WJEC Definitions (A2) – Items in bold italic can be defined using equationPH4

Item Definition from memory Definition from notes / textbookPeriod T for a point describing a circle

Frequency f

Equation relating T and f

Centripetal force (in words)

Centripetal acceleration

Centripetal force

Angular velocity ω.

Simple harmonic motion (shm)

Simple harmonic motion (shm)(Alternative definition)Period T for an oscillating body

Amplitude A of an oscillating object

Equations relating position, velocity and acceleration with time in SHM

Item Definition from memory Definition from notes / textbookPhase

Free oscillations[Natural oscillations]

Damping

Critical damping

Forced oscillations

Resonance

Momentum

Newton’s laws of motion: 1st law

Newton’s laws of motion: 2nd law

Newton’s laws of motion: 3rd law

The principle of conservation of momentum

Elastic collision.

Item Definition from memory Definition from notes / textbookInelastic collision.

Boyle’s law

Charles’ Law

Pressure Law

Ideal gas

The mole

Avogadro constant NA

Internal energy, U, of a system

Heat, Q

Work, W

Temperature

Item Definition from memory Definition from notes / textbookAverage kinetic energy of molecules

Pressure of gas (in terms of molecular properties)

First law of thermodynamics

Specific heat capacity c.

Electric field strength E (definition)

Electric field strength (uniform field only)

Electric field strength around a point charge (spherical field)Coulomb’s Law

Gravitational field strength g.

Gravitational field strength around a point mass (spherical field)Newton’s law of gravitation.

Electric potential VE. (words and equation for uniform field)

Item Definition from memory Definition from notes / textbookElectric potential at a point in a spherical field

Gravitational potential Vg (words and equation for uniform field)Gravitational potential at a point in a spherical field

Kepler’s laws of planetary motion: 1

Kepler’s laws of planetary motion: 2

Kepler’s laws of planetary motion: 3

Kepler’s third law in terms of circular motion and Newton’s Law of Gravitation (derivation)Dark matter

Radial velocity of a star [in the context of Doppler shift]

PH5Item Definition from memory Definition from notes / textbook

Capacitor

Capacitance, C, of a capacitor

1 Farad

Capacitors in series

Capacitors in parallel

Energy stored on a capacitor

Capacitance (in terms of design of capacitor)What is an exponential decay?

Decay of I (or V or Q) with time as capacitor dischargesTime constant

Dielectric

Magnetic field strength, B(Magnetic flux density)

Item Definition from memory Definition from notes / textbook1 Tesla

Force on a moving charge in a magnetic fieldRadius of orbit, r of charged particle, mass m and charge q, moving in a circle at speed v in magnetic field BField strength of a long straight wire

Field strength of a solenoid

Hall voltage

Ampère A

Magnetic flux Φ.

1 Weber

Flux linkage NΦ

Faraday’s law

Item Definition from memory Definition from notes / textbookLenz’s Law.

Root-mean-square (rms) value

Alpha (α) radiation

Beta (β) radiation

Gamma (γ) radiation

notation

Half life of a

nuclide

Activity A

1 Bequerel

Decay constant λ (in words)

Decay constant in terms of half life

Item Definition from memory Definition from notes / textbookRadioactive decay equation(s)

Radio-isotopes

Unified atomic mass unit u.

Electron volt (eV).

Binding energy of a nucleus.

Conservation of mass-energy

Nuclear fission

Chain reaction

Option CItem Definition from memory Definition from notes / textbook

Crystal

Crystalline solid

Amorphous solid

Polymeric solid

Hooke’s Law for rods and wires

Stress

Strain

The Young Modulus

Ductile material

Elastic strain

Plastic (or inelastic) strain

Elastic limit

Item Definition from memory Definition from notes / textbookDislocations in crystals

Grain boundaries

Ductile fracture (necking)

Creep

Fatigue failure

Work-hardening (cold working)

Annealing

Quench-hardening

Brittle material

Brittle fracture

Thermoplastic polymers

Thermosetting polymers

Elastic hysteresis

A2 Definitions (WJEC) – Answers

PH4

Item Definition

Period T for a point describing a circle

Time taken for one complete circuit.

Frequency f The number of circuits or cycles per second.

