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Advanced Higher Physics Success Guide This guide is for learners studying Physics at Advanced Higher to assist in identifying areas of the two and a half main units to be studied for the course exam. There is no guidance given for the Investigation half unit. The three columns are: Key areas and associated learning This interprets SQA mandatory statements and exemplification of key areas from the Course/Unit Support Notes in terms of knowledge and skill that learners should be able to accomplish. Candidates should also ensure they are aware of the current SQA course specifications. http://www.sqa.org.uk/files_ccc/AHCASPhysics.pdf The list of suggested activities from the Course/Unit Support Notes is not referenced in this document. Relationships Relationships to be used in numerical calculations. These are provided when undertaking internal unit assessments and the external course examination. Useful resources These online resources are suggested as a starting point for online exemplification of course content. They are not exhaustive or definitive and many other resources and websites are available. Each underlined term is a hyperlink which will link to a webpage when this document is viewed electronically. Most resources are only referenced once although they may be of use in other parts of the course. Resource Guide Advanced Higher Physics Success Guide page 1 Rotational Motion and Astrophysics Key Areas and Associated Learning Relationships Useful Resources Kinematic relationships o o o o o o dv d2 s YouTube video – Deriving kinematics equations using calculus Use the relationships a = and a = 2 dt d𝑡 to derive the kinematic relationships: v = u + at, s = ut + ½at2 and v2 = u2 + 2as where a is a constant acceleration Use kinematics equations (SUVAT) to calculate instantaneous displacement, velocity and acceleration for motion in straight line with a constant or varying acceleration Use differentiation and integration to determine the instantaneous velocity and acceleration of a body given initial conditions. Interpret graphs of motions for objects and Determine instantaneous velocity from gradients of s-t graphs Determine instantaneous acceleration from the gradients of v-t graphs Determine displacement from the area under v-t graphs Advanced Higher Physics Success Guide BBC video – In Our Time: The laws of motion page 2 Angular motion o o o o o o o o o o o o Convert between degrees and radians using an appropriate relationship Relate linear displacement to angular displacement. State that the angular velocity of a rotating body is the rate of change of angular displacement. State that angular acceleration is the rate of change of angular velocity. Carry out calculations involving angular displacement, angular velocity and angular acceleration. Carry out calculations involving angular and tangential motion. Carry out calculations involving constant angular velocity and period. Distinguish between angular acceleration, tangential acceleration and centripetal (radial or central) acceleration. Explain that consideration of centripetal (radial) acceleration as the rate of change in linear (tangential) velocity leads to the concept of a centripetal (radial) force required to maintain circular motion. Define centripetal (radial or central) acceleration as the rate of change in linear (tangential) velocity 𝑣2 Derive the following relationships for radial acceleration: 𝑎𝑟 = and 𝑎𝑟 = 𝑟 2 𝑟𝜔 Use appropriate relationships to carry out calculations involving centripetal acceleration and centripetal force. 𝑠 = 𝑟𝜃 d dt dw d 2q a= = 2 dt dt 0 t 2 0 2 2 0t 12 t 2 𝑣 = 𝑟𝜔 v2 r 2 r mv 2 F mr 2 r ar March 2015 Advanced Higher Physics Success Guide page 3 YouTube video – Rotational motion 101 physics Education Scotland learner resource – numerical examples. The Young Scottish Physicist learner resource – Angular motion Education Scotland learner resource – numerical examples. YouTube video – Fifth Gear loop the loop NASA video – Centripetal forces VCE physics video – Circular motion: The Wall of Death Illinois University animation – Banked turns Rotational Dynamics o o o o o o o o o o o o o State what is meant by the moment of a force State that Toque is defined as the product of radius and force applied at that radius to an axis of rotation. Explain that an unbalanced torque produces an angular acceleration. State that Nm is the unit of torque. Define the moment of inertia, I, of an object as a measure of its resistance to angular acceleration about a given axis. State that the angular acceleration produced by an unbalanced torque depends on the moment of inertia of the object. State that moment of inertia of an object depends on the mass of the object, and the distribution of the mass about a particular axis. Calculate the moment of inertia of discrete masses, rods, discs and spheres about a given axis given appropriate relationships. State that the angular momentum L of a rigid object is the product of moment of inertia and angular velocity. State that in the absence of external torques, the total angular momentum of a rotating rigid before a collision equal the total angular moment after impact. Solve problems