New Zealand Scholarship Physics flashcards

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

Dimensional homogeneity

A valid physical equation must have identical base dimensions on both sides. Checking dimensions catches algebraic slips and reveals how a quantity scales with its variables before any numbers are substituted.

Fractional uncertainty for products

If z = xⁿyᵐ, the fractional uncertainty is δz/z = sqrt((nδx/x)² + (mδy/y)²). Powers amplify relative uncertainty by the exponent, so small errors in squared terms matter more.

Linearising a power law

Taking logs of y = axⁿ gives log y = log a + n log x, a straight line with gradient n and intercept log a. Fitting the linearised form is more reliable than curve fitting the original data.

Limiting-case check

Substituting extremes such as zero mass, infinite distance, or speed approaching c into a derived formula tests whether it reduces to a known sensible result. Failing this check signals an algebra error.

Centripetal force is net inward force

In circular motion the centripetal force is the resultant of real forces such as tension, gravity, or friction directed toward the centre. It is not an additional force to be added to the free-body diagram.

Work–energy theorem

The net work done on an object equals its change in kinetic energy: W_net = ½mv² − ½mu². This holds even when forces vary, provided W_net is evaluated as the integral of force over displacement.

Elastic versus inelastic collisions

Total momentum is conserved in every collision. Kinetic energy is conserved only in elastic collisions; in inelastic collisions some kinetic energy converts to internal energy, sound, or deformation.

Parallel-axis theorem

The moment of inertia about any axis parallel to one through the centre of mass is I = I_cm + Md², where d is the perpendicular distance between the axes and M the total mass.

Rolling without slipping condition

When a round object rolls without slipping, its centre-of-mass speed and angular speed satisfy v = ωr. Static friction at the contact point does no work, so mechanical energy is conserved.

Gravitational potential energy sign

With zero potential energy defined at infinity, U = −GMm/r is negative everywhere finite. Increasing separation raises U toward zero, and the negative sign reflects the attractive nature of gravity.

Escape velocity

The minimum launch speed to escape a body's gravity is v_esc = sqrt(2GM/r) = sqrt(2gr). It is independent of the projectile's mass and of launch angle, ignoring atmospheric drag and rotation.

Kepler's third law

For orbits around a mass M, the period T and orbital radius r satisfy T² = (4π²/GM) r³. The constant depends only on the central mass, so all satellites of one body share the same T²/r³ ratio.

Simple harmonic motion condition

SHM occurs whenever the restoring force is proportional to displacement and directed oppositely, giving a = −ω²x. The period T = 2π/ω is independent of amplitude for ideal SHM.

Pendulum period small-angle limit

For a simple pendulum, T = 2π sqrt(L/g) holds only for small angular amplitudes, roughly under 10 degrees. Larger swings lengthen the period because the restoring force is no longer proportional to displacement.

Standing wave node spacing

Adjacent nodes, and adjacent antinodes, in a standing wave are separated by half a wavelength. This fixes the allowed frequencies of strings and pipes of a given length and end condition.

Closed pipe resonance

A pipe closed at one end has a node at the closed end and an antinode at the open end, giving resonant frequencies f_n = (2n − 1)v/(4L). Only odd harmonics are present, unlike an open pipe.

Doppler effect formula

For motion along the line joining source and observer, f' = f(v ± v_o)/(v ∓ v_s). Choose signs so that approach raises the observed frequency and recession lowers it.

Total internal reflection

When light travels from a denser to a less dense medium at an angle exceeding the critical angle θ_c = arcsin(n₂/n₁), it is entirely reflected. This requires n₁ greater than n₂.

Thin lens equation

Using the real-is-positive convention, 1/f = 1/v + 1/u and magnification m = −v/u. A negative image distance indicates a virtual image on the same side as the object for a lens.

Young's double-slit fringe spacing

For slits separated by d, screen distance D much greater than d, and wavelength λ, bright fringes are spaced Δy = λD/d. Maxima occur where d sin θ = nλ.

First law of thermodynamics

ΔU = Q − W, where Q is heat added to the system and W is work done by the system. Internal energy rises when heat enters or when work is done on the system.

Carnot efficiency limit

No heat engine operating between hot and cold reservoirs at absolute temperatures T_h and T_c can exceed η = 1 − T_c/T_h. Equality requires a reversible cycle, so real engines fall short.

Kinetic theory average energy

For an ideal gas, the average translational kinetic energy per molecule is (3/2)k_BT, depending only on absolute temperature. Internal energy of a monatomic ideal gas is therefore (3/2)nRT.

Kirchhoff's circuit laws

Charge conservation gives ΣI = 0 at any junction; energy conservation gives ΣV = 0 around any closed loop. Together they determine unknown currents in multi-loop DC circuits.

Capacitor energy storage

A charged capacitor stores energy U = ½CV² = ½QV = Q²/(2C). The energy resides in the electric field between the plates, whose magnitude in a parallel-plate capacitor is V/d.

Charged particle circular path

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

Faraday and Lenz laws

An induced emf equals the negative rate of change of magnetic flux, ε = −dΦ/dt. The minus sign, Lenz's law, means the induced current opposes the flux change that produced it.

Photoelectric threshold frequency

Electrons are emitted only when incident light frequency exceeds f₀ = φ/h, where φ is the work function. Below threshold, no emission occurs regardless of intensity.

Maximum photoelectron kinetic energy

K_max = hf − φ. Increasing light intensity raises the number of emitted electrons but not their maximum kinetic energy; only increasing frequency raises K_max.

Hydrogen energy levels

Hydrogen levels are E_n = −13.6 eV/n². Photon emission occurs when an electron drops to a lower level, with energy equal to the difference between the two levels.

de Broglie wavelength

Every particle has an associated wavelength λ = h/p. It becomes measurable only for very small masses, such as electrons, explaining why wave behaviour is not observed for everyday objects.

Radioactive half-life

Decay follows N = N₀e^(−λt) with half-life t½ = ln2/λ. After each half-life the remaining undecayed nuclei halve, independent of temperature, pressure, or chemical state.