Eqn relating f and T T = 1/f

Centripetal forceThe description of an unbalanced force that causes a body to

move in a circle. The direction of the force is at right angles to the velocity of the body.

Centripetal acceleration

a = v2 / r, or ω2r or V ω

Centripetal force F = mv2 / r

Angular velocity ω.For a point describing a circle at uniform speed, the angular

velocity ω is equal to the angle θ swept out by the radius in time t divided by t . (ω = θ /t) UNIT: [rad] s-1

Simple harmonic motion (shm)

Shm occurs when an object moves such that its acceleration is always directed toward a fixed point and proportional to its

distance from the fixed point. (a = – ω 2x)Simple harmonic

motion (shm)(Alternative definition)

The motion of a point whose displacement x changes with time t according to x = A sin (ω t +ε), where A, ω and ε are constants.

[Variations of this kind are said to be sinusoidal.]

Period T for an oscillating body The time taken for one complete cycle.

Amplitude A of an oscillating object

The maximum value of the object’s displacement (from its equilibrium position).

Equation relating position, velocity

and accel and time for SHM

x = A sin(2 π f t + ε) or x = A sin(ω t + ε)v = A ω cos (ω t + ε)

a = - A ω 2sin (ω t + ε) or a = - ω 2 x

Phase

The phase of an oscillation is the angle (ω t + ε) in the equation x = A sin (ω t + ε). [ε is called the phase

constant.]UNIT: rad

Item Definition

Free oscillations[Natural oscillations]

Free oscillations occur when an oscillatory system (such as a mass on a spring, or a pendulum) is displaced and

released.[The frequency of the free oscillations is called the system’s

natural frequency.]

DampingDamping is the dying away, due to resistive forces, of the

amplitude of free oscillations.

Critical dampingCritical damping is the case when the resistive forces on the

system are just large enough to prevent oscillations occurring at all when the system is displaced and released.

Forced oscillationsThese occur when a sinusoidally varying ‘driving’ force is applied to an oscillatory system, causing it to oscillate with the frequency

of the applied force.

ResonanceIf, in forced vibrations, the frequency of the applied force is equal to the natural frequency of the system (e.g. mass on spring), the amplitude of the resulting oscillations is large. This is resonance.

MomentumThe momentum of an object is its mass multiplied by its velocity.

(p = mv). It is a vector. UNIT: kg m s-1

Newton’s laws of motion: 1st law

An object continues moving at constant speed in a straight line, or remains at rest, unless acted upon by a resultant force.

Newton’s laws of motion: 2nd law

The rate of change of momentum of an object is proportional to the resultant force acting on it, and takes place in the direction of

that force.

Newton’s laws of motion: 3rd law

If a body A exerts a force on a body B, then B exerts an equal and opposite force on A.

The principle of conservation of

momentum

The vector sum of the momenta of bodies in a system stays constant even if forces act between the bodies, provided there are

no forces from outside the system.

Elastic collision. A collision in which there is no change in total kinetic energy.

Inelastic collision. A collision in which kinetic energy is lost.

Boyle’s lawFor a fixed mass of gas at constant temperature [unless its density

is very high], the pressure varies inversely as the volume. pV = k

Charles’ LawFor a fixed mass of gas at constant pressure, the temperature is

directly proportional to the volume. V/T = k

Item Definition

Pressure LawFor a fixed mass of gas at constant volume, the pressure is

directly proportional to the temperature. P/T = k

Ideal gas

An ideal gas strictly obeys the equation of statepV = nRT, in which n is the number of moles, T is the kelvin

temperature and R is the molar gas constant. R = 8.31 J mol-1K-1. Except at very high densities a real gas approximates well to an

ideal gas.

The moleThe mole is the S.I. unit of ‘amount of substance’, n. It is the

amount containing as many particles (e.g. molecules) as there are atoms in 12 g of carbon12.

Avogadro constant NA

This is the number of particles per mole. (NA=6.021023 mol-1).

Internal energy, U, of a system

This is the sum of the kinetic and potential energies of the particles of the system.

Heat

This is energy flow from a region at higher temperature to a region at lower temperature, due to the temperature difference. In

thermodynamics we deal with heat going into or out of a system. It makes no sense to speak of heat in a system.

