Welsh Board A2 Syllabus 

Unit 3 Unit 4 

In the exam, you are expected to demonstrate and apply knowledge of: 

Unit 3 Oscillations and Nuclei 

1. Circular Motion 

(a) 
The terms period of rotation, frequency; 

(b) 
the definition of the unit radian as a measure of angle; 

(c) 
the use of the radian as a measure of angle; 

(d) 
the definition of angular velocity, ω, for an object performing circular motion and performing simple harmonic motion; 

(e) 
the idea that the centripetal force is the resultant force acting on a body moving at constant speed in a circle; 

(f) 
the centripetal force and acceleration are directed towards the centre of the circular motion; 

(g) 
the use of the following equations relating to circular motion:


Further examples of circular motion can be found in Further Mechanics Tutorial 2 

2. Vibrations 

(a) 
The definition of simple harmonic motion as a statement in words; 

(b) 
a = ω^{2}x as a mathematical defining equation of simple harmonic motion; 

(c) 
the graphical representation of the variation of acceleration with displacement during simple harmonic motion; 

(d) 
x = A cos (ωt + ε ) as a solution to ω^{2}x ; (k used in the notes) 

(e) 
the terms frequency, period, amplitude and phase; 

(f) 
period as: ; 

(g) 
v = A sin (ωt + ε) for the velocity during simple harmonic motion; 

(h) 
the graphical representation of the changes in displacement and velocity with time during simple harmonic motion; 

(i) 
the equation:
for the period of a system having stiffness (force per unit extension) k and mass m; 
Further Mechanics 5 
(j) 
the equation:
for the period of a simple pendulum; 

(k) 
the graphical representation of the interchange between kinetic energy and potential energy during undamped simple harmonic motion, and perform simple calculations on energy changes; 

(l) 
free oscillations and the effect of damping in real systems; 

(m) 
practical examples of damped oscillations; 

(n) 
the importance of critical damping in appropriate cases such as vehicle suspensions; 

(o) 
forced oscillations and resonance, and to describe practical examples; 

(p) 
the variation of the amplitude of a forced oscillation with driving frequency and that increased damping broadens the resonance curve; 

(q) 
circumstances when resonance is useful, for example, circuit tuning, microwave cooking and other circumstances in which it should be avoided, for example, bridge design. 

3. Kinetic Theory 

(a) 
The equation of state for an ideal gas expressed as pV = nRT where R is the molar gas constant and pV = NkT where k is the Boltzmann constant; 

(b) 
the assumptions of the kinetic theory of gases which includes the random distribution of energy among the molecules; 

(c) 
the idea that molecular movement causes the pressure exerted by a gas, and use:
where N is the number of molecules; 

(d) 
the definition of Avogadro constant N_{A} and hence the mole; 

(e) 
the idea that the molar mass M is related to the relative molecular mass M_{r} by:
and that the number of moles n is given by total mass ÷ molar mass; 

(f) 


4. Thermal Physics 

(a) 
The idea that the internal energy of a system is the sum of the potential and kinetic energies of its molecules; 

(b) 
absolute zero being the temperature of a system when it has minimum internal energy; 

(c) 
the internal energy of an ideal monatomic gas being wholly kinetic so it is given by:


(d) 
the idea that heat enters or leaves a system through its boundary or container wall, according to whether the system's temperature is lower or higher than that of its surroundings, so heat is energy in transit and not contained within the system; 

(e) 
the idea that if no heat flows between systems in contact, then they are said to be in thermal equilibrium, and are at the same temperature; 

(f) 
the idea that energy can enter or leave a system by means of work, so work is also energy in transit; 

(g) 
the equation W = pDV can be used to calculate the work done by a gas under constant pressure; 

(h) 
the idea that even if p changes, W is given by the area under the p – V graph; 

(i) 
the use of the first law of thermodynamics, in the form DU = Q  W and know how to interpret negative values of ΔU, Q, and W; 

(j) 
the idea that for a solid (or liquid), W is usually negligible, so Q = ΔU; 

(k) 
Q = mcDθ , for a solid or liquid, and this is the defining equation for specific heat capacity, c. 

5. Nuclear Decay 

(a) 
The spontaneous nature of nuclear decay; the nature of α, β and γ radiation, and equations to represent the nuclear transformations using the isotope notation; 

(b) 
different methods used to distinguish between α, β and γ radiation and the connections between the nature, penetration and range for ionising particles; 

(c) 
how to make allowance for background radiation in experimental measurements; 

(d) 
the concept of the halflife, T_{˝}; 
(Inverse Square Law) 
(e) 
the definition of the activity, A, and the Becquerel; 

(f) 
the decay constant, λ, and the equation A = λ N; 

(g) 
the exponential law of decay in graphical and algebraic form:
where x is the number of halflives elapsed – not necessarily an integer; 

(h) 
the derivation and use of: . 

