Physics — Cambridge A-Level

recall and use EK = 21mv2

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define and use distance, displacement, speed, velocity and acceleration

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Forces, density and pressure

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understand that the magnetic field due to the current in a solenoid is increased by a ferrous core

Magnetic Fields Due to Currents

understand that the area under the force–extension graph represents the work done

Elastic and Plastic Behaviour

understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons

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recall and use Φ = BA

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understand that a magnetic field is an example of a field of force produced either by moving charges or by permanent magnets

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Astronomy and cosmology

Production and Use of X-rays

use equations of the form x = x0 sin ωt representing a sinusoidally alternating current or voltage

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recall that wavelengths in the range 400–700 nm in free space are visible to the human eye

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use, for a current-carrying conductor, the expression I = Anvq , where n is the number density of charge carriers

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calculate the energy released in nuclear reactions using E = c2∆m

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recall and use g = GM / r

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distinguish graphically between half-wave and full-wave rectification

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understand that all physical quantities consist of a numerical magnitude and a unit

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derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line

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understand that, while momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place

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understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass

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recall and use E = 21mω2x02 for the total energy of a system undergoing simple harmonic motion

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understand and use the terms load, extension, compression and limit of proportionality

Stress and Strain

derive, using W = Fs, the formula ∆EP = mg∆h for gravitational potential energy changes in a uniform gravitational field

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explain the relevance of binding energy per nucleon to nuclear reactions, including nuclear fusion and nuclear fission

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distinguish between nucleon number and proton number

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understand and use the concept of angular speed

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show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns (it will be assumed that end corrections are negligible; knowledge of the concept of end corrections is not required)

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recall and use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro ( μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)

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infer from the results of the α-particle scattering experiment the existence and small size of the nucleus

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recall the approximate range of wavelengths in free space of the principal regions of the electromagnetic spectrum from radio waves to γ-rays

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represent a magnetic field by field lines

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understand that a satellite in a geostationary orbit remains at the same point above the Earth’s surface, with an orbital period of 24 hours, orbiting from west to east, directly above the Equator

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compare pV = 31Nm<c2> with pV = NkT to deduce that the average translational kinetic energy of a molecule is 23 kT, and recall and use this expression

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define activity and decay constant, and recall and use A = λN

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understand and use the concept of magnetic flux linkage

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distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations

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understand that the weight of an object may be taken as acting at a single point known as its centre of gravity

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use the electronvolt (eV) as a unit of energy

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understand the use of X-rays in imaging internal body structures, including an understanding of the term contrast in X-ray imaging

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understand that centripetal acceleration causes circular motion with a constant angular speed

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explain the use of four diodes (bridge rectifier) for the full-wave rectification of an alternating current

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recall and use Malus’s law ( I = I0 cos2θ ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters (calculation of the effect of a polarising filter on the

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represent a gravitational field by means of field lines

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define and use force as rate of change of momentum

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derive, using the equations of motion, the formula for kinetic energy EK = 21mv2

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recall and use Q = It

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understand that the charge on charge carriers is quantised

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state and apply each of Newton’s laws of motion

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define magnetic flux density as the force acting per unit current per unit length on a wire placed at right- angles to the magnetic field

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understand that, when there is no resultant force and no resultant torque, a system is in equilibrium

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understand that, for a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre

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state Ohm’s law

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understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the

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use V = Q / (4πε0r) for the electric potential in the field due to a point charge

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use the Stefan–Boltzmann law L = 4πσr 2 T

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make reasonable estimates of physical quantities included within the syllabus

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describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance

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recall and use τ = RC for the time constant for a capacitor discharging through a resistor

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recall and use Hubble’s law v . H0d and explain how this leads to the Big Bang theory (candidates will only be required to use SI units)

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understand and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations, and express the period in terms of both frequency and angular frequency

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recall and use Coulomb’s law F = Q1Q2 / (4πε0 r 2) for the force between two point charges in free space

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understand that a photon is a quantum of electromagnetic energy

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understand why g is approximately constant for small changes in height near the Earth’s surface

Gravitational Force Between Point Masses

recall that a tracer that decays by β+ decay is used in positron emission tomography (PET scanning)

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explain photoelectric emission in terms of photon energy and work function energy