Work

If the system is a gas, in a cylinder fitted with a piston, the gas does work of amount pΔV when it exerts a pressure p and pushes

the piston out a small way, so the gas volume increases by ΔV. Work, like heat, is energy in transit from (or to) the system.

Temperature (in K) Average k.e. of particles

r.m.s. speed

The root mean square speed (ie the square root of the mean of the velocity of all the particles squared). The mean square speed (referred to as <c>2 or <v>2) can be calculated using either of the

expressions below.

Average ke of particles

½ m <c>2 = 3/2 kT (k = Bolzmann constant)

Pressure of gas in terms of molecular

propertiesp = 1/3 ρ<c>2

First law of thermodynamics

The increase, ΔU, in internal energy of a system isΔU = Q – W in which Q is the heat entering the system and W is the work done by the system. Any of the terms in the equation can be positive or negative, e.g. if 100 J of heat is lost from a system

Q = –100 J.

Specific heat capacity c.

The heat required, per kilogram, per degree Celsius or Kelvin, to raise the temperature of a substance.

UNIT: J kg-1 K-1 or J kg-1°C-1

Item Definition

Electric field strength E.

The force experienced per unit charge by a small positive charge placed in the field. Unit: V m-1 or N C-1.

Electric field strength (uniform

field)E = V/d

Electric field strength (spherical

field)E = Q / 4πε0r2

Coulomb’s Law

The electrostatic force, F, between two small bodies is proportional to the product of their charges, Q1 and Q2, and

inversely proportional to their separation, r. F = Q1Q2/4π ε 0r2 in which ε 0 is the permittivity of free space. ε 0 = 8.85 x 10-12Fm-1.

Gravitational field strength g.

The force experienced per unit mass by a mass placed in the field. Unit: m s-2 or N kg-1.

Gravitational field strength around

point massg = Gm / r2

Newton’s Law of Gravitation

F = GMm / r2

Electric potential VE.

Electric potential at a point is the work done per unit charge in bringing a positive charge from infinity to that point.

Unit: V. [= JC-1]

Electric potential at a point in a spherical field

E = Q / 4πε0r

Gravitational potential Vg.

Gravitational potential at a point is the work done per unit mass in bringing a mass from infinity to that point. Unit: Jkg-1.

Gravitational potential at a point in a spherical field

Vg = GM/r

Kepler’s laws of planetary motion: 1

Each planet moves in an ellipse with the Sun at one focus.

Kepler’s laws of planetary motion: 2

The line joining a planet to the centre of the Sun sweeps out equal areas in equal times.

Kepler’s laws of planetary motion:

3

T2, the square of the period of the planet’s motion, is proportional to r3, in which r is the semi-major axis of its ellipse. [For orbits

which are nearly circular, r may be taken as the mean distance of the planet from the Sun.]

Kepler’s 3rd Law in terms of circular

motion and Law of

v2/r = GM/ r2where v = 2πr/Tso

T2 = 4π2r3/GM

Item Definition

gravitation

Dark matterMatter which we can’t see, or detect by any sort of radiation, but

whose existence we infer from its gravitational effects.

Radial velocity of a star [in the context

of Doppler shift]

This is the component of a star’s velocity along the line joining it and an observer on the Earth.

PH5

Item Definition

CapacitorA capacitor is a pair of conducting plates separated by an insulator.

If a p.d. is placed across the plates, they acquire equal and opposite charges.

Capacitance, C, of a capacitor

capacitance = charge on either platep.d. between plates

Unit: F (farad) [= C V-1]

1 farad1F = 1 C / V

Capacitors in series

1/Ct = 1/C1 + 1/C2 + …

Capacitors in parallel

Ct = C1 + C2 + …

Energy stored on a capacitor

E = ½ CV2 = ½ QV = ½ Q2/C

Capacitance in terms of design of

capacitorC = ε0A/d

What is an exponential

decay?

This is where one variable increases or decreases by a constant ratio (percentage) in equal intervals of another variable (usually,

time)

Decay of I (or V or Q) with time as

capacitor discharges

I = Ioe-t / RC

Time constant, τ for a capacitor C

discharging through a resistance R

τ = RC

DielectricInsulator between the plates of a capacitor, also serving to make

the capacitance larger than if there were just empty space.

