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 $2πr$
• Linear velocity: $v = \frac{2πr}{T}$
• Angular velocity: $ω = \frac{∆θ}{∆t}$
• Centripetal acceleration: $a_c = \frac{v^2}{r}$
• Period, Velocity, Radius: $Fc = \frac{mv^2}{r}$
• Angular Velocity: $ω = \frac{2π}{T}$
• Energy in UCM: Kinetic energy is constant; no work is done (θ = 90°).
• Torque: measure of turning-capacity of an applied force. $\, τ = rFsinθ$
• Net torque changes rotational motion. For constant rotation, net torque = 0.

5.3 Gravitational Fields

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

6. Electromagnetism

6.1 Charges in E and B fields

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

6.2 The Motor Effect

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

6.3 Electromagnetic Induction

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

6.4 Transformers

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

7. Nature of Light

7.1 Electromagnetic Spectrum

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

7.2 Evidence for the Nature of Light

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

7.3 Quantum Theory

• Energy levels: $E_n = -\frac{13.6 eV}{n^2}$
• Energy transitions: $∆E = hf$

7.4 Quantum Mechanical Model of the Atom

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