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recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point

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describe the composition, mass and charge of α-, β- and γ-radiations (both β– (electrons) and β+ (positrons) are included)

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determine acceleration using the gradient of a velocity–time graph

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understand the terms interference and coherence

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show an understanding of experiments that demonstrate diffraction including the qualitative effect of the gap width relative to the wavelength of the wave; for example diffraction of water waves in a ripple tank

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explain the use of a single diode for the half-wave rectification of an alternating current

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recall and use hf = Φ + 21mvmax2

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define and use density

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derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in parallel

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describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks

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use graphical methods to represent distance, displacement, speed, velocity and acceleration

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recall and use the circuit symbols shown in section 6 of this syllabus

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recall and use V = W / Q

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describe the effect of a uniform electric field on the motion of charged particles

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understand that mass is the property of an object that resists change in motion

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understand that nucleon number and charge are conserved in nuclear processes

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define the potential difference across a component as the energy transferred per unit charge

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define capacitance, as applied to both isolated spherical conductors and to parallel plate capacitors

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use the equations v = v0 cos ωt and v = ± ω ()xx022−

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recall and use the formula for the spring constant k = F / x

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understand that computed tomography (CT) scanning produces a 3D image of an internal structure by first combining multiple X-ray images taken in the same section from different angles to obtain a 2D image of the section, then repeating this process a

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show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing as speed increases is sufficie

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define and use linear momentum as the product of mass and velocity

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understand that a force might act on a current-carrying conductor placed in a magnetic field

Force on a Current‑Carrying Conductor

express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate

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recall and use E = hf

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use a vector triangle to represent coplanar forces in equilibrium

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define and use the terms stress, strain and the Young modulus

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define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point

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understand that deformation is caused by tensile or compressive forces (forces and deformations will be assumed to be in one dimension only)

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describe an experiment to determine the Young modulus of a metal in the form of a wire

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represent simple nuclear reactions by nuclear equations of the form NH eO H714 24 817 11" ++

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recall Kirchhoff’s second law and understand that it is a consequence of conservation of energy

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understand that a tracer is a substance containing radioactive nuclei that can be introduced into the body and is then absorbed by the tissue being studied

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understand the distinction between precision and accuracy

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understand that an object of known luminosity is called a standard candle

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understand that an antiparticle has the same mass but opposite charge to the corresponding particle, and that a positron is the antiparticle of an electron

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understand the origin of the Hall voltage and derive and use the expression VH = BI / (ntq), where t = thickness

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state the principle of conservation of momentum

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use Kirchhoff’s laws to solve simple circuit problems

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describe the interchange between kinetic and potential energy during simple harmonic motion

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understand that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction

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define the radian and express angular displacement in radians

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recall that, for an elastic collision, total kinetic energy is conserved and the relative speed of approach is equal to the relative speed of separation

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recall and use λ = h / p

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define resistance

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recall that protons and neutrons are not fundamental particles and describe protons and neutrons in terms of their quark composition

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describe the motion of a charged particle moving in a uniform magnetic field perpendicular to the direction of motion of the particle

Force on a Current‑Carrying Conductor

define and apply the torque of a couple

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define and use the terms mass defect and binding energy

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understand that energy is transferred by a progressive wave

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understand and use the terms threshold frequency and threshold wavelength

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state that (electron) antineutrinos are produced during β– decay and (electron) neutrinos are produced during β+ decay

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define and use specific latent heat and distinguish between specific latent heat of fusion and specific latent heat of vaporisation

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understand the equivalence between energy and mass as represented by E = mc2 and recall and use this equation

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describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of an object is equal to the product of its mass and the acceleration of free fall

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understand the difference between scalar and vector quantities and give examples of scalar and vector quantities included in the syllabus

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understand and explain the effects of systematic errors (including zero errors) and random errors in measurements

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calculate the energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair

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recall and use hf = E1 – E2

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recall and use Newton’s law of gravitation F = Gm1m2 / r2 for the force between two point masses

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recall and use I = I0e–μx for the attenuation of X-rays in matter

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distinguish between root-mean-square (r.m.s.) and peak values and recall and use I r.m.s. = I0 / 2 and Vr.m.s. = V0 / 2 for a sinusoidal alternating current

