  Cambridge Pre-University Physics Syllabus Waves    Superposition   Atomic and Nuclear Processes   Quantum Ideas   Rotational Dynamics Oscillations    Electric Fields    Gravitation   Electromagnetism   Special Relativity Syllabus statements marked with an asterisk (*) are only assessed in Paper 3 Section 2. Equations are written in italics . When you see the word recall (underlined), you have to remember the equation.  It will not be given on the data sheet. In the exam, you are expected to be able to: 1.  Mechanics (a) Distinguish between scalar and vector quantities and give examples of each; (b) resolve a vector into two components at right angles to each other by drawing and by calculation; (c) combine any number of coplanar vectors at any angle to each other by drawing; (d) calculate the moment of a force and use the conditions for equilibrium to solve problems (restricted to coplanar forces); (See and for more applications of moments of forces.) (e) construct displacement-time and velocity-time graphs for uniformly accelerated motion; (f) identify and use the physical quantities derived from the gradients of displacement-time and areas and gradients of velocity-time graphs, including cases of non-uniform acceleration; (g) recall and use: ; (In the notes, the code s  is used for displacement instead of x .) (h) recognise and use the kinematic equations for motion in one dimension with constant acceleration: ; (i) recognise and make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity; (See also for Free Fall, and for Friction and Drag.) (j) recognise that internal forces on a collection of objects sum to zero vectorially; (k) recall and interpret statements of Newton’s laws of motion; (l) recall and use F = ma in situations where mass is constant (m) understand the effect of kinetic friction and static friction; (n) recall and use Fk = μkN  and Fs = μsN, where N is the normal contact force and μk and μs are the coefficients of kinetic friction and static friction, respectively; (o) recall and use the independent effects of perpendicular components of a force; (p) recall and use p = mv and apply the principle of conservation of linear momentum to problems in one dimension; (q) distinguish between elastic and inelastic collisions; (r) relate resultant force to rate of change of momentum in situations where mass is constant and recall and use: (s) recall and use the relationship impulse = change in momentum (t) recall and use the fact that the area under a force-time graph is equal to the impulse; (u) apply the principle of conservation of linear momentum to problems in two dimensions; (v) recall and use density = mass ÷ volume; (w) recall and use pressure = force ÷ area; (x) recall and use p = ρgh for pressure due to a liquid. Top 2.  Gravitational Fields (a) Recall and use the fact that the gravitational field strength g is equal to the force per unit mass and hence that weight: W = mg ; (b) recall that the weight of a body appears to act from its centre of gravity; (c) sketch the field lines for a uniform gravitational field (such as near the surface of the Earth); (d) explain the distinction between gravitational field strength and force and explain the concept that a field has independent properties. 3.  Deformation of Solids (a) Distinguish between elastic and plastic deformation of a material; Materials 2 (b) recall the terms brittle, ductile, hard, malleable, stiff, strong and tough, explain their meaning and give examples of materials exhibiting such behaviour; (c) explain the meaning of, and recall and use the appropriate equations to calculate tensile/compressive stress, tensile/compressive strain, spring constant, strength, breaking stress, stiffness and Young modulus; Materials 3 (d) draw force-extension, force-compression and tensile/compressive stress-strain graphs, and explain the meaning of the limit of proportionality, elastic limit, yield point, breaking force and breaking stress; (e) state Hooke’s law and identify situations in which it is obeyed; (f) account for the stress-strain graphs of metals and polymers in terms of the microstructure of the material. 4.  Energy Concepts (a) Recall and use the concept of work in terms of the product of a force and a displacement in the direction of that force, including situations where the force is not along the line of motion; Mechanics 13 (b) calculate the work done in situations where the force is a function of displacement using the area under a force-displacement graph; Mechanics 13 (c) understand that a heat engine is a device that is supplied with thermal energy and converts some of this energy into useful work; Engineering Physics 3 (d) calculate power from the rate at which work is done or energy is transferred; Mechanics 13 (e) recall and use P = Fv ; Mechanics 13 (f) recall and use ΔE = mgΔh for the gravitational potential energy transferred near the Earth’s surface; Mechanics 15 (g) recall and use gΔh as change in gravitational potential; Mechanics 15 (h) recall and use for the elastic strain energy in a deformed material sample obeying Hooke’s law; Materials 2 (i) use the area under a force-extension graph to determine elastic strain energy; Materials 2 (j) derive, recall and use: ; Materials 2 (k) derive, recall and use: for the kinetic energy of a body; Mechanics 15 (l) apply the principle of conservation of energy to solve problems; Mechanics 15 (m) recall and use: Mechanics 14 (n) recognise and use ΔE = mc Δθ, where c is the specific heat capacity; Thermal Physics 1 (o) recognise and use ΔE = mL, where L is the specific latent heat of fusion or of vaporisation. Thermal Physics 1 5.  