involving the principle of conservation of angular momentum. State that the rotational kinetic energy of a rigid object depends on its moment of inertia and angular velocity. Use appropriate relationships to carry out calculations involving potential energy, rotational kinetic energy, translational kinetic energy, angular velocity, linear velocity, moment of inertia and mass. T Fr , T I For discrete masses: I mr 2 , Moments of inertia for several familiar shapes: I 121 ml 2 rod about centre - 2 1 rod about end - I 3 ml disc about centre sphere - centre - I 12 mr 2 I 52 mr 2 𝐿 = 𝑚𝑣𝑟 = 𝑚𝑟𝜔2 = 𝐼𝜔 L I const (no external torque). E 12 I 2 Ep = Ek (translational)) + Ek (rotational) Advanced Higher Physics Success Guide page 4 YouTube video – Walter Lewin demonstrates moment of inertia Education Scotland learner resource – Numerical examples. YouTube video – Physics of spins in figure skating YouTube video – The physics of diving YouTube video – KERS bicycle technology university project at AIT Wikimedia animation – Lucas Barbosa: Objects down a slope with different moments of inertia Gravitation o o o o o o o o o o o o o o o o o Vimeo video – BBC Beautiful Equations Newton’s equation of universal gravitation Define gravitational field strength in terms of force and mass. Sketch field lines and gravitational field patterns around a planet and a planet–moon system. Apply gravitational forces to orbital motion. Perform calculations involving period of orbit and distance from centre of Earth. Analyse satellites in (circular) orbit in terms of centripetal forces and period. Applications of satellites include Data-gathering satellites: weather, telecommunications, mapping, surveying, etc. Tides, tidal forces, tidal energy. Describe the principles of the Cavendish/Boys and Maskelyne Schiehallion experiments. Define gravitational potential in terms of potential energy and mass. Define gravitational potential as the work done in moving unit mass from infinity to a point in space. State that gravitational potential and gravitational potential energy have the value zero at infinity. Calculate changes in both potential and kinetic energy when a satellite alters orbit. Describe a Gravitational potential ‘well’. Explain why smaller planets have no atmosphere and the low incidence of helium in Earth’s atmosphere etc. State that escape velocity is the minimum velocity required to allow a mass to escape a gravitational field, achieving zero kinetic energy and maximum (zero) gravitational potential energy at infinity. Derive escape velocity by consideration of energy. Consider implications of escape velocity for space flight. Calculation of escape velocity using appropriate relationship. Advanced Higher Physics Success Guide YouTube video – Universal gravitation experiment Counting thoughts resource – Weigh the world Nowykurier animation – Gravity simulation Donald Simanek teacher resource – Tidal misconceptions University of Massachusetts learner resource – Gravity and escape velocity tutorial Splung.com animation – The gravitational field University of Nebraska animation – Atmospheric loss Education Scotland learner resource – Numerical examples (pages 5 & 11) page 5 General Relativity o o o o o o o o o o State that Special Relativity deals with motion in inertial (nonaccelerating) frames of reference. State that General Relativity deals with motion in non-inertial (accelerating) frames of reference. State the Equivalence Principle (an observer cannot tell the difference between a uniform gravitational field and a constant acceleration) Describe the consequences of the Equivalence Principle: Clocks in non-inertial reference frames e.g. accelerating spacecraft Clocks at altitude i.e. clocks run at different speeds in different gravitational field strengths Precession of Mercury’s orbit Gravitational lensing of light State that spacetime is a representation of four dimensional space. State that light or a freely moving object follows a geodesic (the shortest distance between two points) in spacetime. State that mass curves spacetime, and that gravity arises from the curvature of spacetime. Recognise on spacetime diagrams the world lines for objects which are stationary, moving with constant velocity and accelerating. Use an appropriate relationship to solve problems relating to the Schwarzschild radius/event horizon of a black hole. State that time appears to be frozen at the event horizon of a black hole. BBC video – General relativity BBC audio – In Our Time: relativity YouTube video – An introduction to spacetime The Kings Centre animation – Michelson-Morley, Muon decay and spacetime diagrams TED animation – The fundamentals of space-time YouTube video – Gravity visualised 2𝐺𝑀 𝑟= 2 𝑐 BBC audio – In Our Time: black holes BBC audio – In Our Time: life of stars Spacetelescope video – Gravitational lensing in action BBC video – What are gravitational lenses? Guardian learner resource – Physics of the movie Interstellar Advanced Higher Physics Success Guide page 6 Stellar physics o o o o o o Describe properties of stars such as radius, surface temperature, luminosity and apparent brightness. Use of appropriate relationships to solve problems relating to luminosity, apparent