  Welsh Board A2 Syllabus Home       AS       A2   Options Unit 3    Unit 4 In the exam, you are expected to demonstrate and apply knowledge of: Oscillations and Nuclei 1.  Circular Motion (a) The terms period of rotation, frequency; Further Mechanics 1 (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; Further Mechanics 4 (b) a = -ω2x 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 -ω2x ;  (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; Further Mechanics 6 (l) free oscillations and the effect of damping in real systems; Further Mechanics 3 (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; Thermal Physics 3 (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 NA and hence the mole; Thermal Physics 2 (e) the idea that the molar mass M is related to the relative molecular mass Mr by: and that the number of moles n is given by total mass ÷ molar mass; (f) Thermal Physics 3 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; Thermal Physics 3 (b) absolute zero being the temperature of a system when it has minimum internal energy; Thermal Physics 2 (c) the internal energy of an ideal monatomic gas being wholly kinetic so it is given by: Thermal Physics 3 (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; Engineering Physics 6 (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; Engineering Physics 3   Engineering Physics 4 (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. Thermal Physics 1 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 half-life, T½; (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 half-lives elapsed – not necessarily an integer; (h) the derivation and use of: . 6.  Nuclear Energy (a) The association between mass and energy and that E = mc2; (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. Top 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 vacuum-spaced 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 ΔUP = 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; (b) Newton's law of gravitation: in simple examples, including the motion of planets and satellites; (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; (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 exo-planet) 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 (H0) relates galactic radial velocity (v) to distance (D) and it is defined by v = H0D; (l) why 1/H0 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. Top 4.  Magnetic Fields (a) How to determine the direction of the force on a current carrying conductor in a magnetic field; (b) how to calculate the magnetic field, B, by considering the force on a current carrying conductor in a magnetic field i.e. understand how to use F = BIl sinθ; (c) how to use F = Bqv sinθ for a moving charge in a magnetic field; (d) the processes involved in the production of a Hall voltage and understand that VH ∝ B for constant I; (e) the shapes of the magnetic fields due to a current in a long straight wire and a long solenoid; (f) the equations: for the field strengths due to a long straight wire and in a long solenoid; (In the notes, r is used, not a for separation) (g) the fact that adding an iron core increases the field strength in a solenoid; (h) the idea that current carrying conductors exert a force on each other and to predict the directions of the forces (i) quantitatively, how ion beams of charged particles, are deflected in uniform electric and magnetic fields; (j) the motion of charged particles in magnetic and electric fields in linear accelerators, cyclotrons and synchrotrons. Top 5.  Electromagnetic Induction (a) The definition of magnetic flux as Φ = AB cos θ and flux linkage = NΦ; (b) the laws of Faraday and Lenz; (c) how to apply the laws of Faraday and Lenz (i.e. emf = - rate of change of flux linkage) (d) the idea that an emf is induced in a linear conductor moving at right angles to a uniform magnetic field; (e) qualitatively, how the instantaneous emf induced in a coil rotating at right angles to a magnetic field is related to the position of the coil, flux density, coil area and angular velocity. Top Now go on to the Options