Electricity (a) Discuss electrical phenomena in terms of electric charge; Electricity 1 (b) describe electric current as the rate of flow of charge and recall and use: ; Electricity 1 (c) understand potential difference in terms of energy transfer and recall and use: Electricity 1 (d) recall and use the fact that resistance is defined by: and use this to calculate resistance variation for a variety of voltage-current characteristics; Electricity 1 (e) define and use the concepts of emf and internal resistance and distinguish between emf and terminal potential difference; Electricity 8 (f) derive, recall and use E = I (R + r ) and E = V + Ir ; Electricity 8 (g) derive, recall and use P = VI and W = VIt , and derive and use P = I 2R ; Electricity 5 (h) recall and use: ; Electricity 4 (i) recall the formula for the combined resistance of two or more resistors in series RT = R1 + R2 + … and use it to solve problems; Electricity 7 (j) recall the formula for the combined resistance of two or more resistors in parallel: and use it to solve problems; Electricity 7 (k) recall Kirchhoff’s first and second laws and apply them to circuits containing no more than two supply components and no more than two linked loops; Electricity 7 (l) appreciate that Kirchhoff’s first and second laws are a consequence of the conservation of charge and energy, respectively; Electricity 7 (m) use the idea of the potential divider to calculate potential differences and resistances. Electricity 6 6.  Waves (a) Understand and use the terms displacement, amplitude, intensity, frequency, period, speed and wavelength; Waves 1 (b) recall and apply: to a variety of situations not limited to waves; Waves 1 (c) recall and use the wave equation v = f λ; Waves 1 (d) recall that a sound wave is a longitudinal wave which can be described in terms of the displacement of molecules or changes in pressure; Waves 2 (e) recall that light waves are transverse electromagnetic waves, and that all electromagnetic waves travel at the same speed in a vacuum; Waves 2 (f) recall the major divisions of the electromagnetic spectrum in order of wavelength, and the range of wavelengths of the visible spectrum; Waves 2 (g) recall and use that the intensity of a wave is directly proportional to the square of its amplitude; Waves 1 (h) use graphs to represent transverse and longitudinal waves, including standing waves; Waves 1 (i) explain what is meant by a plane-polarised wave; Waves 2 (j) recall Malus’ law (intensity ∝ cos2 θ) and use it to calculate the amplitude and intensity of transmission through a polarising filter; (A more detailed discussion of polarisation is given in Physics 6 Tutorial 8) Waves 2 (k) recognise and use the expression for refractive index: ; Waves 6 (l) derive and recall: and use it to solve problems; Waves 6 (m) recall that optical fibres use total internal reflection to transmit signals; Waves 6 (n) recall that, in general, waves are partially transmitted and partially reflected at an interface between media. Waves 6 7.  Superposition (a) Explain and use the concepts of coherence, path difference, superposition and phase; Waves 1 (b) understand the origin of phase difference and path difference, and calculate phase differences from path differences; Waves 7 (c) understand how the phase of a wave varies with time and position; Physics 6 Tutorial 6 (d) determine the resultant amplitude when two waves superpose, making use of phasor diagrams; (Link to my other website.) Link (e) explain what is meant by a standing wave, how such a wave can be formed, and identify nodes and antinodes; (See also for the physics of music.) Waves 4 (f) understand that a complex wave may be regarded as a superposition of sinusoidal waves of appropriate amplitudes, frequencies and phases; Physics 6 Tutorial 6 (g) recall that waves can be diffracted and that substantial diffraction occurs when the size of the gap or obstacle is comparable to the wavelength; Waves 8 (h) recall qualitatively the diffraction patterns for a slit, a circular hole and a straight edge; Waves 8 (i) recognise and use the equation nλ = b sin θ to locate the positions of destructive superposition for single slit diffraction, where b is the width of the slit; (In the notes, a  is used for slit width.  I think there is a typo in the syllabus.  The equation nλ = d  sin θ is used for multiple slits.  