brightness, power per unit area, stellar radius and stellar surface temperature. Knowledge of the stages in the proton-proton chain in stellar fusion reactions which convert hydrogen to helium. Know the stages of stellar evolution the corresponding positions in the Hertzsprung-Russell (H-R) diagram. Know the classification of stars and be able to identify their positions in the Hertzsprung-Russell (H-R) diagram. Be able to predict the colour of stars from their position in the Hertzsprung-Russell (H-R) diagram. Stars are born in interstellar clouds that are particularly cold and dense (relative to the rest of space). Stars form when gravity overcomes thermal pressure and causes a molecular cloud to contract until the central object becomes hot enough to sustain nuclear fusion. The mass of a new star determines its luminosity and surface temperature. The Hertzsprung-Russell (H-R) diagram is a representation of the classification of stars. The luminosity and surface temperature determine the location of a star in the H-R diagram. The lifetime of a star depends on its mass. During the hydrogen fusing stage, the star is located in the main-sequence. As the fuel is used up, the balance between gravity and thermal pressure changes and the star may change its position on the H-R diagram. The ultimate fate of a star is determined by its mass. Supernovae, neutron stars and black holes can be the eventual fate of some stars. Advanced Higher Physics Success Guide 𝑏= 𝐿 4𝜋𝑟 2 power per unit area = 𝜎𝑇 4 Education Scotland resources – Stellar evolution, star brightness Education Scotland resources – Stellar Physics 𝐿 = 4𝜋𝑟 2 𝜎𝑇 4 Schools observatory learner resource – Stars section BBC audio – In Our Time: neutrinos BBC video – Stars National STEM centre video – The life cycle of stars University of Utah interactive quiz –Hertzsprung-Russell (H-R) diagram page 7 Quanta and Waves Key areas and associated learning Relationships Useful resources Introduction to quantum theory o Education Scotland teacher resource – Quanta theory advice for teachers. Understand the challenges to classical theory by considering experimental observations that could not be explained by classical physics: Black-body radiation curves (“ultraviolet catastrophe”) Planck’s suggestion that the absorption and emission of radiation could only take place in ‘jumps’, photoelectric effect could not be explained using classical physics, Einstein’s suggestion that the energy of electromagnetic radiation is quantisised, The Bohr model of the atom, which explains the characteristics of atomic spectra in terms of electron energy states, Bohr’s quantisation of angular momentum, De Broglie suggested that electrons have wave properties, the de Broglie relationship between wavelength and momentum and electron diffraction is evidence for wave/particle duality. Photoelectric effect o Use an appropriate relationship to solve problems involving photon energy and frequency. o Describe the Bohr model of the atom. o Use an appropriate relationship to solve problems involving the angular momentum of an electron and its principal quantum number. Advanced Higher Physics Success Guide Education Scotland learner resource – Quanta and waves numerical examples Softpedia learner resource – Why is Quantum Mechanics so weird? Hyperphysics learner resource – Early photoelectric effect data PhET animation – Black body spectrum AboutPhysics learner resource – The ultraviolet catastrophe SSERC activity – Determination of Planck’s constant using tungsten lamp E = hf page 8 Wave particle duality o o Describe experimental evidence for wave/particle duality including double-slit experiments with single particles (photons and electrons). Examine evidence of wave/particle duality. Examples include: electron diffraction, photoelectric effect and Compton scattering. De Broglie waves o Use of an appropriate relationship to solve problems involving the de Broglie wavelength of a particle and its momentum. Uncertainty principle o o o o o o TED Ed animation – The uncertainty location of electrons. Understand how quantum mechanics can resolve the dilemmas that could not be explained by classical physics and the dual nature of matter. State that in quantum mechanics the nature of matter is not predictable. A Newtonian, mechanistic view, in principle allows all future states of a system to be known if the starting details are known. Quantum mechanics indicates that we can only calculate probabilities. Understand the Uncertainty principle in terms of how it is impossible to simultaneously measure both wave and particle properties. Describe the principles of double slit experiments with single particles (photons or electrons) and how they produce nonintuitive results. Quantum mechanics gives excellent agreement with experimental observations. Describe the Uncertainty Principle in terms of location and momentum. Advanced Higher Physics Success Guide Chad Orzel animation – Quantum mechanics 101 YouTube video – What is the uncertainty principle? About Physics learner resource – Quantum physics overview YouTube video – Double slit experiment explained by Jim Al-Khalili The Guardian teacher resource – What is Heisenberg’s uncertainty principle? YouTube