PAU Physics (Castilla y León) key terms

Force per unit mass experienced by a small test mass placed at a point; a vector pointing toward the attracting body, equal to GM/r² outside a spherical mass.

Work done per unit mass by an external agent to bring a small mass from infinity to a point, taken as zero at infinity; always negative near a mass, equal to −GM/r.

Minimum launch speed needed for a projectile to move from a body's surface to infinity with zero remaining kinetic energy; equals √(2GM/R) and is independent of launch direction.

Speed of a satellite in a circular orbit of radius r, set by gravity supplying the centripetal force; equals √(GM/r), so larger orbits are slower.

For planets or satellites, the square of the orbital period is proportional to the cube of the semi-major axis; for circular orbits T² = 4π²r³/(GM), with the constant fixed by the central mass.

Circular equatorial orbit in which a satellite has a period of one sidereal day and moves eastward, so it stays above one point on Earth's surface; radius is about 42,000 km from Earth's centre.

Electrostatic force per unit positive charge at a point; a vector measured in newtons per coulomb, equal to kQ/r² for the field of a point charge.

Work done per unit positive charge by an external agent in bringing charge from infinity to a point, zero at infinity; a scalar measured in volts, equal to kQ/r for a point charge.

Surface on which every point has the same electric potential; no work is done moving charge along it, so field lines always cross it at right angles.

Scalar product of electric field and area, summed over a surface; measures how much field passes through that surface, with units of volt metres or newton metres squared per coulomb.

Total electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space; useful for finding fields of symmetric charge distributions such as spheres and infinite sheets.

Charge stored on one plate of a capacitor divided by the potential difference between the plates; measured in farads, and for parallel plates equal to ε₀εᵣA/d.

Insulating material placed between capacitor plates; its molecules polarise, reducing the internal field and multiplying capacitance by the relative permittivity while keeping the same charge.

Vector B describing the magnetic force on a moving charge, F = qv × B; measured in tesla, where one tesla gives one newton on a coulomb moving at one metre per second perpendicular to the field.

Total electromagnetic force on a charge, qE + qv × B; the magnetic part acts perpendicular to velocity, so it changes direction but never does work on the particle.

For a charged particle moving perpendicular to a uniform magnetic field, the magnetic force supplies the centripetal force, giving r = mv/(|q|B); faster or heavier particles curve less tightly.

Scalar product of magnetic flux density and area, Φ = B·A = BAcosθ; measured in webers and equal to the field passing normally through a surface.

Induced electromotive force in a circuit equals the negative rate of change of magnetic flux through it; changing field strength, area, or orientation all generate an emf.

Induced current flows in the direction whose magnetic field opposes the change producing it; this is the origin of the minus sign in Faraday's law and follows from energy conservation.

Property of a coil whereby a changing current in it induces an emf opposing that change; defined as flux linkage per unit current and measured in henries.

Device with two coils sharing a magnetic core that changes alternating voltage; the ratio of secondary to primary voltage equals the turns ratio, and ideal power is conserved.

Oscillation in which acceleration is proportional to displacement from equilibrium and directed opposite to it; described by x = A cos(ωt + φ), with period independent of amplitude.

Rate of change of phase in an oscillation or wave, ω = 2πf = 2π/T, measured in radians per second; it links period and frequency in harmonic equations.

Distance a wave crest travels per unit time; equals frequency times wavelength, v = fλ, and for a stretched string also equals √(T/μ).

Pattern formed when two identical waves travel in opposite directions and superpose; nodes stay at rest, antinodes oscillate with maximum amplitude, and only certain frequencies fit fixed boundaries.

Lowest frequency of a standing wave allowed by a system's boundary conditions; for a string fixed at both ends it corresponds to a wavelength of twice the string length.

Any standing-wave mode whose frequency is an integer multiple of the fundamental; the nth harmonic on a string has n half-wavelengths between the fixed ends.

Quantity expressing loudness on a logarithmic scale, β = 10 log(I/I₀) decibels, where I₀ is 10⁻¹² W/m²; equal steps in decibels mean equal ratios of intensity.

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

Relation between angles of incidence and refraction at an interface: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index of each medium.

Angle of incidence in the denser medium for which the refracted ray grazes the interface at 90°; given by sin θc = n₂/n₁, and beyond it total internal reflection occurs.

Complete reflection of light at a boundary when it travels from a denser to a less dense medium at an angle greater than the critical angle; the basis of optical fibres.

Relation 1/f = 1/v − 1/u between focal length, image distance and object distance, using the sign convention in which real objects have negative u.

Ratio of image height to object height, equal to image distance divided by object distance for a thin lens or mirror; negative values indicate an inverted image.

Unit of optical power equal to the reciprocal of focal length in metres; a converging lens of 50 cm focal length has a power of +2 dioptres.

Relativistic effect in which a clock moving relative to an observer ticks more slowly by the factor γ = 1/√(1 − v²/c²); the effect is symmetric between inertial frames.

Dimensionless quantity γ = 1/√(1 − v²/c²) that scales time intervals, lengths and relativistic momentum; it approaches one at low speed and grows without limit near light speed.

Relation E = mc² stating that mass and energy are interchangeable; a small mass defect in a nucleus releases a large amount of energy.

Difference between the total mass of a nucleus's separate nucleons and the mass of the bound nucleus; multiplied by c² it gives the binding energy holding the nucleus together.

Energy required to separate a nucleus completely into its individual protons and neutrons; equals the mass defect times c² and peaks near iron, explaining energy release in fission and fusion.

Spontaneous transformation of an unstable nucleus emitting alpha, beta or gamma radiation; the number of undecayed nuclei falls exponentially with a characteristic half-life.

Time taken for half the nuclei in a sample to decay; after n half-lives the remaining fraction is (1/2)ⁿ, and the decay constant equals ln2 divided by the half-life.

Number of nuclear decays per unit time in a sample, measured in becquerels; it decreases exponentially and equals the decay constant times the number of undecayed nuclei.

Minimum energy needed to remove an electron from a metal surface; in the photoelectric effect no emission occurs below a threshold frequency set by this energy.

Emission of electrons from a metal illuminated by light above a threshold frequency; maximum kinetic energy depends on frequency, not intensity, supporting the photon model.

Reverse voltage that just prevents the fastest photoelectrons from reaching the collector; multiplied by the electron charge it gives their maximum kinetic energy.

Quantified doubt about a measured value, often quoted as half the smallest scale division for analogue instruments or as the standard deviation of repeated readings.

Absolute error is the difference between a measured and accepted value, in the same units; relative or percentage error expresses that difference as a fraction of the accepted value.

Rules for combining uncertainties: for sums and differences add absolute uncertainties, for products and quotients add fractional uncertainties, and for a power multiply the fractional uncertainty by the exponent.

Digits in a result that carry meaning about precision; a final answer should keep roughly the same number of significant figures as the least precise input.

Statistical method fitting the straight line that minimises squared deviations of data from the line; the slope and intercept give the physical constants sought in a graph-based experiment.

Straight line drawn through plotted data so that points are balanced above and below it; its gradient and intercept are then used to extract physical quantities.