Impulse, Momentum and Circular Motion

Further Mechanics

• This topic covers impulse, conservation of momentum in two dimensions, and circular motion, with applications like modern rail transportation.
• Impulse is defined by the equation: impulse = FΔt = Δp (Newton's second law of motion).
• Core practical 9 investigates the relationship between force exerted on an object and its change of momentum.
• Conservation of linear momentum can be applied to problems in two dimensions.
• Core practical 10 uses ICT to analyse collisions between small spheres, such as ball bearings on a table top.
• Collisions can be classified as either elastic or inelastic based on energy conservation.
• The kinetic energy of a non-relativistic particle can be expressed as E = p²/2m.
• Angular displacement can be expressed in radians or degrees, and conversions between these units are possible.
• Angular velocity is related to linear velocity by v = ωr, and to period by ω = 2π/T.
• Vector diagrams can be used to derive the equations for centripetal acceleration: a = v²/r = rω².
• A resultant force (centripetal force) is required to produce and maintain circular motion.
• The formula for centripetal force is F = ma = mv²/r = mrω².

Electric and Magnetic Fields

• This topic includes Coulomb's law, capacitors, magnetic flux density, and electromagnetic induction.
• An electric field (or force field) is a region where a charged particle experiences a force.
• Electric field strength is defined as E = F/Q.
• The force between two charges can be calculated using the formula: F = Q₁Q₂ / 4πε₀r².
• The electric field due to a point charge is given by: E = Q / 4πε₀r².
• There's a relationship between electric field and electric potential.
• For an electric field between parallel plates, the equation E = V/d applies.
• The electric potential for a radial field can be calculated using V = Q / 4πε₀r.
• Field lines and equipotentials can be used to describe radial and uniform electric fields.
• Capacitance is defined as C = Q/V.
• The energy stored by a capacitor is W = ½QV.
• This equation can be derived from the area under a potential difference against charge graph.
• Additional equations for energy stored in a capacitor include W = ½CV² and W = Q²/C.
• Charge and discharge curves for resistor-capacitor circuits can be drawn and interpreted, and the time constant RC is important.
• Core practical 11 involves using an oscilloscope or data logger to display and analyse the potential difference across a capacitor as it charges and discharges through a resistor.
• During exponential discharge in a resistor-capacitor circuit, the equations Q = Q₀e^(-t/RC), I = I₀e^(-t/RC) and V = V₀e^(-t/RC) apply.
• Related logarithmic equations are ln Q = ln Q₀ - t/RC, ln I = ln I₀ - t/RC, and ln V = ln V₀ - t/RC.
• Terms like magnetic flux density B, flux Φ, and flux linkage NΦ are important in electromagnetism.
• The force on charged particles moving in a magnetic field is given by F = Bqv sinθ, and Fleming's left-hand rule applies.
• For current-carrying conductors in a magnetic field, F = BIl sinθ, and Fleming's left-hand rule is used.
• Factors affecting induced e.m.f. in a coil are important.
• Faraday's law determines the magnitude of an induced e.m.f., and is combined with Lenz's law in the equation ε = -d(NΦ)/dt.

Nuclear and Particle Physics

• This topic encompasses atomic structure, particle accelerators, and the standard quark-lepton model.
• Key concepts include alpha scattering, the nuclear model of the atom, accelerating particles, and interaction interpretation.
• Nucleon number (mass number) and proton number (atomic number) must be understood.
• Large-angle alpha particle scattering provides evidence for the nuclear model of the atom.
• Electrons are released in thermionic emission and can be accelerated by electric and magnetic fields.
• Electric and magnetic fields are key to particle accelerators (linac and cyclotron) and detectors (ionization and deflection).
• The equation r = p/BQ is used for charged particle motion in a magnetic field.
• Conservation laws of charge, energy, and momentum apply to particle interactions.
• High energies are required to probe the structure of nucleons.
• ΔE = c²Δm relates energy and mass in creation/annihilation events.
• Units of MeV, GeV, MeV/c²,and GeV/c² are used and converted to SI units.
• Relativistic effects on particle lifetime can be significant.
• The standard model classifies particles as baryons (three quarks), mesons (quark-antiquark), leptons (fundamental particles) and photons.
• Every particle has an antiparticle, with properties that can be deduced from the particle.
• Conservation laws determine if particle interactions are possible.
• Particle equations can be written and interpreted.