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understand the use of a galvanometer in null methods

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recall and use E = ∆V / ∆d to calculate the field strength of the uniform field between charged parallel plates

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understand how the concept of electric potential leads to the electric potential energy of two point charges and use EP = Qq / (4πε0 r)

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sketch the variation of binding energy per nucleon with nucleon number

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use IR / I0 = (Z1 – Z2)2 / (Z1 + Z2)2 for the intensity reflection coefficient of a boundary between two media

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recall and use W = p∆V for the work done when the volume of a gas changes at constant pressure and understand the difference between the work done by the gas and the work done on the gas

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understand that polarisation is a phenomenon associated with transverse waves

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use Wien’s displacement law and the Stefan–Boltzmann law to estimate the radius of a star

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understand that a resistive force acting on an oscillating system causes damping

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recall and use F = qE for the force on a charge in an electric field

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assess the uncertainty in a derived quantity by simple addition of absolute or percentage uncertainties

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understand that α-particles have discrete energies but that β-particles have a continuous range of energies because (anti)neutrinos are emitted in β-decay

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understand the appearance and formation of emission and absorption line spectra

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derive, from the definitions of pressure and density, the equation for hydrostatic pressure ∆p = ρg∆h

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recall F = ma and solve problems using it, understanding that acceleration and resultant force are always in the same direction

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understand the principle of a potential divider circuit

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define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point

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understand that an electric current is a flow of charge carriers

Electric Current

understand that objects moving against a resistive force may reach a terminal (constant) velocity

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solve problems using P = W / t

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understand that regions of equal temperature are in thermal equilibrium

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represent an electric field by means of field lines

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use ∆λ / λ . ∆f / f . v / c for the redshift of electromagnetic radiation from a source moving relative to an observer

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understand and use the terms period, frequency and peak value as applied to an alternating current or voltage

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understand that, for a point outside a spherical conductor, the charge on the sphere may be considered to be a point charge at its centre

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represent α- and β-decay by a radioactive decay equation of the form UT h92238 90234

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understand how wavelength may be determined from the positions of nodes or antinodes of a stationary wave

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draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus

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Quantum physics

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explain why redshift leads to the idea that the Universe is expanding

Cambridge A‑Level Physics 9702 – Stellar Radii and Cosmic Redshift

understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency

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Magnetic fields

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explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions

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describe an experiment to determine the acceleration of free fall using a falling object

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explain the origin of the forces between current-carrying conductors and determine the direction of the forces

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Capacitance

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explain how electric and magnetic fields can be used in velocity selection

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analyse the effect of a single capacitor in smoothing, including the effect of the values of capacitance and the load resistance

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Work, energy and power An understanding of the forms of energy and energy transfers from Cambridge IGCSE/O Level Physics or equivalent is assumed.

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determine the direction of the force on a charge moving in a magnetic field

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recall and use W = 21QV = 21CV2

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understand that a photon has momentum and that the momentum is given by p = E / c

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derive P = Fv and use it to solve problems

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understand that the lowest possible temperature is zero kelvin on the thermodynamic temperature scale and that this is known as absolute zero

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explain and use the principle of superposition

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recall and use the principle of the potentiometer as a means of comparing potential differences

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understand that the lines in the emission and absorption spectra from distant objects show an increase in wavelength from their known values

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understand how ultrasound waves are generated and detected by a piezoelectric transducer

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define half-life

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recall and use I = I0e–μx for the attenuation of ultrasound in matter

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Waves An understanding of colour from Cambridge IGCSE/O Level Physics or equivalent is assumed.

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explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and light intensity

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understand the de Broglie wavelength as the wavelength associated with a moving particle

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analyse and interpret graphical representations of transverse and longitudinal waves

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understand the term luminosity as the total power of radiation emitted by a star

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recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)

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understand that a piezo-electric crystal changes shape when a p.d. is applied across it and that the crystal generates an e.m.f. when its shape changes

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explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum wavelength of X-rays produced from the accelerating p.d.