video – What is quantum tunnelling? Wimp video – Dr Quantum Double slit page 9 o o experiment To gain precise information about the position of a particle requires the use of short wavelength radiation. This has high energy which changes the momentum of the particle. The Guardian teacher resource – Understanding quantum tunnelling Describe the Uncertainty Principle in terms of energy and time and apply to the concept of quantum tunneling. Potential wells form barriers which would not normally allow particles to escape. ‘Borrowing’ energy for a short period of time allows particles to escape from the potential well. YouTube video – The secrets of quantum physics: Einstein’s nightmare (Episode 1) BBC audio – In Our Time: Heisenberg BBC audio – In Our Time: Quantum theory Use of mathematical statements of the Uncertainty Principle to solve problems involving the uncertainties in position, momentum, energy and time. Advanced Higher Physics Success Guide page 10 Particles from space Education Scotland teacher resource – Particles from space advice for practitioners Cosmic rays o o o o State the origin and composition of cosmic rays, the interaction of cosmic rays with Earth’s atmosphere and the helical motion of charged particles in the Earth’s magnetic field. Use an appropriate relationships to solve problems involving the force on a charged particle, its charge, its mass, its velocity, the radius of its path and the magnetic induction of a magnetic field. Explain how aurorae are produced in the upper atmosphere. Compare the variety and energies of cosmic rays with particles generated by particle accelerators. TED video – How cosmic rays help us understand the universe F = Bqv School Physics learner resource – Charged particles in electric and magnetic fields. Solar wind Describe of the interaction of the solar wind with Earth’s magnetic field and the composition of the solar wind as charged particles (eg protons and electrons) in the form of plasma. Advanced Higher Physics Success Guide The Alpha magnetic spectrometer experiment learner resource – Particles & energy levels page 11 Simple harmonic motion o o o o o Salford University animation – Simple harmonic motion Define SHM in terms of the restoring force and acceleration proportional and in the opposite direction to the displacement from the rest position. Use appropriate relationships to solve problems involving the displacement, velocity, acceleration, angular frequency, period and energy of an object executing SHM. Examples of SHM include Simple pendulum, mass on spring, loaded test tube, etc. Describe of the effects of damping in SHM (to include underdamping, critical damping’ and overdamping) Examples of damping include: Car shock absorbers, bridges, bungee cords, trampolines, diving boards, etc. Nuffield foundation activity – Examples of SHM Faraday animation – Circular motion and SHM YouTube video – When a physics teacher knows his stuff! Teaching advanced physics teacher resource – Energy in SHM YouTube video – iPad simple harmonic motion SparkVue activity – SHM using a mobile device SSERC activity – Wiimote® physics angular acceleration Education Scotland learner resource – Course questions (page 6) Advanced Higher Physics Success Guide page 12 Waves PhET animation – Fourier o o o o o o o o o o o Use an appropriate relationship to solve problems involving the energy transferred by a wave and its amplitude. Use various forms of mathematical representation of travelling waves to identify wave parameters such as frequency, wavespeed, wavelength, direction and amplitude The displacement y is given by the combination of the particle’s transverse SHM and the phase angle between each particle. Use of appropriate relationships to solve problems involving wave motion, phase difference and phase angle. Knowledge of the superposition of waves and stationary waves. Stationary waves are formed by the interference of two waves, of the same frequency and amplitude, travelling in opposite directions. A stationary wave can be described in terms of nodes, antinodes. Stationary waves can be used to measure the wavelength of sound waves and microwaves. Applications of superposition of waves include: Synthesisers related to addition of waves — Fourier analysis. Musical instruments — wind and string. Fundamental and harmonic frequencies. Beats — tuning of musical instruments. E kA2 x y A sin 2( ft ) 2x Falstad animations – Wave phenomena YouTube video – Amazing resonance experiment Help my physics animation – Reflecting plate interference using microwaves Education Scotland learner resource – Course questions (page 2) YouTube video – Ruben's tube, known frequencies, speed of sound, beat YouTube video – Guitar and beat frequencies Vimeo video – CYMATICS: Science vs music YouTube video – Wave model with bowling ball pendulums Advanced Higher Physics Success Guide page 13 Interference o o o Know the conditions for constructive and destructive interference in terms of coherence and phase. Understand the effect of the nature of boundary on the phase of a reflected wave. State the conditions for two light beams to be coherent. Optical path difference = n x geometrical path difference School Physics learner