The correct equation for a single slit is λ = a  sin θ .) Waves 8 (j) recognise and use the Rayleigh criterion: resolving power of a single aperture, where b is the width of the aperture; ( In the notes, a  is the aperture width. ) Waves 8 (k) describe the superposition pattern for a diffraction grating and for a double slit and use the equation nλ = d sin θ to calculate the angles of the principal maxima; Waves 8 (l) use the equation: for double-slit interference using light. (In the notes, the code w  is used instead of a , and s  is used instead of x  .) Waves 7 8.  Atomic and Nuclear Processes (a) Understand the importance of the α-particle scattering experiment in determining the nuclear model; Nuclear Physics 2 (b) describe atomic structure using the nuclear model; Particle Physics 1 (c) show an awareness of the existence and main sources of background radiation; Nuclear Physics 1 (d) recognise nuclear radiations (α, β–, γ) from their penetrating power and ionising ability, and recall the nature of these radiations; Nuclear Physics 1 (e) write and interpret balanced nuclear transformation equations using standard notation; Nuclear Physics 3 (f) understand and use the terms nucleon number (mass number), proton number (atomic number), nuclide and isotope; Particles Physics 2 (g) appreciate the spontaneous and random nature of nuclear decay; Nuclear Physics 5 (h) define and use the concept of activity as the number of decays occurring per unit time; Nuclear Physics 5 (i) understand qualitatively how a constant decay probability leads to the shape of a radioactive decay curve; Nuclear Physics 5 (j) determine the number of nuclei remaining or the activity of a source after a time which is an integer number of half-lives Nuclear Physics 5 (k) understand the terms thermonuclear fusion, induced fission and chain reaction Nuclear Physics 7 (l) recall that thermonuclear fusion and the fission of uranium-235 and plutonium-239 release large amounts of energy. Nuclear Physics 7 9.  Quantum Ideas (a) Recall that, for monochromatic light, the number of photoelectrons emitted per second is proportional to the light intensity and that emission occurs instantaneously; Particle Physics 3 (b) recall that the kinetic energy of photoelectrons varies from zero to a maximum, and that the maximum kinetic energy depends on the frequency of the light, but not on its intensity; Quantum Physics 2 (c) recall that photoelectrons are not ejected when the light has a frequency lower than a certain threshold frequency which varies from metal to metal Quantum Physics 1 Quantum Physics 2 (d) understand how the wave description of light fails to account for the observed features of the photoelectric effect and that the photon description is needed; Particle Physics 3 (e) recall that the absorption of a photon of energy can result in the emission of a photoelectron; Quantum Physics 2 (f) recall and use E = hf ; Particle Physics 3 (g) understand and use the terms threshold frequency and work function and recall and use: ; Quantum Physics 2 (h) understand the use of stopping potential to find the maximum kinetic energy of photoelectrons and convert energies between joules and electron-volts; Quantum Physics 1 (i) plot a graph of stopping potential against frequency to determine the Planck constant, work function and threshold frequency; Quantum Physics 2 (j) understand the need for a wave model to explain electron diffraction; Quantum Physics 6 (k) recognise and use: for the de Broglie wavelength. Quantum Physics 6 10.  Rotational Dynamics (a) Define and use the radian; Further Mechanics 1 (b) understand the concept of angular velocity, and recall and use the equations: ; Further Mechanics 1 (c) derive, recall and use the equations for centripetal acceleration: ; Further Mechanics 1 (d) recall that F = ma applied to circular motion gives resultant force: ; (More examples of applications of circular motion can be found in .) Further Mechanics 1 (e) describe qualitatively the motion of a rigid solid object under the influence of a single force in terms of linear acceleration and rotational acceleration; Engineering Physics 1 (f) *recall and use: to calculate the moment of inertia of a body consisting of three or fewer point particles fixed together; Engineering Physics 1 (g) *use integration to calculate the moment of inertia of a ring, a disk and a rod; Engineering Physics 1 B (h) *deduce equations for rotational motion by analogy with Newton’s laws for linear motion, including: (In the notes, τ (tau) is used as the Physics Code for torque rather than Γ (Gamma).) Engineering Physics 1 (i) *apply the laws of rotational motion to perform kinematic calculations regarding a rotating object when the moment of inertia is given. Engineering Physics 1 11.  