South 고등학교 3학년 Physics I

Chapters: 3

1. Mechanics and energy

Kinds of motion · Newton's laws and 1D motion · Newton's third law · Momentum conservation in collisions · Impulse and momentum · Mechanical energy conservation · Heat engines · Second law of thermodynamics · Special relativity · Mass-energy equivalence

Motion: Distance, Speed, Velocity, Acceleration and Graphs – An object is in motion when its position changes with time. Distance is the full path length (a scalar); displacement is the straight gap from start to finish with a direction (a vector). Speed = distance ÷ time; velocity = displacement ÷ time. Acceleration = change in velocity ÷ time. The slope of an s–t graph gives velocity, the slope of a v–t graph gives acceleration, and the area under a v–t graph gives the distance. For uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
Inertia, First Law, Momentum, Second Law and Impulse – A body keeps its state of rest or uniform motion unless a net external force acts on it (first law). Inertia is this laziness to change, and mass measures it. Momentum p = mv. The rate of change of momentum equals the net force: F = dp/dt, which gives F = ma when mass is constant (second law). Impulse J = F × Δt = Δp; a longer stopping time means a smaller force.
Third Law, Conservation of Momentum and Equilibrium of Forces – Forces always come in pairs: if A pushes B, B pushes A with an equal and opposite force at the same instant (third law). The pair acts on different bodies. For a system with no net external force, the total linear momentum stays constant, which explains recoil, rockets and collisions. A particle is in equilibrium when all forces on it add to zero; three concurrent forces in equilibrium form a closed triangle.
Potential Energy, Spring Energy and Conservative Forces – Potential energy U is energy stored because of position or shape. Near the Earth U = mgh; in a stretched or squeezed spring U = ½kx². A force is conservative if its work depends only on the start and end points, not on the path (gravity, spring force). Then F = −dU/dx and mechanical energy K + U stays constant. Friction and air drag are non-conservative: they turn mechanical energy into heat.
Second Law of Thermodynamics, Heat Engines and Refrigerators – The first law says energy is conserved; the second law says which way heat and energy can go. Heat flows by itself only from hot to cold (Clausius). No engine can turn all the heat it takes into work; some must be thrown into a colder body (Kelvin–Planck). A heat engine takes Q₁ from a hot source, does work W and rejects Q₂: efficiency η = W/Q₁ = 1 − Q₂/Q₁. A refrigerator uses work W to move Q₂ from cold to hot: COP α = Q₂/W. The best possible engine, the Carnot engine, has η = 1 − T₂/T₁.
Special Relativity – Special relativity (Einstein, 1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in a vacuum, c ≈ 3.00 × 10⁸ m/s, is the same for every observer. It follows that moving clocks run slow (t = γt₀), moving objects are shorter along their motion (L = L₀/γ), and mass is a form of energy (E = mc²), with γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1, so Newton's mechanics works; near c it fails.
Nuclear Fission and Fusion – Fission is the splitting of a large, unstable nucleus such as uranium-235 or plutonium-239. A slow neutron is absorbed, the nucleus splits into two smaller nuclei and releases 2 or 3 neutrons, gamma rays and a lot of energy. The new neutrons can split more nuclei: a chain reaction. In a nuclear reactor, a moderator slows neutrons and control rods absorb some, so the chain reaction stays steady. Fusion is the joining of two light nuclei, such as hydrogen, to make a heavier nucleus, such as helium. Some mass turns into energy. Fusion powers the Sun and stars, but it needs very high temperature and pressure.