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apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between objects in both one and two dimensions (knowledge of the concept of coefficient of restitution is not required)

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use molar quantities where one mole of any substance is the amount containing a number of particles of that substance equal to the Avogadro constant NA

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understand that there are discrete electron energy levels in isolated atoms (e.g. atomic hydrogen)

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recall and use the charge of each flavour of quark and understand that its respective antiquark has the opposite charge (no knowledge of any other properties of quarks is required)

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understand that isotopes are forms of the same element with different numbers of neutrons in their nuclei

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state and apply the principle of moments

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understand that electromagnetic radiation has a particulate nature

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use SI base units to check the homogeneity of physical equations

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calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)

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compare transverse and longitudinal waves

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recall and use the first law of thermodynamics ∆U = q + W expressed in terms of the increase in internal energy, the heating of the system (energy transferred to the system by heating) and the work done on the system

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understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelength and speed

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understand how the concept of gravitational potential leads to the gravitational potential energy of two point masses and use EP = –GMm / r

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Dynamics An understanding of forces from Cambridge IGCSE/O Level Physics or equivalent is assumed.

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understand the exponential nature of radioactive decay, and sketch and use the relationship x = x0e–λt, where x could represent activity, number of undecayed nuclei or received count rate

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understand that a force of constant magnitude that is always perpendicular to the direction of motion causes centripetal acceleration

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understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases

Resistance and Resistivity

understand the conditions required if two-source interference fringes are to be observed

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describe the use of a diffraction grating to determine the wavelength of light (the structure and use of the spectrometer are not included)

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define and use specific heat capacity

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derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in series

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recall and use E = Q / (4πε0 r 2) for the electric field strength due to a point charge in free space

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understand that the root-mean-square speed cr.m.s. is given by c<>

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Ideal gases

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understand that a gas obeying pV ∝ T, where T is the thermodynamic temperature, is known as an ideal gas

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understand that amount of substance is an SI base quantity with the base unit mol

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state the basic assumptions of the kinetic theory of gases

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analyse and interpret graphical representations of the variations of displacement, velocity and acceleration for simple harmonic motion

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recall and use intensity = power/area and intensity ∝ (amplitude )2 for a progressive wave

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understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference

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use the expression fο = f sv / (v ± vs) for the observed frequency when a source of sound waves moves relative to a stationary observer

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recall and use the equation F = BIL sin θ, with directions as interpreted by Fleming’s left-hand rule

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use the capacitance formulae for capacitors in series and in parallel

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recall and use the fact that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current

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understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure

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recall and use R = ρL / A

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understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties, including the density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m

Temperature Scales

describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

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understand that fluctuations in count rate provide evidence for the random nature of radioactive decay

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solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance

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describe the changes to quark composition that take place during β– and β+ decay

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state that all electromagnetic waves are transverse waves that travel with the same speed c in free space

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understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency (understanding of the Doppler effect for a stationary source and a moving observer is not required)

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understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence for a wave nature

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understand that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system

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represent a vector as two perpendicular components

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recall and use P = VI, P = I 2R and P = V 2 / R

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understand how the reflection of pulses of ultrasound at boundaries between tissues can be used to obtain diagnostic information about internal structures

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describe a simple model for the nuclear atom to include protons, neutrons and orbital electrons

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Temperature

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use the formula for the combined resistance of two or more resistors in parallel

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define the specific acoustic impedance of a medium as Z = ρc, where c is the speed of sound in the medium

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define and use pressure

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add and subtract coplanar vectors

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define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

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Electric fields

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recall and use Hooke’s law

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describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles

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recall and use F = mrω2 and F = mv2 / r

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sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp

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show an understanding of experiments that demonstrate two-source interference using water waves in a ripple tank, sound, light and microwaves

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understand that an electric field is an example of a field of force and define electric field as force per unit positive charge

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understand that photoelectrons may be emitted from a metal surface when it is illuminated by electromagnetic radiation

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determine the elastic potential energy of a material deformed within its limit of proportionality from the area under the force–extension graph

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understand the use of a Hall probe to measure magnetic flux density

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understand and use the terms elastic deformation, plastic deformation and elastic limit

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recall and understand that the efficiency of a system is the ratio of useful energy output from the system to the total energy input

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explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes

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understand the concept of work, and recall and use work done = force × displacement in the direction of the force

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derive, using the definitions of speed, frequency and wavelength, the wave equation v = f λ

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use the unified atomic mass unit (u) as a unit of mass

