Valencian Community PAU Physics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's law of gravitation

Two point masses attract with force F = G·m₁·m₂/r², directed along the line joining them. G = 6.67×10⁻¹¹ N·m²·kg⁻². The force is always attractive and pairs by Newton's third law.

Gravitational field strength

Force per unit mass at a point: g = F/m = G·M/r², directed toward the source mass. It equals the local free-fall acceleration and is independent of the test mass placed there.

Gravitational potential

Work per unit mass to bring a small mass from infinity to the point: V = −G·M/r. It is negative, zero at infinity, and equals the potential energy per unit mass U/m.

Escape velocity

Minimum launch speed for a body to escape a mass M of radius R without further propulsion: v_e = √(2GM/R). For Earth it is about 11.2 km·s⁻¹, independent of the projectile's mass.

Kepler's third law

For circular or elliptical orbits, T² = 4π²·r³/(GM), so the square of the period is proportional to the cube of the orbital radius. It follows from equating gravitational and centripetal force.

Simple harmonic motion condition

Motion in which acceleration is proportional and opposite to displacement: a = −ω²x. The solution is x = A·sin(ωt + φ₀), with ω = 2π/T and amplitude A fixed by initial conditions.

Spring–mass period

A mass on an ideal spring oscillates with T = 2π√(m/k), where k is the spring constant. The period does not depend on amplitude for Hookean springs, and total energy is ½kA².

Simple pendulum period

For small angular amplitudes, T = 2π√(L/g), where L is the pendulum length and g the local gravitational field strength. The period is independent of the bob mass and of small amplitude.

Wave speed relation

For any periodic wave, v = λ·f = λ/T, linking propagation speed, wavelength, frequency and period. Frequency is set by the source; speed depends on the medium, so wavelength adjusts on refraction.

Standing wave on a string

A string of length L fixed at both ends supports wavelengths λ_n = 2L/n and frequencies f_n = n·v/(2L). Nodes are separated by λ/2; the fundamental has one antinode in the middle.

Doppler effect formula

Observed frequency f' = f·(v ± v_o)/(v ∓ v_s), with v the wave speed and observer/source speeds along the line. Use the upper signs for approach, giving a higher observed frequency.

Coulomb's law

Force between point charges: F = k·q₁·q₂/r² with k = 1/(4πε₀) ≈ 9×10⁹ N·m²·C⁻². Like charges repel, unlike attract; the force acts along the line joining them.

Electric potential of a point charge

V = k·Q/r, zero at infinity, with k = 1/(4πε₀). Potential is a scalar, so potentials from several charges add algebraically, unlike fields which add as vectors.

Gauss's law

The electric flux through a closed surface equals the enclosed charge divided by ε₀: ∮E·dA = Q_enc/ε₀. It gives E = σ/(2ε₀) near an infinite plane and E = λ/(2πε₀r) near a line.

Magnetic force on a charge

A charge q moving with velocity v in field B experiences F = q·v×B, magnitude qvB·sinθ. The force is perpendicular to v, so it changes direction but not speed or kinetic energy.

Charged particle circular motion

A charge moving perpendicular to a uniform magnetic field follows a circle of radius r = mv/(qB). The period T = 2πm/(qB) is independent of speed, the basis of the cyclotron.

Faraday–Lenz law

Induced emf equals the negative rate of change of magnetic flux: ε = −dΦ/dt, with Φ = B·A·cosθ. The minus sign (Lenz) means the induced current opposes the change producing it.

Motional emf

A conducting rod of length L moving at speed v perpendicular to a magnetic field B develops emf ε = B·L·v. This follows from the magnetic force on charge carriers in the rod.

Snell's law

At an interface, n₁·sinθ₁ = n₂·sinθ₂, with angles measured from the normal and n = c/v. Frequency stays constant; wavelength and speed change according to the refractive index.

Total internal reflection

Occurs when light travels from a denser to a less dense medium at angles beyond the critical angle, given by sinθ_c = n₂/n₁. No refracted ray exists beyond θ_c and all light reflects.

Thin lens equation

1/f = 1/s' − 1/s with real-is-positive sign convention, and magnification m = −s'/s. A converging lens has f > 0; a diverging lens has f < 0 and forms virtual images.

Double-slit fringe spacing

For slits separated by d and a screen at distance D, bright fringes occur at d·sinθ = m·λ. For small angles the spacing is Δy = λ·D/d, so it grows with wavelength and D.

Single-slit diffraction minima

Dark fringes occur where a·sinθ = m·λ for m = ±1, ±2, …, with a the slit width. The central bright maximum is twice the angular width of the secondary maxima.

Photoelectric equation

Einstein's equation: h·f = W₀ + E_k,max, where W₀ is the work function. Stopping potential satisfies e·V₀ = h·f − W₀; below threshold frequency f₀ = W₀/h no electrons are emitted.

Time dilation

A clock moving at speed v relative to an observer runs slow: Δt = γ·Δt₀, with γ = 1/√(1 − v²/c²). Proper time Δt₀ is measured in the clock's own rest frame.

Relativistic energy–mass relation

Total energy E = γ·m·c² and rest energy E₀ = m·c². Kinetic energy is E_c = (γ − 1)·m·c², which reduces to ½mv² at speeds much less than c.

de Broglie wavelength

Every particle has wavelength λ = h/p, where p is its momentum. For an electron accelerated through V volts, λ ≈ 1.23/√V nanometres, explaining electron diffraction.

Bohr energy levels of hydrogen

E_n = −13.6 eV/n². A transition between levels emits or absorbs a photon of energy h·f = E_f − E_i, giving the spectral series including Lyman and Balmer lines.

Radioactive decay law

Number of undecayed nuclei follows N = N₀·e^(−λt), with decay constant λ. Half-life is T½ = ln2/λ, and activity A = λ·N is measured in becquerels (decays per second).

Mass defect and binding energy

A nucleus has less mass than its separate nucleons; the difference Δm gives binding energy ΔE = Δm·c². Using 1 u = 931.5 MeV/c², binding energy per nucleon peaks near iron-56.

Adding uncertainties

For sums or differences z = x ± y, absolute uncertainties add: Δz = Δx + Δy. For products, quotients or powers, relative uncertainties add, so z = xⁿ gives Δz/z = |n|·Δx/x.

Linearising a graph

Rearrange the theoretical relation into straight-line form y = m·x + c before plotting. The gradient then yields the physical constant; for a pendulum, plotting T² against L gives g = 4π²/slope.