Lessons

Physical Quantities and Units

a physical quantity = a numerical magnitude × a unit; the seven SI base quantities and units · derived units expressed in SI base units (e.g. N = kg m s⁻²) · prefixes from pico to tera · checking the homogeneity of an equation by its base units · making order-of-magnitude estimates of physical quantities

Kinematics and Vectors

be able to use the equations for uniformly accelerated motion in one dimension: s = (u + v)t / 2; v = u + at; s = ut + 1/2 at^2; v^2 = u^2 + 2as · be able to draw and interpret displacement-time, velocity-time and acceleration-time graphs · know the physical quantities derived from the slopes and areas of displacement-time, velocity-time and acceleration-time graphs, including cases of non-uniform acceleration and understand how to use the quantities · understand scalar and vector quantities and know examples of each type of quantity and recognise vector notation · be able to resolve a vector into two components at right angles to each other by drawing and by calculation · be able to find the resultant of two coplanar vectors at any angle to each other by drawing, and at right angles to each other by calculation · understand how to make use of the independence of vertical and horizontal motion of a projectile moving freely under gravity

Forces and Newton's Laws

be able to draw and interpret free-body force diagrams to represent forces on a particle or on an extended but rigid body using the concept of centre of gravity of an extended body · be able to use the equation sum(F) = ma, and understand how to use this equation in situations where m is constant (Newton's second law of motion), including Newton's first law of motion where a = 0, objects at rest or travelling at constant velocity. Use of the term 'terminal velocity' is expected. · be able to use the equations for gravitational field strength g = F/m and weight W = mg · CORE PRACTICAL 1: Determine the acceleration of a freely-falling object · know and understand Newton's third law of motion and know the properties of pairs of forces in an interaction between two bodies

Momentum and Impulse

understand how to use the equation impulse = F t = p (Newton's second law of motion) · CORE PRACTICAL 9: Investigate the relationship between the force exerted on an object and its change of momentum · understand how to apply conservation of linear momentum to problems in two dimensions · CORE PRACTICAL 10: Use ICT to analyse collisions between small spheres, e.g. ball bearings on a table top · understand how to determine whether a collision is elastic or inelastic · be able to derive and use the equation Ek = p^2 / 2m for the kinetic energy of a non-relativistic particle

Density and Pressure

be able to use the equation density rho = m/V · understand how to use the relationship upthrust = weight of fluid displaced · (a) be able to use the equation for viscous drag (Stokes' Law), F = 6 pi eta r v. (b) understand that this equation applies only to small spherical objects moving at low speeds with laminar flow (or in the absence of turbulent flow) and that viscosity is temperature dependent · CORE PRACTICAL 2: Use a falling-ball method to determine the viscosity of a liquid

Work, Energy and Power

be able to use the equation for work W = Fs, including calculations when the force is not along the line of motion · be able to use the equation Ek = 1/2 mv^2 for the kinetic energy of a body · be able to use the equation Egrav = mg h for the difference in gravitational potential energy near the Earth's surface · know, and understand how to apply, the principle of conservation of energy including use of work done, gravitational potential energy and kinetic energy · be able to use the equations relating power, time and energy transferred or work done P = E/t and P = W/t · be able to use the equations efficiency = useful energy output / total energy input and efficiency = useful power output / total power input

Stress, Strain and Elasticity

be able to use the Hooke's law equation, F = k x, where k is the stiffness of the object · understand how to use the relationships (tensile or compressive) stress = force/cross-sectional area; (tensile or compressive) strain = change in length/original length; Young modulus = stress/strain. · (a) be able to draw and interpret force-extension and force-compression graphs. (b) understand the terms limit of proportionality, elastic limit, yield point, elastic deformation and plastic deformation and be able to apply them to these graphs · be able to draw and interpret tensile or compressive stress-strain graphs, and understand the term breaking stress · CORE PRACTICAL 3: Determine the Young modulus of a material · be able to calculate the elastic strain energy Eel in a deformed material sample, using the equation Eel = 1/2 F x, and from the area under the force-extension graph. The estimation of area and hence energy change for both linear and non-linear force-extension graphs is expected.