Magnetic field strength, B

(Magnetic flux density)

This is a vector quantity. Its direction is that in which the North pole of a freely-pivoted magnet points. Its magnitude is defined by

in which F is the force on a length l of wire carrying a

current I, placed perpendicular to the direction of the field. Unit: T (tesla) [= NA-1m-1]

1 tesla1T = 1 N A-1 m-1

Force on current carrying conductor at angle to a

magnetic fieldF = BIlsin

Force on charge q as it moves at angle

through a magnetic field

F = Bqvsin

Radius of orbit, r of charged particle,

mass m and charge q, moving in a circle

at speed v in magnetic field B

r = mv / Bq

Field strength of a long straight wire

B = μ0I / 2πa

Field strength of a solenoid

B = μ0nI

Hall voltage

When a magnetic field, B, is applied to conductor carrying a current I, at right angles to the field direction, a so-called Hall voltage appears across the specimen, at right angles to the B and I

directions.

Ampère A

The 18mpere is that current which, when flowing through two infinite, thin, parallel wires, one metre apart in vacuum, produces a force between the wires of exactly 2 10-7N per metre of length.

Unit: A.

Magnetic flux Φ.

If a single-turn coil of wire encloses an area A, and a magnetic field B makes an angle θ with the normal to the plane of the coil, the

magnetic flux through the coil is given by Φ = AB cos θ.Unit: weber (Wb) =Tm2.

1 weber 1Wb = 1Tm2

Flux linkage NΦIf the above coil consists of N turns, the flux linkage is given by N.

Unit: Wb or Wb turn.

Faraday’s law

When the flux linking an electrical circuit is changing, an emf is induced in the circuit of magnitude equal to the rate of change of

flux linkage.

[Note: The sign is from Lenz’s Law, see below]

Lenz’s Law.The direction of any current resulting from an induced emf is such as to oppose the change in flux linkage that is causing the current.

Root-mean-square (rms) value

If an alternating voltage is read at regular intervals throughout a cycle, giving the values V1, V2 … Vn, the rms p.d., Vrms, is defined as

Vrms 1n (V1

2 V22 .....Vn

2)

Ims, is defined similarly for current.[A Steady p.d. of magnitude Vrms (and a steady current

of Irms)  would give the same power dissipation in a resistor as the

alternating p.d. and current.”]

Alpha (α) radiationFast moving particles, helium nuclei, ejected from certain

radioactive nuclei.

Beta (β) radiationElectrons with speeds just less than the speed of light, ejected from

certain radioactive nuclei.

Gamma (γ) radiationPhotons of high energy (high frequency, short wavelength) ejected

from radioactive nuclei.

notationX is the chemical symbol of the element, A the mass number

(number of protons plus number of neutrons) and Z the atomic number (number of protons).

Half life of a

nuclide

The time taken for the number of radioactive nuclei N (or the activity A) to reduce to one half of the initial value. Unit: s.

Activity AThe rate of decay (number of disintegrations per second) of a

sample of radioactive nuclei. A = λNUnit: Becquerel (Bq) = s-1.

1 bequerel 1 disintegration per second

Decay constant λ

The constant which appears in the exponential decay law and determines the rate of decay (the greater λ, the

more rapid the rate of decay). λ is related to half life by

λ = ln2/ . Unit: s-1

Decay constant in terms of half life λ = ln2 / t1/2

Radioactive decay equation

N = No e-λt

Radio-isotopesIsotopes (of an element) have the same atomic number Z but

different mass number A; radio-isotopes are simply isotopes which are radioactive.

Unified atomic mass unit u.

The unified atomic mass unit is defined as exactly one twelfth of the mass of one atom of carbon 12. Thus one atom of has a mass

of exactly 12u.(1u = 10-3 kg / NA = 1.66 x10-27kg)

Electron volt (eV).

This is the energy transferred when an electron moves between two points with a potential difference of 1 volt between them.

1 eV = 1.6 x 10-19 JSo for an electron being accelerated it is the K.E. acquired when

accelerated through a pd of 1V.