resource – Phase shift Optical path difference =m m Molecular expressions animation – Interference phenomena in soap bubbles PHYSCLIPS animation – Interference Division of amplitude o o o o Conditions for constructive and destructive interference in terms of optical path difference and potential boundary phase changes. Explain interference by division of amplitude, including optical path length, geometrical path length, phase difference, optical path difference. Examples of interference by division of amplitude include thin film interference and wedge fringes, oil films, soap bubbles. Use of appropriate relationships to solve problems involving interference of waves by division of amplitude. Blooming of lenses. YouTube video – Newton's rings SSERC activity – Newton’s rings Exploratorium learner resource – Bubble colors Division of wavelength o o YouTube video – Doc Physics: Phase shifts for reflected waves of light and air wedge example Astrosurf teacher resource – Coating, anti-reflection and dispersion Explanation of interference by division of wavefront, including Young’s slits interference. Use of appropriate relationships to solve problems involving interference of waves by division of wavefront. YouTube video – Young’s slits with sunlight Education Scotland learner resource – Course questions (pages 21 – 25) Advanced Higher Physics Success Guide page 14 Polarisation o o o o o o Explain the polarisation of transverse waves, including polarisers/analysers and Brewster’s angle. Use an appropriate relationship to solve problems involving Brewster’s angle and refractive index. State that a plane polarised wave can be produced by using a filter to absorb the vibrations in all directions except one. State Polarisation can also be produced by reflection. Brewster’s angle is the angle of incidence that causes reflected light to be linearly polarised. Examples of polarisation include: Liquid crystal displays, computer/phone displays, polarising lenses, optical activity, photoelasticity and saccharimetry. Stress analysis of Perspex models of structures. Advanced Higher Physics Success Guide Upscale learner resource – Polarisation of light SSERC activity – Other experiments polarisation n = tan ip YouTube video – Polarised light YouTube video – Stress concentration in acrylic under polarized light page 15 Electromagnetism Key Areas and Associated Learning Relationships Useful Resources Fields o o o o o o o o o o o Define electric field strength in terms of force and unit charge. Sketch electric field patterns around single charges, a system of charges and a uniform electric field. Define electrical potential in terms of work done. State that the energy required to move charge between two points in an electric field is independent of the path taken. Use appropriate relationships to solve problems involving electric force, electric potential and electric field strength around a point charge and a system of charges. Use appropriate relationships to solve problems involving charge, energy, potential difference and electric field strength in situations involving a uniform electric field. Use appropriate relationships to solve problems involving the motion of charged particles in uniform electric fields. State that the electronvolt is a unit of energy. Convert between electronvolt and joules State and explain the magnetic effect called ferromagnetism which occurs in certain metals Sketch magnetic field patterns between magnetic poles, and around solenoids, including the magnetic field pattern around the Earth. Advanced Higher Physics Success Guide Education Scotland learner resource – Electromagnetism questions and solutions E Q 40 r 2 F Q1Q2 40 r 2 V Q 40 r Physics Flash Animations animation – Coulomb’s Law experiment PhET activity – Electric field hockey Teaching advanced physics teacher resource – Electric field line plotting Highland galvanisers teacher resource – What is powder coating, how does it compare to paint and why use it? F = QE V = Ed YouTube video – Coulomb’s law Ew = QV Charles University activity – Coulomb’s law Oswego City School District animation – Electrical energy and electrical potential YouTube video – Compton scattering page 16 o o o State the comparisons between; gravitational, electrostatic, magnetic and nuclear forces, in terms of magnitude and range. Use appropriate relationships to solve problems involving magnetic induction around a current carrying wire, its radius and the current in it. Use appropriate relationships to solve problems involving the forces acting on a current carrying wire and a charged particle in a magnetic field. YouTube video – 3B Scientific Teltron electron deflection tubes F IlB sin B SSERC activity – Force on a current carrying conductor 0 I 2r YouTube video – Ferromagnetism Alexander Martin video – Ferromagnetism F Bqv YouTube video – Forces due to magnetism Electronics Tutorials teacher resource – electromagnetism. YouTube video – Hall effect UCL teacher resource – The use of fields in particle accelerators YouTube animation – Millikan oil drop experiment Education Scotland learner resource – Course question, pages 13 - 20. SSERC experiment – electromagnetic braking (download “other experiments” pages 9 - 