Wave Properties

understand the terms amplitude, frequency, period, speed and wavelength · be able to use the wave equation v = f lambda · be able to describe longitudinal waves in terms of pressure variation and the displacement of molecules · be able to describe transverse waves · be able to draw and interpret graphs representing transverse and longitudinal waves including standing/stationary waves · CORE PRACTICAL 4: Determine the speed of sound in air using a 2-beam oscilloscope, signal generator, speaker and microphone

Stationary Waves

know and understand what is meant by wavefront, coherence, path difference, superposition, interference and phase · be able to use the relationship between phase difference and path difference · know what is meant by a standing/stationary wave and understand how such a wave is formed, know how to identify nodes and antinodes · be able to use the equation for the speed of a transverse wave on a string v = sqrt(T/mu) · CORE PRACTICAL 5: Investigate the effects of length, tension and mass per unit length on the frequency of a vibrating string or wire · be able to use the equation for the intensity of radiation I = P/A

Diffraction and the Diffraction Grating

know and understand that at the interface between medium 1 and medium 2, n1 sin theta1 = n2 sin theta2 where refractive index is n = c/v · be able to calculate critical angle using sin C = 1/n · be able to predict whether total internal reflection will occur at an interface · understand how to measure the refractive index of a solid material · understand what is meant by plane polarisation · understand what is meant by diffraction and use Huygens' construction to explain what happens to a wave when it meets a slit or an obstacle · be able to use n lambda = d sin theta for a diffraction grating · CORE PRACTICAL 6: Determine the wavelength of light from a laser or other light source using a diffraction grating

Current, Potential Difference and Power

understand that electric current is the rate of flow of charged particles and be able to use the equation I = Q/t · understand how to use the equation V = W/Q · understand that resistance is defined by R = V/I and that Ohm's law is a special case when I is proportional to V for constant temperature

Resistance and Resistivity

be able to use the equation R = rho l / A · CORE PRACTICAL 7: Determine the electrical resistivity of a material · be able to use I = nqvA to explain the large range of resistivities of different materials · understand how changes of resistance with temperature may be modelled in terms of lattice vibrations and number of conduction electrons and understand how to apply this model to metallic conductors and negative temperature coefficient thermistors · understand how changes of resistance with illumination may be modelled in terms of the number of conduction electrons and understand how to apply this model to LDRs.

Kirchhoff's Laws

(a) understand how the distribution of current in a circuit is a consequence of charge conservation. (b) understand how the distribution of potential differences in a circuit is a consequence of energy conservation · be able to derive the equations for combining resistances in series and parallel using the principles of charge and energy conservation, and be able to use these equations · be able to use the equations P = VI, W = VIt and be able to derive and use related equations, e.g. P = I^2 R and P = V^2/R · understand how to sketch, recognise and interpret current-potential difference graphs for components, including ohmic conductors, filament bulbs, thermistors and diodes

Potential Dividers and Internal Resistance

understand how the potential along a uniform current-carrying wire varies with the distance along it · understand the principles of a potential divider circuit and understand how to calculate potential differences and resistances in such a circuit · be able to analyse potential divider circuits where one resistance is variable including thermistors and light dependent resistors (LDRs) · know the definition of electromotive force (e.m.f.) and understand what is meant by internal resistance and know how to distinguish between e.m.f. and terminal potential difference · CORE PRACTICAL 8: Determine the e.m.f. and internal resistance of an electrical cell

Fundamental Particles

know that in the standard quark-lepton model particles can be classified as: baryons (e.g. neutrons and protons), which are made from three quarks; mesons (e.g. pions), which are made from a quark and an antiquark; leptons (e.g. electrons and neutrinos), which are fundamental particles; photons; and that the symmetry of the model predicted the top quark · know that every particle has a corresponding antiparticle and be able to use the properties of a particle to deduce the properties of its antiparticle and vice versa · understand how to use laws of conservation of charge, baryon number and lepton number to determine whether a particle interaction is possible · be able to write and interpret particle equations given the relevant particle symbols.

Circular Motion

be able to express angular displacement in radians and in degrees, and convert between these units · understand what is meant by angular velocity and be able to use the equations v = omega r and T = 2 pi / omega · be able to use vector diagrams to derive the equations for centripetal acceleration a = v^2/r = r omega^2 and understand how to use these equations · understand that a resultant force (centripetal force) is required to produce and maintain circular motion · be able to use the equations for centripetal force F = ma = m v^2 / r = m r omega^2.