Oscillations (a) Recall the condition for simple harmonic motion and hence identify situations in which simple harmonic motion will occur; Further Mechanics 4 (b) *show that the condition for simple harmonic motion leads to a differential equation of the form: and that x = A cos ωt  is a solution to this equation; Further Mechanics 4 (c) *use differential calculus to derive the expressions v = –A ω sin ωt and a = –Aω2 cos ωt  for simple harmonic motion; Further Mechanics 4 (d) *recall and use the expressions x = A cos ωt,  v = –Aω sin ωt, a = –A ω2 cos ωt , and F = –mω2x to solve problems; Further Mechanics 4 (e) recall and use: as applied to a simple harmonic oscillator; (SHM in a pendulum and a spring oscillator is covered in ) (The link between SHM and Circular Motion is discussed in ) Further Mechanics 1 (f) understand the phase differences between displacement, velocity and acceleration in simple harmonic motion; Further Mechanics 4 (g) *show that the total energy of an undamped simple harmonic system is given by: and recognise that this is a constant; Further Mechanics 6 (h) recall and use: to solve problems; Further Mechanics 6 (i) distinguish between free, damped and forced oscillations; Further Mechanics 3 (j) recall how the amplitude of a forced oscillation changes at and around the natural frequency of a system and describe, qualitatively, how damping affects resonance. Further Mechanics 3 12.  Electric Fields (a) Explain what is meant by an electric field and recall and use: for electric field strength; Capacitors 1 (b) recall that applying a potential difference to two parallel plates stores charge on the plates and produces a uniform electric field in the central region between them; Capacitors 1 (c) derive and use the equations Fd = QV and: for a charge moving through a potential difference in a uniform electric field; Fields 4 (d) recall that the charge stored on parallel plates is proportional to the potential difference between them; Capacitors 1 (e) recall and use for capacitance; Capacitors 1 (f) derive, recall and use W = ½QV  for the energy stored by a capacitor, derive the equation from the area under a graph of charge stored against potential difference, and derive and use related equations such as W = ½ CV 2 ; Capacitors 1 (g) analyse graphs of the variation with time of potential difference, charge and current for a capacitor discharging through a resistor; Capacitors 2 (h) define and use the time constant of a discharging capacitor; Capacitors 2 (i) analyse the discharge of a capacitor using equations of the form: ; Capacitors 2 (j) understand that the direction and electric field strength of an electric field may be represented by field lines (lines of force), and recall the patterns of field lines that represent uniform and radial electric fields; Fields 4 (k) understand electric potential and equipotentials; Fields 5 (l) understand the relationship between electric field and potential gradient, and recall and use: Fields 5 (m) recognise and use: for point charges; Fields 4 (n) derive and use: for the electric field due to a point charge; Fields 4 (o) *use integration to derive: from for point charges; Fields 5 (p) *recognise and use: for the electrostatic potential energy for point charges. Fields 5 13.  Gravitation (a) State Kepler’s laws of planetary motion:   (i) planets move in elliptical orbits with the Sun at one focus  (ii) the Sun-planet line sweeps out equal areas in equal times (iii) the orbital period squared of a planet is proportional to its mean distance from the Sun cubed; Fields 3 (b) Recognise and use: ; Fields 1 (c) use Newton’s law of gravity and centripetal force to derive r 3 ∝ T 2 for a circular orbit; Fields 3 (d) understand energy transfer by analysis of the area under a gravitational force-distance graph; Fields 2 (e) derive and use: for the magnitude of the gravitational field strength due to a point mass Fields 1 (f) recall similarities and differences between electric and gravitational fields; Fields 2 (g) recognise and use the equation for gravitational potential energy for point masses: ; Fields 2 (h) calculate escape velocity using the ideas of gravitational potential energy, or area under a force-distance graph and energy transfer; Fields 3 (i) calculate the distance from the centre of the Earth and the height above its surface required for a geostationary orbit. Fields 3 Top (a) Understand and use the terms magnetic flux density, flux and flux linkage; Magnetic Fields 4 (b) understand that magnetic fields are created by electric currents; Magnetic Fields 1 (c) recognise and use F = BIl sin θ; Magnetic Fields 1 (d) recognise and use F = BQv sin θ; Magnetic Fields 3 (e) use Fleming’s left-hand rule to solve problems; Magnetic Fields 1 (f) explain qualitatively the factors affecting the emf induced across a coil when there is relative motion between the coil and a permanent magnet or when there is a change of current in a primary coil linked with it Magnetic Fields 5 (g) recognise and use: and explain how it is an expression of Faraday’s and Lenz’s laws Magnetic Fields 5 (h) derive, recall and use: for the radius of curvature of a deflected charged particle Magnetic Fields 3 (i) explain the Hall effect, and derive and use V = Bvd. Magnetic Fields 3B Top 15.  