2. Matter and electromagnetic fields

Electrons bound in atoms · Discrete energy levels · Energy bands · Diodes and semiconductors · Magnetic effect of current · Magnetic materials · Electromagnetic induction

Atoms: From Alpha Scattering to the Bohr Model – Rutherford shot alpha particles at thin gold foil and found that an atom is mostly empty, with a tiny, heavy, positive nucleus in the middle. Bohr then said the electron in hydrogen can move only on fixed orbits where its angular momentum is nh/2π. In orbit n the radius is 0.529 n² Å, the speed is (2.19 × 10⁶)/n m/s and the energy is −13.6/n² eV. When the electron jumps down, the energy difference comes out as light of one exact colour, which gives the line spectrum of hydrogen.
Semiconductors and the p-n Junction Diode – A semiconductor has a small energy gap (about 1 eV), so a little heat frees some electrons. Pure silicon is intrinsic (electrons = holes). Adding a 5-valence atom makes n-type; a 3-valence atom makes p-type. Joining p and n makes a junction with a depletion layer and a barrier (about 0.7 V for Si). The diode conducts in forward bias, almost not in reverse bias, so it can change AC into one-way DC (rectifier).
Magnetic Field due to a Current: Biot-Savart Law and Ampere's Law – A current makes a magnetic field around it (Oersted, 1820). The Biot-Savart law gives the field of a tiny piece of wire: dB = (μ₀/4π)·I dl sinθ / r². Adding all pieces of a circular loop gives B = μ₀NI / 2R at the centre and μ₀NIR² / 2(R² + x²)^{3/2} on the axis. Ampere's circuital law ∮B·dl = μ₀I gives B = μ₀I / 2πr for a long straight wire. A long solenoid has a strong, uniform field B = μ₀nI inside and almost none outside.
Magnetism and Matter – A bar magnet behaves like a solenoid: tiny current loops of electrons inside it line up. Its field on the axis (2m/r³ form) is twice the field on the equator at the same distance, and points the other way. In a uniform field a magnet feels a torque τ = m × B that turns it to line up with B. Field lines are closed loops that never cross. Materials react differently: diamagnetic ones are pushed out of a field (χ small and negative), paramagnetic ones are pulled in weakly (χ small and positive), ferromagnetic ones are pulled in strongly (χ very large). Magnetisation M is the magnetic moment per unit volume; B = μ₀(H + M), χ = M/H, μᵣ = 1 + χ. Heating reduces magnetism: paramagnets follow Curie law χ = C/T, and a ferromagnet turns paramagnetic above its Curie temperature.
Electromagnetic Induction – When the magnetic flux through a coil changes, an emf is produced in it: ε = −N dΦ/dt (Faraday). The minus sign is Lenz's law: the induced current always opposes the change that made it. Moving a rod in a field gives motional emf ε = Blv. A changing current makes an emf in its own coil (self-induction, L) and in a nearby coil (mutual induction, M).
Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.

3. Waves and communication

Frequency, wavelength, speed · Total internal reflection · Electromagnetic spectrum · Interference · Wave-particle duality of light · Matter waves

Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
Refraction, Total Internal Reflection and the Prism – Light bends when it crosses from one medium to another: n₁ sin i = n₂ sin r. Going from a denser to a rarer medium it bends away from the normal; beyond the critical angle C (sin C = 1/n) no light escapes and all of it reflects back: total internal reflection. Optical fibres use this to carry light. In a prism, r₁ + r₂ = A and deviation δ = i + e − A; at minimum deviation n = sin((A + δm)/2) / sin(A/2).
Electromagnetic Waves – A changing electric field acts like a current, called the displacement current, and it makes a magnetic field. A changing magnetic field makes an electric field. Together they travel as an electromagnetic (EM) wave at c = 3 × 10⁸ m/s, even through empty space. E and B are at right angles to each other and to the direction of travel, so EM waves are transverse. Sorted by wavelength, they form the spectrum: radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.
Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.
Photoelectric Effect and Einstein's Equation – When light of high enough frequency falls on a metal, electrons jump out at once. Light comes in packets called photons, each with energy E = hν. One photon gives all its energy to one electron: hν = φ + KEmax, where φ is the work function. Below the threshold frequency ν₀ = φ/h no electron comes out, however bright the light.
Matter Waves and the de Broglie Relation – Light behaves like a wave and a particle. In 1924 Louis de Broglie said matter does the same: every moving particle has a wave with wavelength λ = h/p = h/mv. For a body of kinetic energy K, λ = h/√(2mK); for an electron accelerated through V volts, λ = 1.227/√V nm. Everyday objects have far too tiny a λ to notice, but electrons have λ about the size of atoms.