Binding energy of a nucleus.

The energy that has to be supplied in order to dissociate a nucleus into its constituent nucleons. [It is therefore not energy which a

nucleus possesses.] Unit: J [or MeV]

Conservation of mass-energy

Energy cannot be lost or gained, only transferred from one form to another. We can measure the energy in a body by multiplying its

mass by c2.

Nuclear fission

Certain nuclei of large mass number (e.g. Uranium-235) can absorb a neutron and will then split into (usually) two smaller, beta-

radioactive, nuclei. Two or more neutrons are also released. The ‘fragments’ have large kinetic energies. This is nuclear fission.

Chain reactionA chain reaction is repeated events of nuclear fission in a sample of fissile material, initiated by neutrons released in previous fissions.

Option C

Item Definition

Crystal Solid in which atoms are arranged in a regular array.

Crystalline solidSolid consisting of a crystal, or of many crystals, usually

arranged randomly. The latter is strictly a polycrystalline solid. Metals are polycrystalline.

Amorphous solid

A truly amorphous solid would have atoms arranged quite randomly. Examples are rare. In practice we include solids such as glass or brick in which there is no long range order in the way

atoms are arranged, though there may be ordered clusters of atoms.

Polymeric solid Solid made up of chain-like molecules.

Hooke’s Law for rods and wires

The tension in a rod or wire is proportional to its extension from its natural length, provided the extension is not too great.

StressStress is the force per unit cross-sectional area when equal

opposing forces act on a body.Unit: pascal (Pa) or Nm-2.

StrainStrain is defined as the extension per unit length due to an

applied stress. Unit: none

The Young ModulusYoung Modulus

Unless otherwise indicated this is defined for the Hooke’s Law region. Unit: Pa or Nm-2

Ductile materialA material which can be drawn out into a wire. This implies that

plastic strain occurs under enough stress.

Elastic strainThis is strain that disappears when the stress is removed, that is

the specimen returns to its original size and shape.

Plastic (or inelastic) strain

This is strain that decreases only slightly when the stress is removed. In a metal it arises from the sliding of layers of atoms

over each other in the crystals.

Elastic limit

This is the point at which deformation ceases to be elastic. For a specimen it is usually measured by the maximum force, and for a material, by the maximum stress, before the strain ceases to

be elastic.

Dislocations in crystals

Certain faults in crystals which (if there are not too many) reduce the stress needed for planes of atoms to slide. The

easiest dislocation to picture is an edge dislocation: the edge of an intrusive, incomplete plane of atoms.

Grain boundariesThe boundaries between crystals (grains) in a polycrystalline

material.

Ductile fracture (necking)

The characteristic fracture process in a ductile material. Fracture of a rod or wire is preceded by local thinning,

increasing the stress.

CreepThis is an increase of strain with time, which may sometimes

occur even if the stress is kept constant.

Fatigue failure

If a metal specimen is subjected to many cycles of increasing and decreasing stress, even if the stress is always below the

elastic limit, the metal is likely to develop cracks and eventually break.

Work-hardening (cold working)

This is the process of causing inelastic strain in a metal, through at least one application of stress. It raises the elastic limit, but

reduces the extent of the ductile region between elastic limit and fracture.

AnnealingThis is the process of heating a metal, in order to alter its

mechanical properties. In the case of copper, it will restore most of the ductility destroyed by any previous work-hardening.

Quench-hardeningThis is the heating and rapid cooling of certain steels to produce

changes in the crystal structure. The effects include raising of the elastic limit.

Brittle materialMaterial with no region of plastic flow, which, under tension, fails

by brittle fracture.

Brittle fractureThis is the fracture under tension of brittle materials by means of

crack propagation.

Thermoplastic polymersWhen heated, thermoplastic polymers soften, and at higher

temperatures melt. They solidify on cooling. The process can be repeated.

Thermosetting polymersAfter one episode of heating and cooling, usually during

manufacture of an object, any further heating of a thermosetting polymer may result in cracking and/or charring, but not melting.

Elastic hysteresis

When a material such as rubber is put under stress and the stress is then relaxed, the stress-strain graphs for increasing

and decreasing stress do not coincide, but form a loop. This is hysteresis (literally, lag).