Special Relativity (a) *Recall that Maxwell’s equations describe the electromagnetic field and predict the existence of electromagnetic waves that travel at the speed of light (Maxwell’s equations are not required); Turning Points 3 (b) *recall that analogies with mechanical wave motion led most physicists to assume that electromagnetic waves must be vibrations in an electromagnetic medium (the aether) filling absolute space; Turning Points 5 (c) *recall that experiments to measure variations in the speed of light caused by the Earth’s motion through the aether gave null results; Turning Points 5 (d) *understand that Einstein’s theory of special relativity dispensed with the aether and postulated that the speed of light is a universal constant; Turning Points 5 (e) *state the postulates of Einstein’s special principle of relativity; Turning Points 6 (f) *explain how Einstein’s postulates lead to the idea of time dilation and length contraction that undermines the idea of absolute time and space; Turning Points 6 (g) *recognise and use: Turning Points 6 (h) *understand that two events which are simultaneous in one frame of reference may not be simultaneous in another; explain this in terms of the fundamental postulates of relativity and distinguish this from the phenomenon of time dilation. (Evidence for Einstein's Theory of Special Relativity is discussed in ) Turning Points 6 Top 16.  Molecular Kinetic Theory (a) Explain how empirical evidence leads to the gas laws and to the idea of an absolute scale of temperature; Thermal Physics 2 (b) use the units Kelvin and degrees Celsius and convert from one to the other; Thermal Physics 2 (c) recognise and use the Avogadro constant N A = 6.02 × 1023 mol–1; Thermal Physics 2 (d) recall and use pV = nRT  as the equation of state for an ideal gas; Thermal Physics 2 (e) describe Brownian motion and explain it in terms of the particle model of matter; Thermal Physics 3 (f) understand that the kinetic theory model is based on the assumptions that the particles occupy no volume, that all collisions are elastic, and that there are no forces between particles until they collide; Thermal Physics 3 (g) understand that a model will begin to break down when the assumptions on which it is based are no longer valid, and explain why this applies to kinetic theory at very high pressures or very high or very low temperatures; Thermal Physics 3 (h) derive pV = 1/3 Nm from first principles to illustrate how the microscopic particle model can account for macroscopic observations; Thermal Physics 3 (i) recognise and use 1/2 m = 3/2 kT ; Thermal Physics 3 (j) understand and calculate the root mean square speed for particles in a gas; Thermal Physics 3 (k) understand the concept of internal energy as the sum of potential and kinetic energies of the molecules; Thermal Physics 3 (l) recall and use the first law of thermodynamics expressed in terms of the change in internal energy, the heating of the system and the work done on the system; Thermal Physics 3 (m) recognise and use W = p ΔV  for the work done on or by a gas; Thermal Physics 4 (n) understand qualitatively how the random distribution of energies leads to the Boltzmann factor: as a measure of the chance of a high energy Thermal Physics 5 (o) apply the Boltzmann factor to activation processes including rate of reaction, current in a semiconductor and creep in a polymer; Thermal Physics 5 (p) *describe entropy qualitatively in terms of the dispersal of energy or particles and realise that entropy is related to the number of ways in which a particular macroscopic state can be realised; Thermal Physics 4 (q) *recall that the second law of thermodynamics states that the entropy of an isolated system cannot decrease and appreciate that this is related to probability; Thermal Physics 4 (r) *understand that the second law provides a thermodynamic arrow of time that distinguishes the future (higher entropy) from the past (lower entropy; Thermal Physics 4 (s) *understand that systems in which entropy decreases (e.g. humans) are not isolated and that when their interactions with the environment are taken into account their net effect is to increase the entropy of the Universe; Thermal Physics 4 (t) *understand that the second law implies that the Universe started in a state of low entropy and that some physicists think that this implies it was in a state of extremely low probability. Thermal Physics 4 Top 17.  