6. Nuclear Energy 

(a) 
The association between mass and energy and that E = mc^{2}; 

(b) 
the binding energy for a nucleus and hence the binding energy per nucleon, making use, where necessary, of the unified atomic mass unit (u); 

(c) 
how to calculate binding energy and binding energy per nucleon from given masses of nuclei; 

(d) 
the conservation of mass / energy to particle interactions – for example: fission, fusion; 

(e) 
the relevance of binding energy per nucleon to nuclear fission and fusion making reference when appropriate to the binding energy per nucleon versus nucleon number curve. 

Unit 4 Fields and Options 

1. Capacitance 

(a) 
The idea that a simple parallel plate capacitor consists of a pair of equal parallel metal plates separated by a vacuum or air; 

(b) 
a capacitor storing energy by transferring charge from one plate to the other, so that the plates carry equal but opposite charges (the net charge being zero); 

(c) 
the definition of capacitance as: ; 

(d) 
the use of
for a parallel plate capacitor, with no dielectric; 

(e) 
the idea that a dielectric increases the capacitance of a vacuumspaced capacitor; 

(f) 
the E field within a parallel plate capacitor being uniform and the use of the equation: ; 

(g) 
the equation U = 1/2 QV for the energy stored in a capacitor; (E, not U is used in the notes.) 

(h) 
the equations for capacitors in series and in parallel; 

(i) 
the process by which a capacitor charges and discharges through a resistor; 

(j) 
the equations:
where RC is the time constant. 

2. Electrostatic and Gravitational Fields of Force 

(a) 
The features of electric and gravitational fields as specified in the table below: ; 
(Gravity Force) (Energy in Gravity Fields)
(Electrostatic Force) (Energy in Electric Fields) 
(b) 
the idea that the gravitational field outside spherical bodies such as the Earth is essentially the same as if the whole mass were concentrated at the centre; 

(c) 
field lines (or lines of force) giving the direction of the field at a point, thus, for a positive point charge, the field lines are radially outward; 

(d) 
equipotential surfaces joining points of equal potential and are therefore spherical for a point charge; 

(e) 
how to calculate the net potential and resultant field strength for a number of point charges or point masses; 

(f) 
the equation ΔU_{P} = mgΔh for distances over which the variation of g is negligible. 

3. Orbits and the Wider Universe 

(a) 
Kepler's three laws of planetary motion; 
Fields 3 
(b) 
Newton's law of gravitation:
in simple examples, including the motion of planets and satellites; 
Fields 1 
(c) 
how to derive Kepler's 3rd law, for the case of a circular orbit from Newton's law of gravity and the formula for centripetal acceleration; 
Fields 3 
(d) 
how to use data on orbital motion, such as period or orbital speed, to calculate the mass of the central object; 

(e) 
how the orbital speeds of objects in spiral galaxies implies the existence of dark matter; 

(f) 
how the recently discovered Higgs boson may be related to dark matter; 

(g) 
how to determine the position of the centre of mass of two spherically symmetric objects, given their masses and separation, and calculate their mutual orbital period in the case of circular orbits; 

(h) 
the Doppler relationship in the form: ; 

(i) 
how to determine a star's radial velocity (i.e. the component of its velocity along the line joining it and an observer on the Earth) from data about the Doppler shift of spectral lines; 

(j) 
the use of data on the variation of the radial velocities of the bodies in a double system (for example, a star and orbiting exoplanet) and their orbital period to determine the masses of the bodies for the case of a circular orbit edge on as viewed from the Earth; 

(k) 
how the Hubble constant (H_{0}) relates galactic radial velocity (v) to distance (D) and it is defined by v = H_{0}D; 

(l) 
why 1/H_{0} approximates the age of the universe; 

(m) 
how the equation:
for the critical density of a 'flat' universe can be derived very simply using conservation of energy. 

4. The Nature of Waves 

(a) 
The idea that a progressive wave transfers energy without any transfer of matter; 
Waves 1 
(b) 
the difference between transverse and longitudinal waves; 
Waves 2 
(c) 
the term polarisation; 

(d) 
the terms in phase and in antiphase; 
Waves 1 
(e) 
the terms displacement, amplitude, wavelength, frequency, period and velocity of a wave; 

(f) 
graphs of displacement against time, and displacement against position for transverse waves only; 
Waves 2 
(g) 
the equation c = fλ; 
Waves 1 
(h) 
the idea that all points on wavefronts oscillate in phase, and that wave propagation directions (rays) are at right angles to wavefronts. 