Gravitational Fields

understand that a gravitational field is a region in which a mass experiences a force, and define field strength g = F/m · recall and use Newton's law of gravitation F = G m1 m2 / r^2 · derive and use g = GM/r^2 for the field due to a point mass · use gravitational potential phi = -GM/r for a radial field · analyse circular orbits and geostationary satellites using gravitation and circular motion

Specific and Latent Heat

be able to use the equations E = mc theta and E = L m · CORE PRACTICAL 12: Calibrate a thermistor in a potential divider circuit as a thermostat · CORE PRACTICAL 13: Determine the specific latent heat of a phase change

Ideal Gases and Internal Energy

understand the concept of internal energy as the random distribution of potential and kinetic energy amongst molecules · understand the concept of absolute zero and how the average kinetic energy of molecules is related to the absolute temperature · be able to use the equation pV = NkT for an ideal gas · CORE PRACTICAL 14: Investigate the relationship between pressure and volume of a gas at fixed temperature · be able to derive and use the equation 1/2 m <c^2> = 3/2 kT

First Law of Thermodynamics

internal energy = the random distribution of kinetic and potential energy of the molecules · the first law of thermodynamics ΔU = q + W with the sign convention (q heat supplied TO the system, W work done ON the system) · work done on/by a gas, W = pΔV at constant pressure · applying the first law to simple processes

Simple Harmonic Motion

understand that the condition for simple harmonic motion is F = -kx, and hence understand how to identify situations in which simple harmonic motion will occur · be able to use the equations a = -omega^2 x, x = A cos(omega t), v = -A omega sin(omega t), a = -A omega^2 cos(omega t), and T = 1/f = 2 pi / omega and omega = 2 pi f as applied to a simple harmonic oscillator · be able to use equations for a simple harmonic oscillator T = 2 pi sqrt(m/k), and a simple pendulum T = 2 pi sqrt(l/g) · be able to draw and interpret a displacement-time graph for an object oscillating and know that the gradient at a point gives the velocity at that point · be able to draw and interpret a velocity-time graph for an oscillating object and know that the gradient at a point gives the acceleration at that point

Resonance and Damping

understand what is meant by resonance · CORE PRACTICAL 16: Determine the value of an unknown mass using the resonant frequencies of the oscillation of known masses · understand how to apply conservation of energy to damped and undamped oscillating systems · understand the distinction between free and forced oscillations · understand how the amplitude of a forced oscillation changes at and around the natural frequency of a system and know, qualitatively, how damping affects resonance · understand how damping and the plastic deformation of ductile materials reduce the amplitude of oscillation.

Electric Fields

understand that an electric field (force field) is defined as a region where a charged particle experiences a force · understand that electric field strength is defined as E = F/Q and be able to use this equation · be able to use the equation F = Q1 Q2 / (4 pi epsilon0 r^2) for the force between two charges · be able to use the equation E = Q / (4 pi epsilon0 r^2) for the electric field due to a point charge · know and understand the relation between electric field and electric potential · be able to use the equation E = V/d for an electric field between parallel plates · be able to use V = Q / (4 pi epsilon0 r) for a radial field · be able to draw and interpret diagrams using field lines and equipotentials to describe radial and uniform electric fields

Capacitors and Energy Stored

understand that capacitance is defined as C = Q/V and be able to use this equation · be able to use the equation W = 1/2 QV for the energy stored by a capacitor, be able to derive the equation from the area under a graph of potential difference against charge stored and be able to derive and use the equations W = 1/2 C V^2 and W = 1/2 Q^2 / C · be able to draw and interpret charge and discharge curves for resistor capacitor circuits and understand the significance of the time constant RC · CORE PRACTICAL 11: Use an oscilloscope or data logger to display and analyse the potential difference (p.d.) across a capacitor as it charges and discharges through a resistor · be able to use the equation Q = Q0 e^(-t/RC) and derive and use related equations for exponential discharge in a resistor-capacitor circuit, I = I0 e^(-t/RC), and V = V0 e^(-t/RC) and the corresponding log equations ln Q = ln Q0 - t/RC, ln I = ln I0 - t/RC and ln V = ln V0 - t/RC

Magnetic Fields and Electromagnetic Induction

understand and use the terms magnetic flux density B, flux phi and flux linkage N phi · be able to use the equation F = Bqv sin theta and apply Fleming's left-hand rule to charged particles moving in a magnetic field · be able to use the equation F = BIl sin theta and apply Fleming's left-hand rule to current carrying conductors in a magnetic field · understand the factors affecting the e.m.f. induced in a coil when there is relative motion between the coil and a permanent magnet · understand the factors affecting the e.m.f. induced in a coil when there is a change of current in another coil linked with this coil · understand how to use Faraday's law to determine the magnitude of an induced e.m.f. and be able to use the equation that combines Faraday's and Lenz's laws E = - d(N phi)/dt.

