C = ε₀εᵣA/d.

Magnetic force per unit current per unit length on a conductor placed perpendicular to the field, a vector measured in tesla; B = F/(IL) for perpendicular orientation.

Total force on a charge q moving with velocity v in electric field E and magnetic field B: F = qE + qv × B; the magnetic part acts perpendicular to v.

The magnetic field contribution from a short current element is proportional to I dl sinθ divided by r², with direction given by the right-hand rule; used for wires and loops.

The line integral of magnetic flux density around a closed loop equals μ₀ times the current enclosed by the loop; convenient for long straight wires and solenoids.

A charge moving perpendicular to a uniform magnetic field follows a circle of radius r = mv/(qB); the field does no work, so speed and kinetic energy stay constant.

Product of magnetic flux density and the area perpendicular to it, Φ = BA cosθ, measured in webers; its rate of change drives electromagnetic induction.

The induced electromotive force in a circuit equals the negative rate of change of magnetic flux through it, ε = −dΦ/dt; it can arise from changing B, area or orientation.

The direction of an induced current opposes the change in flux that produced it, a consequence of energy conservation; explains the minus sign in Faraday's law.

Property of a coil whereby a changing current induces an emf in the same coil, ε = −L dI/dt; L is measured in henries and depends on coil geometry.

Relation y(x,t) = A sin(ωt − kx) or equivalent, linking amplitude A, angular frequency ω = 2πf and wave number k = 2π/λ for a travelling harmonic wave.

Speed at which a wave disturbance propagates, v = λf; on a stretched string v = √(T/μ) and for sound in air v depends mainly on temperature.

When two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements; this underlies interference and standing waves.

Reinforcement or cancellation when coherent waves overlap; constructive interference occurs at path differences of nλ and destructive at (n + ½)λ for in-phase sources.

Spreading of waves when they pass through an aperture or around an obstacle, noticeable when the obstacle or slit size is comparable to the wavelength.

Pattern formed by two identical waves travelling in opposite directions, with fixed nodes and antinodes; allowed wavelengths depend on boundary conditions of the medium.

Frequencies at which a string fixed at both ends resonates: f_n = nv/(2L), producing n half-wavelengths between the fixed ends; the lowest is the fundamental.

Whole-number multiples of the fundamental frequency in a resonant system; the nth harmonic contains n times the fundamental frequency.

Change in observed frequency when source and observer move relative to each other; approaching motion raises frequency and receding motion lowers it, for sound and for light.

Relation n₁ sinθ₁ = n₂ sinθ₂ at a refracting interface; light bends toward the normal when entering a denser medium and away when leaving it.

Ratio of light speed in vacuum to that in a medium, n = c/v; absolute values exceed 1 for all material media and determine bending at interfaces.

Complete reflection at an interface when light travels from denser to less dense medium at an angle beyond the critical angle, where sinθ_c = n₂/n₁.

Relation 1/f = 1/s' − 1/s (or 1/s + 1/s' depending on sign convention) linking focal length, object distance and image distance for a thin lens.

Point where rays parallel to the principal axis converge after passing a converging lens or mirror, or from which they appear to diverge for a diverging element.

Ratio of image height to object height, also equal to image distance divided by object distance with sign conventions; negative values indicate inverted images.

Emission of electrons from a metal surface when light of frequency above a threshold falls on it; kinetic energy depends on frequency, not intensity.

Quantum of electromagnetic radiation carrying energy E = hf and momentum p = h/λ, where h is Planck's constant; explains blackbody radiation and the photoelectric effect.

Minimum energy needed to remove an electron from a metal surface; related to threshold frequency by W = hf₀ and used in Einstein's photoelectric equation.

Wavelength associated with a particle of momentum p, given by λ = h/p; observable for electrons and other low-mass particles, confirming wave–particle duality.

Device with many equally spaced slits producing sharp interference maxima at angles where d sinθ = nλ; used to measure wavelengths precisely.

Model in which electrons occupy quantised circular orbits with angular momentum nh/2π, emitting or absorbing photons of energy equal to the level difference.

Relativistic effect whereby a clock moving relative to an observer ticks more slowly, with interval Δt = γΔt₀ and Lorentz factor γ = 1/√(1 − v²/c²).

Energy equivalent of an object's rest mass, E₀ = mc²; mass and energy are interchangeable, so total energy of a moving body is γmc².

Interval expressing the range within which the true value is expected to lie, combining resolution, reading error and statistical spread of repeated readings.

Scatter in repeated readings caused by unpredictable fluctuations; reduced by averaging many measurements and estimated by the standard deviation of the mean.

Consistent offset in one direction caused by faulty instruments, calibration or method; it shifts the mean and cannot be reduced by repeating measurements.

Absolute uncertainty carries the same units as the quantity; relative uncertainty is the absolute value divided by the measurement, often expressed as a percentage.

Rules for combining uncertainties: add absolute uncertainties for sums and differences, add relative uncertainties for products and quotients, multiply by n for powers.

Plotting data to test a relationship, often linearising it so the slope and intercept give physical constants; error bars and lines of best fit support the conclusion.

Straight line drawn through plotted points minimising deviations, ideally by least squares; its gradient and intercept are extracted with their own uncertainties.

Digits in a result that carry meaning about precision; a final answer should have no more significant figures than the least precise input data.