Year 12 Physics Notes

5. Advanced Mechanics

5.1 Projectile Motion

  • Vertical motion: uniform acceleration
  • Horizontal motion: constant velocity
  • Applications:
    • Time of flight
    • Maximum height
    • Range (horizontal distance)
  • Vector Decomposition

5.2 Circular Motion

  • Uniform Circular Motion (UCM): constant speed in a perfect circle.
  • Velocity changes constantly in direction, magnitude stays the same.
  • Centripetal force (Fc) always acts towards the center of rotation, perpendicular to velocity.
  • Increase speed of rotation, require more force; decrease radius, need more force.
  • Distance in one revolution (T): circumference 2πr2πr
  • Linear velocity: v=2πrTv = \frac{2πr}{T}
  • Angular velocity: ω=∆θ∆tω = \frac{∆θ}{∆t}
  • Centripetal acceleration: ac=v2ra_c = \frac{v^2}{r}
  • Period, Velocity, Radius: Fc=mv2rFc = \frac{mv^2}{r}
  • Angular Velocity: ω=2πTω = \frac{2π}{T}
  • Energy in UCM: Kinetic energy is constant; no work is done (θ = 90°).
  • Torque: measure of turning-capacity of an applied force.  τ=rFsinθ\, τ = rFsinθ
  • Net torque changes rotational motion. For constant rotation, net torque = 0.

5.3 Gravitational Fields

  • Newton’s Law of Universal Gravitation: F=GMmr2F = G\frac{Mm}{r^2}, where GG is the gravitational constant.
  • Acceleration: g=GMr2g = G\frac{M}{r^2}
  • Circular Satellite Orbits: Gravitational force provides centripetal force.
  • Kepler’s Laws:
    • First Law: Law of Ellipses.
    • Second Law: Law of Areas.
    • Third Law: T2∝r3T^2 ∝ r^3
  • Orbital speed: v=2πrTv = \frac{2πr}{T}
  • Gravitational Potential Energy (GPE): U=−GMmrU = -G\frac{Mm}{r}
  • Total energy of an orbiting satellite: E=K+UE = K + U
  • Escape velocity: minimum velocity to escape gravitational field. KE=−UKE = -U

6. Electromagnetism

6.1 Charges in E and B fields

  • Force on charged particles in electric fields: F=qEF = qE
  • Constant electric fields between parallel plates: E=VdE = \frac{V}{d}
  • Magnetic force on a moving charge: F=qvBsinθF = qvBsinθ
  • Right-hand palm rule: Thumb = velocity, fingers = field, palm = force.
  • UCM in magnetic fields: qvB=mv2rqvB = \frac{mv^2}{r}

6.2 The Motor Effect

  • Force on a current-carrying wire: F=BILsinθF = BILsinθ
  • Force per unit length between parallel wires: FL=μ<em>0I</em>1I22πr\frac{F}{L} = \frac{μ<em>0I</em>1I_2}{2πr}
  • Torque on a motor coil: τ=NBIAcosθτ = NBIAcosθ

6.3 Electromagnetic Induction

  • Magnetic flux: Φ=BAcosθΦ = BAcosθ
  • Faraday’s Law: EMF=−N∆Φ∆tEMF = -N\frac{∆Φ}{∆t}
  • Lenz’s Law: Induced EMF opposes the change in flux.

6.4 Transformers

  • Voltages ratio: V<em>pV</em>s=N<em>pN</em>s\frac{V<em>p}{V</em>s} = \frac{N<em>p}{N</em>s}
  • Ideal transformer: P<em>p=P</em>sP<em>p = P</em>s and V<em>pI</em>p=V<em>sI</em>sV<em>pI</em>p = V<em>sI</em>s

7. Nature of Light

7.1 Electromagnetic Spectrum

  • Light as an electromagnetic wave: c=fλc = fλ, where c=3×108m/sc = 3 × 10^8 m/s
  • Photon energy: E=hfE = hf, where h=6.626×10−34Jsh = 6.626 × 10^{-34} Js
  • Spectrum Order: Radio < Microwave < Infrared < Visible < UV < X-rays < Gamma rays

7.2 Evidence for the Nature of Light

  • Photoelectric Effect: Ek=hf−ϕE_k = hf - ϕ
  • Young’s Double Slit Experiment: y=λDdy = \frac{λD}{d}
  • Wave-particle duality.

7.3 Quantum Theory

  • Energy levels: En=−13.6eVn2E_n = -\frac{13.6 eV}{n^2}
  • Energy transitions: ∆E=hf∆E = hf

7.4 Quantum Mechanical Model of the Atom

  • Heisenberg Uncertainty Principle: ∆x∆p≥ℏ2∆x∆p ≥ \frac{ℏ}{2}
  • Schrödinger Equation: Describes electron as a wavefunction.
  • Orbitals: s, p, d, f