Thermodynamics

• Specific heat capacity, specific latent heat, internal energy, and the gas equation are central.
• Equations ΔE = mcΔθ and ΔE = LΔm relate energy changes to temperature and phase.
• Core practical 12 involves calibrating a thermistor in a potential divider circuit.
• Core practical 13 is determining the specific latent heat of a phase change.
• Internal energy is the random distribution of potential and kinetic energy among molecules.
• Absolute zero is understood in relation to the average kinetic energy of molecules.
• pV = NkT is the ideal gas equation.
• Core practical 14 investigates the relationship between pressure and volume of a gas at fixed temperature.
• ½m<c²> = ³/₂kT relates average kinetic energy to temperature.

Nuclear Physics

• Nuclear binding energy is related to mass deficit by ΔE = c²Δm.
• The atomic mass unit (u) is used to express small masses.
• Nuclear fusion and fission are understood via the binding energy per nucleon curve.
• Nuclear fusion requires high densities and temperatures.
• Background radiation should be accounted for.
• Nature, penetration, ionising ability, and range of nuclear radiations (alpha, beta, gamma) are key.
• Nuclear equations are written and interpreted.
• Core practical 15 investigates the absorption of gamma radiation by lead.
• Nuclear decay is spontaneous and random.
• Half-life is determined graphically and used in equations like A = λN, dN/dt = -λN, λ = ln2/t₁/₂, N = N₀e^(-λt) and A = A₀e^(-λt).

Oscillations

• Simple harmonic motion and damping.
• Simple harmonic motion occurs when F = -kx.
• Equations for SHM: a = -ω²x, x = Acos ωt, v = -Aω sin ωt, ω = 2πf, T = 1/f.
• Equations for a simple harmonic oscillator: T = 2π√(m/k) and a simple pendulum T = 2π√(l/g)
• Displacement-time graphs give the velocity as the gradient.
• Velocity-time graphs give the acceleration as the gradient.
• Resonance is a key concept.
• Core practical 16 involves determining an unknown mass using resonant frequencies.
• Conservation of energy applies to damped and undamped oscillations
• Distinction between free and forced oscillations.
• Amplitude of forced oscillations changes near the natural frequency, and damping affects resonance.
• Damping and plastic deformation reduce oscillation amplitude.

Astrophysics and Cosmology

• Gravitational fields, astronomical observations, star formation/evolution, and the universe's history/future.
• A gravitational field (force field) is a region where mass experiences a force.
• Gravitational field strength is g = F/m.
• Newton's law of universal gravitation: F = Gm₁m₂/r².
• Gravitational field due to a point mass: g = Gm/r².
• Radial gravitational field: Vgrav = -Gm/r.
• Electric and gravitational fields can be compared.
• Newton's laws and universal gravitation are applied to orbital motion.
• Black body radiators can be interpreted via radiation curves.
• Stefan-Boltzmann law for black body radiators: L = σAT⁴.
• Wien's law: λmaxT = 2.898 x 10⁻³ m K.
• Intensity equation: I = L/4πd² when L is luminosity and d is the distance from the source.
• Astronomical distances are determined by trigonometric parallax.
• Standard candles (objects of known luminosity) give distance.
• Hertzsprung-Russell diagrams relate stellar luminosity to surface temperature.
• Hertzsprung-Russell diagrams relate to the life cycle of stars.
• Doppler effect: movement of a source relative to an observer/detector affects wave frequency.
• Redshift equations are: z ≈ Δλ/λ ≈ Δf/f ≈ v/c.
• v = Hod (for objects at cosmological distances).
• Controversy exists over the age and ultimate fate of the universe.
• This is associated with the Hubble constant and the existence of dark matter.