PIEAS Test key terms

A method that checks equations and predicts relationships by comparing the base units (mass, length, time, current) on each side, since only quantities with matching dimensions can be added or equated.

The seven foundational units of the International System: metre, kilogram, second, ampere, kelvin, mole, and candela. All other units are derived from combinations of these.

A unit formed by multiplying or dividing base units, such as the newton (kg·m/s²) for force or the pascal (N/m²) for pressure. It carries no independent dimension of its own.

The digits in a measured value that carry real information about precision. Rules govern how many to keep when multiplying, dividing, adding, or subtracting, and results are rounded to match the least precise input.

The procedure for combining uncertainties of measured quantities to find the uncertainty of a calculated result. For sums, absolute errors add; for products and quotients, fractional errors add in quadrature.

A measure of how spread out repeated measurements are around their mean, equal to the square root of the average squared deviation. A small value indicates tightly clustered, precise data.

Fitting a straight line y = mx + c to data by choosing slope and intercept that minimise the sum of squared vertical deviations. Used to extract physical constants from experimental graphs.

The net force on a body equals its mass times acceleration (F = ma). It links cause (force) to effect (acceleration) and underlies nearly all classical mechanics problems.

In an isolated system with no external net force, total linear momentum stays constant. This principle solves collision and explosion problems without needing details of the forces involved.

A collision in which both total momentum and total kinetic energy are conserved. Hard spheres and ideal gas molecules are modelled this way; real macroscopic collisions are usually partly inelastic.

The ratio of relative speed of separation to relative speed of approach for two colliding bodies. A value of 1 means perfectly elastic, 0 means perfectly inelastic (they stick together).

The net work done on a body by all forces equals its change in kinetic energy. It converts force-and-displacement problems into energy bookkeeping and often simplifies variable-force situations.

Energy cannot be created or destroyed, only transformed between forms. In mechanics, the sum of kinetic and potential energy stays constant when only conservative forces act.

Energy stored because of a body's position or configuration in a conservative field, such as mgh in gravity or ½kx² in a spring. It is defined relative to a chosen reference point.

Oscillation where restoring force is proportional to displacement and directed toward equilibrium, giving sinusoidal motion with period independent of amplitude. Springs and small pendulums approximate it.

A large amplitude response that occurs when a driving frequency matches a system's natural frequency. It can amplify signals usefully in circuits or cause destructive vibration in structures.

The turning effect of a force, equal to force times perpendicular distance from the pivot (τ = rF sin θ). It plays the role in rotation that force plays in linear motion.

A body's resistance to angular acceleration, depending on mass and how it is distributed about the axis. It is the rotational analogue of mass in τ = Iα.

The rotational quantity L = Iω for a rigid body. It is conserved when no external torque acts, explaining why a spinning skater speeds up when pulling in their arms.

For steady, incompressible, non-viscous flow along a streamline, the sum of pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume stays constant.

For incompressible fluid in a pipe, the product of cross-sectional area and flow speed is constant (A₁v₁ = A₂v₂). Narrow sections therefore carry faster flow.

A dimensionless ratio of inertial to viscous forces in fluid flow. Low values indicate smooth laminar flow; high values indicate turbulent flow with chaotic eddies.

The change in internal energy of a system equals heat added to it minus work done by it (ΔU = Q − W). It is energy conservation applied to thermal systems.

A measure of disorder or of the number of microscopic arrangements matching a macrostate. In any spontaneous process the total entropy of an isolated system cannot decrease.

The maximum possible efficiency of a heat engine operating between hot and cold reservoirs, equal to 1 − T_cold/T_hot with temperatures in kelvin. No real engine can exceed it.

The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation, acting along the line joining them.

The force per unit positive charge at a point in space, a vector quantity. Field lines point away from positive charges and toward negative ones, and their density shows field strength.

The work done per unit positive charge in bringing a test charge from infinity to a point. It is a scalar, measured in volts, and equals the negative gradient of potential energy.

The charge stored per unit potential difference across a capacitor (C = Q/V), measured in farads. For a parallel-plate capacitor it equals ε₀A/d with a dielectric multiplying the value.

The total electric flux through any closed surface equals the enclosed charge divided by ε₀. It gives quick field results for symmetric charge distributions such as spheres and cylinders.

Two rules for circuits: the sum of currents entering a junction equals the sum leaving (charge conservation), and the sum of potential differences around any closed loop is zero (energy conservation).

For an ohmic conductor at constant temperature, current is directly proportional to potential difference (V = IR). Materials that violate this, such as diodes, are called non-ohmic.

The total opposition to alternating current from resistance plus reactance, a complex quantity measured in ohms. Its magnitude sets current amplitude and its phase sets the current-voltage shift.

A changing magnetic flux through a circuit induces an electromotive force proportional to the rate of change of flux. Lenz's law fixes the direction so the induced current opposes the change.

Emission of electrons from a metal surface when light above a threshold frequency strikes it. It proves light delivers energy in discrete quanta, since electron energy depends on frequency, not intensity.

The minimum energy needed to remove an electron from a metal surface. In the photoelectric equation, maximum electron kinetic energy equals photon energy minus the work function.

The wavelength associated with a moving particle, equal to Planck's constant divided by its momentum (λ = h/p). It explains electron diffraction and quantised atomic energy levels.

The time for half the nuclei in a radioactive sample to decay. It is constant for a given isotope and relates to the decay constant by t½ = ln 2 / λ.

The number of undecayed nuclei falls exponentially with time, N = N₀e^(−λt), where λ is the decay constant. Activity follows the same exponential form.

The energy required to separate all nucleons in a nucleus completely. Binding energy per nucleon peaks near iron, which explains energy release in both fission and fusion.