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relate a rise in temperature of an object to an increase in its internal energy

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explain how molecular movement causes the pressure exerted by a gas and derive and use the relationship pV = 31Nm<c2>, where < c2> is the mean-square speed (a simple model considering one-dimensional collisions and then extending to three dimensions

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recall and use d sin θ = nλ

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explain why the maximum kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity

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explain that the resistance of a filament lamp increases as current increases because its temperature increases

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recall and use C = Q / V

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understand that a quark is a fundamental particle and that there are six flavours (types) of quark: up, down, strange, charm, top and bottom

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use equations of the form x = x0 e–(t / RC) where x could represent current, charge or potential difference for a capacitor discharging through a resistor

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recall and use the equation of state for an ideal gas expressed as pV = nRT, where n = amount of substance (number of moles) and as pV = NkT, where N = number of molecules

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determine velocity using the gradient of a displacement–time graph

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understand that a hadron may be either a baryon (consisting of three quarks) or a meson (consisting of one quark and one antiquark)

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sketch magnetic field patterns due to the currents in a long straight wire, a flat circular coil and a long solenoid

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recall that electrons and neutrinos are fundamental particles called leptons

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understand that the scale of thermodynamic temperature does not depend on the property of any particular substance

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analyse graphs of the variation with time of potential difference, charge and current for a capacitor discharging through a resistor

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recall and use F = BQv sin θ

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recall and apply the principle of conservation of energy

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recall and use the formula ∆EP = mg∆h for gravitational potential energy changes in a uniform gravitational field

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derive, using C = Q / V, formulae for the combined capacitance of capacitors in series and in parallel

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recall and use λ = ax / D for double-slit interference using light

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recall and use a = rω2 and a = v2 / r

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understand that a couple is a pair of forces that acts to produce rotation only

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use λ = 0.693 / t

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understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature

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use the formula for the combined resistance of two or more resistors in series

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understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)

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recall and use the inverse square law for radiant flux intensity F in terms of the luminosity L of the source F = L / (4πd 2)

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recall and use v = f λ

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define and apply the moment of a force

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analyse circular orbits in gravitational fields by relating the gravitational force to the centripetal acceleration it causes

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define power as work done per unit time

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understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties, including the density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m

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use ϕ = –GM / r for the gravitational potential in the field due to a point mass

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define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit

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derive, from Newton’s law of gravitation and the definition of gravitational field, the equation g = GM / r 2 for the gravitational field strength due to a point mass

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convert temperatures between kelvin and degrees Celsius and recall that T / K = θ / °C + 273.

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use a = –ω2x and recall and use, as a solution to this equation, x = x0 sin ωt

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explain what is meant by nuclear fusion and nuclear fission

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recall and use V = IR

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show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing as speed increases is sufficie

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explain the meaning of the term diffraction

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understand the use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

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use the equation ∆p = ρg∆h

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recall and use Malus’s law ( I = I0 cos2θ ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters (calculation of the effect of a polarising filter on the

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understand and use the terms light, critical and heavy damping and sketch displacement–time graphs illustrating these types of damping

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recall Kirchhoff’s first law and understand that it is a consequence of conservation of charge

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Gravitational fields

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determine displacement from the area under a velocity–time graph

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determine the electric potential energy stored in a capacitor from the area under the potential–charge graph

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recall that the Boltzmann constant k is given by k = R / NA

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understand and use the notation A Z X for the representation of nuclides

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recall and use EP = 21 Fx = 21 kx2 for a material deformed within its limit of proportionality

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use the concept of efficiency to solve problems

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understand the use of standard candles to determine distances to galaxies

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understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process

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recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the peak surface temperature of a star

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recall and use Faraday’s and Lenz’s laws of electromagnetic induction

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recall and use ω = 2π / T and v = rω

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understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the

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Oscillations

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understand that computed tomography (CT) scanning produces a 3D image of an internal structure by first combining multiple X-ray images taken in the same section from different angles to obtain a 2D image of the section, then repeating this process a

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understand that radioactive decay is both spontaneous and random

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explain how molecular movement causes the pressure exerted by a gas and derive and use the relationship pV = 31Nm<c2>, where < c2> is the mean-square speed (a simple model considering one-dimensional collisions and then extending to three dimensions

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