Alternating Currents

sinusoidal a.c.: peak value, period, frequency and ω = 2πf · r.m.s. value I_rms = I₀/√2 and why it gives the equivalent d.c. heating · mean power = ½ I₀V₀ = I_rms V_rms; peak power = twice the mean · half-wave and full-wave (bridge) rectification · smoothing an a.c. supply with a capacitor across the load

The Photoelectric Effect and Wave-Particle Duality

understand how diffraction experiments provide evidence for the wave nature of electrons · be able to use the de Broglie equation lambda = h/p · understand that waves can be transmitted and reflected at an interface between media · understand how a pulse-echo technique can provide information about the position of an object and how the amount of information obtained may be limited by the wavelength of the radiation or by the duration of pulses · understand how the behaviour of electromagnetic radiation can be described in terms of a wave model and a photon model, and how these models developed over time · be able to use the equation E = hf, that relates the photon energy to the wave frequency · understand that the absorption of a photon can result in the emission of a photoelectron · understand the terms 'threshold frequency' and 'work function' and be able to use the equation hf = phi + 1/2 m v_max^2 · be able to use the electronvolt (eV) to express small energies · understand how the photoelectric effect provides evidence for the particle nature of electromagnetic radiation · understand atomic line spectra in terms of transitions between discrete energy levels and understand how to calculate the frequency of radiation that could be emitted or absorbed in a transition between energy levels.

Mass Defect and Binding Energy

understand the concept of nuclear binding energy and be able to use the equation E = c^2 m in calculations of nuclear mass (including mass deficit) and energy · use the atomic mass unit (u) to express small masses and convert between this and SI units · understand the processes of nuclear fusion and fission with reference to the binding energy per nucleon curve · understand the mechanism of nuclear fusion and the need for very high densities of matter and very high temperatures to bring about and maintain nuclear fusion

Radioactive Decay and Half-Life

understand that there is background radiation and how to take appropriate account of it in calculations · understand the relationships between the nature, penetration, ionising ability and range in different materials of nuclear radiations (alpha, beta and gamma) · be able to write and interpret nuclear equations given the relevant particle symbols · CORE PRACTICAL 15: Investigate the absorption of gamma radiation by lead · understand the spontaneous and random nature of nuclear decay · be able to determine the half-lives of radioactive isotopes graphically and be able to use the equations for radioactive decay activity A = lambda N, dN/dt = -lambda N, lambda = ln 2 / t_half, N = N0 e^(-lambda t) and A = A0 e^(-lambda t) and derive and use the corresponding log equations.

Medical Physics

ultrasound: piezoelectric transducer, acoustic impedance Z = ρc, reflection coefficient and gel coupling · attenuation of a beam in tissue, I = I₀ e^(−μx) · X-ray production in an X-ray tube; minimum wavelength λ_min = hc/(eV); attenuation, contrast and CT · PET: a β⁺ tracer, electron–positron annihilation into two 0.511 MeV γ-photons, coincidence detection

Stars and Stellar Radiation

understand what is meant by a black body radiator and be able to interpret radiation curves for such a radiator · be able to use the Stefan-Boltzmann law equation L = sigma A T^4 for black body radiators · be able to use Wien's law equation lambda_max T = 2.898 x 10^-3 m K for black body radiators · be able to use the equation, intensity I = L / (4 pi d^2) where L is luminosity and d is distance from the source · understand how astronomical distances can be determined using trigonometric parallax · understand how astronomical distances can be determined using measurements of intensity received from standard candles (objects of known luminosity) · be able to sketch and interpret a simple Hertzsprung-Russell diagram that relates stellar luminosity to surface temperature · understand how to relate the Hertzsprung-Russell diagram to the life cycle of stars

Cosmology and Hubble's Law

understand how the movement of a source of waves relative to an observer/detector gives rise to a shift in frequency (Doppler effect) · be able to use the equations for redshift z = lambda/lambda ≈ f/f ≈ v/c for a source of electromagnetic radiation moving relative to an observer and v = H0 d for objects at cosmological distances · understand the controversy over the age and ultimate fate of the universe associated with the value of the Hubble constant and the possible existence of dark matter.

Practical Skills: Recording, Graphs & Uncertainties

recording & uncertainty: instrument resolution sets the absolute uncertainty; consistent significant figures / decimal places in a results table; absolute vs fractional vs percentage uncertainty · graphs & gradients: choosing sensible axes and scales, plotting points with error bars, drawing a best-fit line, reading the gradient with a large gradient triangle (m = Δy/Δx from the line) · uncertainty in results & evaluation: worst-acceptable-fit line → uncertainty in the gradient Δm = |m_best − m_worst|; combining percentage uncertainties (add for products/quotients, multiply by the power); identifying anomalies; stating limitations and improvements