Nuclear Physics (a) Recall and show that the random nature of radioactive decay leads to the differential equation: and that: is a solution to this equation; Nuclear Physics 5 (b) recall that activity: and show that: ; Nuclear Physics 5 (c) show that the half-life: ; Nuclear Physics 5 (d) use the equations in (a), (b) and (c) to solve problems; Nuclear Physics 5 (e) recognise and use the equation: as applied to attenuation losses; (f) recall that radiation emitted from a point source and travelling through a non-absorbing material obeys an inverse square law and use this to solve problems; Nuclear Physics 4 (g) estimate the size of a nucleus from the distance of closest approach of a charged particle; Nuclear Physics 2 (h) understand the concept of nuclear binding energy, and recognise and use the equation: (binding energy will be taken to be positive); Nuclear Physics 7 (i) recall, understand and explain the curve of binding energy per nucleon against nucleon number; Nuclear Physics 7 (j) recall that antiparticles have the same mass but opposite charge and spin to their corresponding particles; Particle Physics 6 (k) relate the equation: to the creation or annihilation of particle-antiparticle pairs; Particle Physics 6 (l) recall the quark model of the proton (uud) and the neutron (udd); Particle Physics 8 (m) understand how the conservation laws for energy, momentum and charge in beta-minus decay were used to predict the existence and properties of the antineutrino; Particle Physics 11 (n) balance nuclear transformation equations for alpha, beta-minus and beta-plus emissions; Nuclear Physics 3 (o) recall that the standard model classifies matter into three families: quarks (including up and down), leptons (including electrons and neutrinos) and force carriers (including photons and gluons); Particle Physics 7 (p) recall that matter is classified as baryons and leptons and that baryon numbers and lepton numbers are conserved in nuclear transformations. Particle Physics 11 18.  The Quantum Atom (a) Explain atomic line spectra in terms of photon emission and transitions between discrete energy levels; Quantum Physics 4 (b) apply E = hf  to radiation emitted in a transition between energy levels; Quantum Physics 4 (c) show an understanding of the hydrogen line spectrum, photons and energy levels as represented by the Lyman, Balmer and Paschen series; Physics 6 Tutorial 16 (d) recognise and use the energy levels of the hydrogen atom as described by the empirical equation: ; Physics 6 Tutorial 16 (e) *explain energy levels using the model of standing waves in a rectangular one-dimensional potential well; Physics 6 Tutorial 16 (f) *derive the hydrogen atom energy level equation: algebraically using the model of electron standing waves, the de Broglie relation and the quantisation of angular momentum. Physics 6 Tutorial 16 19.  Interpreting Quantum Theory (a) *Interpret the double-slit experiment using the Copenhagen interpretation (and collapse of the wavefunction), Feynman’s sum-over-histories and Everett’s many-worlds theory; Physics 6 Tutorial 17 (b) *describe and explain Schrödinger’s cat paradox and appreciate the use of a thought experiment to illustrate and argue about fundamental principles; (c) *recognise and use: as a form of the Heisenberg uncertainty principle and interpret it; (d) *recognise that the Heisenberg uncertainty principle places limits on our ability to know the state of a system and hence to predict its future; (e) *recall that Newtonian physics is deterministic, but quantum theory is indeterministic; (f) *understand why Einstein thought that quantum theory undermined the nature of reality by being: (i) indeterministic (initial conditions do not uniquely determine the future) (ii) non-local (for example, wave-function collapse) (iii) incomplete (unable to predict precise values for properties of particles). 20.  Astrophysics You may find it useful look at to learn about stellar distances. You can find out more about General Relativity in . (a) Understand the term luminosity; Astrophysics 5 (b) recall and use the inverse square law for radiant flux intensity F in terms of the luminosity L of the source: ; Astrophysics 5 (c) understand the need to use standard candles to help determine distances to galaxies; Astrophysics 6 (d) recognise and use Wien’s displacement law: to estimate the peak surface temperature of a star either graphically or algebraically; Astrophysics 5 (e) recognise and use Stefan’s law for a spherical body: ; Astrophysics 5 (f) use Wien’s displacement law and Stefan’s law to estimate the radius of a star; Astrophysics 5 (g) understand that the successful application of Newtonian mechanics and gravitation to the Solar System and beyond indicated that the laws of physics apply universally and not just on Earth; Astrophysics 7 (h) recognise and use: for a source of electromagnetic radiation moving relative to an observer; Astrophysics 7 (i) state Hubble’s law and explain why galactic red-shift leads to the idea that the Universe is expanding and to the Big Bang theory; Astrophysics 7 (j) explain how microwave background radiation provides empirical support for the Big Bang theory; Astrophysics 7 (k) understand that the theory of the expanding Universe involves the expansion of space-time and does not imply a pre-existing empty space into which this expansion takes place or a time prior to the Big Bang; Astrophysics 7 (l) recall and use the equation: for objects at cosmological distances; Astrophysics 7 (m) derive an estimate for the age of the Universe by recalling and using the Hubble time: Astrophysics 7 And that's it