5. Wave Properties 

(a) 
Diffraction occurring when waves encounter slits or obstacles; 
Waves 8 
(b) 
the idea that there is little diffraction when λ is much smaller than the dimensions of the obstacle or slit; 

(c) 
the idea that if λ is equal to or greater than the width of a slit, waves spread as roughly semicircular wavefronts, but if λ is less than the slit width the main beam spreads through less than 180° 

(d) 
how two source interference occurs; 
Waves 7 
(e) 
the historical importance of Young’s experiment; 
Turning Points 3 
(f) 
the principle of superposition, giving appropriate sketch graphs; 
Waves 3 
(g) 
the path difference rules for constructive and destructive interference between waves from in phase sources; 
Waves 7 
(h) 
the use of: ; (Note that the terms w and s are used in the notes) 

(i) 
the derivation and use of d sin θ = nλ for a diffraction grating; 
Waves 8 
(j) 
the idea that for a diffraction grating a very small d makes beams (“orders”) much further apart than in Young’s experiment, and that the large number of slits makes the bright beams much sharper; 

(k) 
the idea that coherent sources are monochromatic with wavefronts continuous across the width of the beam and, (when comparing more than one source) with a constant phase relationship; 
Waves 7 
(l) 
examples of coherent and incoherent sources; 

(m) 
the idea that for two source interference to be observed, the sources must have a zero or constant phase difference and have oscillations in the same direction; 

(n) 
the differences between stationary and progressive waves; 
Waves 4 
(o) 
the idea that a stationary wave can be regarded as a superposition of two progressive waves of equal amplitude and frequency, travelling in opposite directions, and that the internodal distance is λ/2. 

6. Refraction of Light 

(a) 
the refractive index, n, of a medium being defined as c/v, in which v is the speed of light in the medium and c is the speed of light in a vacuum 
Waves 6 
(b) 
the use of the equations: n_{1}v_{1} = n_{2}v_{2} and n_{1} sin θ_{1} = n_{2} sin θ_{2} (regarded as Snell’s law); 

(c) 
how Snell's law relates to the wave model of light propagation and for diagrams of plane waves approaching a plane boundary obliquely, and being refracted; 

(d) 
the conditions for total internal reflection; 

(e) 
the derivation and use of the equation for the critical angle: ; 

(f) 
how to apply the concept of total internal reflection to multimode optical fibres; 

(g) 
the problem of multimode dispersion with optical fibres in terms of limiting the rate of data transfer and transmission distance; 

(h) 
how the introduction of monomode optical fibres has allowed for much greater transmission rates and distances. 

7. Photons 

(a) 
The fact that light can be shown to consist of discrete packets (photons) of energy; 
Quantum Physics 1 
(b) 
how the photoelectric effect can be demonstrated; 

(c) 
how a vacuum photocell can be used to measure the maximum kinetic energy, E_{k max}, of emitted electrons in eV and hence in J; 
Quantum Physics 2 
(d) 
the graph of E_{k max} against frequency of illuminating radiation; 

(e) 
how a photon picture of light leads to Einstein's equation:
and how this equation correlates with the graph of E_{k max} against frequency; 

(f) 
the fact that the visible spectrum runs approximately from 700 nm (red end) to 400 nm (violet end) and the orders of magnitude of the wavelengths of the other named regions of the electromagnetic spectrum; 
Particles 3 
(g) 
typical photon energies for these radiations; 

(h) 
how to produce line emission and line absorption spectra from atoms; 
Quantum Physics 3 
(i) 
the appearance of such spectra as seen in a diffraction grating; 
Waves 8 
(j) 
simple atomic energy level diagrams, together with the photon hypothesis, line emission and line absorption spectra; 
Quantum Physics 4 
(k) 
how to determine ionisation energies from an energy level diagram; 

(l) 
the demonstration of electron diffraction and that particles have a wavelike aspect; 
Quantum Physics 6 
(m) 
the use of the relationship:
for both particles of matter and photons; 

(n) 
the calculation of radiation pressure on a surface absorbing or reflecting photons. 
Quantum Physics 7 
8. LASERS 

(a) 
The process of stimulated emission and how this process leads to light emission that is coherent; 
Quantum Physics 8 
(b) 
the idea that a population inversion (N_{2} > N_{1}) is necessary for a laser to operate; 

(c) 
the idea that a population inversion is not (usually) possible with a 2level energy system 

(d) 
how a population inversion is attained in 3 and 4level energy systems; 

(e) 
the process of pumping and its purpose; 

(f) 
the structure of a typical laser i.e. an amplifying medium between two mirrors, one of which partially transmits light; 

(g) 
the advantages and uses of a semiconductor laser i.e. small, cheap, far more efficient than other types of laser, and it is used for CDs, DVDs, telecommunication etc 

And that is it for the AS level 