10) Advanced Higher Physics Success Guide page 17 Circuits o o o o o Describe variation of current and potential difference with time in a CR circuit during charging and discharging. Define the time constant for a CR circuit. Determine the time constant of a CR circuit numerically and graphically. Define capacitive reactance. Use appropriate relationships to solve problems involving capacitive reactance, voltage, current, frequency and capacitance. Inductors in d.c. circuits o o o o Tutor Homework simulation – Charging a capacitor t RC XC REUK teacher resource – Smoothing capacitors V I Electrical4U teacher resource – Lenz law of electromagnetic induction 1 XC 2fC Teaching advanced physics teacher resource – Electromagnetic induction YouTube video – Back e.m.f. in a large solenoid E 12 LI 2 State what is meant by the self inductance of a coil. Definition of inductance and of back e.m.f.. Use Lenz’s Law to solve inductance problems. Use appropriate relationships to calculate energy stored by an inductor. St Andrew’s University learner resource – Reactance of a capacitor Hyperphysics learner resource – Crossover networks for loudspeakers YouTube video – Self-inductance of coil lighting a neon bulb Inductors in a.c. circuits o o o Define Inductive reactance. Use an appropriate relationship to solve problems involving back e.m.f., inductance (self inductance) and rate of change of current. Use appropriate relationships to solve problems relating to inductive reactance, voltage, current, frequency, energy and inductance (self inductance). Advanced Higher Physics Success Guide L dI dt page 18 Electromagnetic radiation o o o Cabrillo College animations – Characteristics of electromagnetic waves Know how electricity and magnetism are linked in Electromagnetic radiation. Understand that electromagnetic radiation exhibits wave properties and is made up of electric and magnetic field components. Use an appropriate relationship to solve problems involving the speed of light, the permittivity of free space, and permeability of free space. EMANIM animation – Animations of electromagnetic waves. University of West of Scotland activity – Measurement of Capacitance and Permittivity of Air New York University activity – Determination of permeability using current balance Advanced Higher Physics Success Guide page 19 Units, prefixes and uncertainties Key Areas and Associated Learning o o o o o Use appropriate units, prefixes and scientific notation, eg electronvolt, light year. Use of an appropriate number of significant figures in final answers. (significant figures are based on original data) Knowledge and use, where appropriate, of uncertainties, including systematic uncertainties, scale reading uncertainties, random uncertainties, and calibration uncertainties. Calculations involving absolute uncertainties and fractional/percentage uncertainties Appropriate use of significant figures in absolute uncertainties. Relationships Useful Resources SSERC handbook on data handling DW = DX + DY + DZ 2 2 2 DW æ DX ö æ DY ö æ DZ ö = ç ÷ +ç ÷ +ç ÷ W è X ø è Y ø è Z ø 2 2 Education Scotland guidance on data handling and uncertainties 2 Data analysis o o o o o o o State appropriate reading uncertainty associated with instrument scales. Calculate random uncertainty associated with repeated measurements. State calibration uncertainty associated with manufacturer’s claim for the accuracy of an instrument. Calculate absolute and percentage/ fractional uncertainty. Combine various types of uncertainties to obtain the total uncertainty in a measurement. Systematic uncertainties occur when readings taken are either all too small or all too large. They can arise due to measurement techniques or experimental design. SSERC handbook on uncertainties Calibration uncertainty is a manufacturer’s claim for the accuracy of an instrument compared with an approved standard. Advanced Higher Physics Success Guide page 20 o o o o o o o o o Absolute uncertainty should be rounded to one significant figure. Combination of uncertainties in measured values to obtain the total uncertainty in a calculated value. Graphical interpretation Use of error bars to represent absolute uncertainties on graphs. Estimation of uncertainty in the gradient and intercept of a linear graph. Understanding the meaning of the terms accuracy and precision with reference to the comparison of an obtained value with a true value. Sum, difference, product, quotient of quantities and quantities raised to a power. Various methods possible including the use of functions available in graph drawing software eg linest and trendline functions in Excel. Understanding the meaning of the terms accuracy and precision with reference to the comparison of an obtained value with a true value. The accuracy of a measurement compares how close the measurement is to the ‘true’ or accepted value. The precision of a measurement gives an indication of the uncertainty in the measurement. Education Scotland guide to using Excel in the Sciences Graphical interpretation o o Use of error bars to represent absolute uncertainties on graphs. Estimation of uncertainty in the gradient and intercept of a linear graph. Advanced Higher Physics Success Guide page 21