Ontario Grade 12 SPH4U Physics (Grade 12, University Preparation)
Chapters: 6
1. A. Scientific Investigation Skills and Career Exploration
A1 Scientific Investigation Skills · A2 Career Exploration
- The Scientific Method – The scientific method is the careful way scientists find out how the world works. Observe something, ask a testable question, make a hypothesis (a clear, testable guess), test it with a fair experiment (change one variable, measure one, keep the rest the same), repeat and record data, analyse it, draw a conclusion and share it so others can check. Results that fail the test are useful too: they send you back to a new hypothesis.
2. B. Dynamics
B1 Relating Science to Technology, Society, and the Environment · B2 Developing Skills of Investigation and Communication · B3 Understanding Basic Concepts
- Dynamics: Forces, Friction, Inclines and Circular Motion – Dynamics explains why things move the way they do. Newton's laws work in inertial (non-accelerating) frames; in accelerating frames we feel fictitious forces. Draw a free-body diagram, add the forces (gravity, normal, applied, tension, friction) and use ΣF = ma. Static friction holds things still up to μₛN; kinetic friction μₖN acts while sliding. On an incline, weight splits into mg sinθ and mg cosθ. Connected objects share one acceleration. In uniform circular motion a = v²/r points to the centre and F = mv²/r.
3. C. Energy and Momentum
C1 Relating Science to Technology, Society, and the Environment · C2 Developing Skills of Investigation and Communication · C3 Understanding Basic Concepts
- Elastic and Inelastic Collisions in 1D and 2D – In every collision, total momentum is conserved (no outside force during the short hit). In an elastic collision kinetic energy is also conserved. In an inelastic collision some kinetic energy becomes heat, sound or dent energy; if the bodies stick together it is perfectly inelastic. In 1D, elastic collision gives v₁ = (m₁ − m₂)u₁/(m₁ + m₂) and v₂ = 2m₁u₁/(m₁ + m₂) when body 2 starts at rest. In 2D, momentum is conserved separately along x and y.
4. D. Gravitational, Electric, and Magnetic Fields
D1 Relating Science to Technology, Society, and the Environment · D2 Developing Skills of Investigation and Communication · D3 Understanding Basic Concepts
- Electric Charges and Fields – Charge comes in two kinds, is conserved and comes in whole-number packets of e = 1.6 × 10⁻¹⁹ C. Two point charges push or pull with F = kq₁q₂/r² (k = 9 × 10⁹ N m² C⁻²). Forces and fields from many charges add as vectors (superposition). The field E = F/q₀ of a point charge is kq/r²; field lines show it. A dipole (±q a distance 2a apart) has moment p = q·2a; in a uniform field it feels zero net force but a torque τ = pE sinθ. Electric flux Φ = E·A, and Gauss's law says the flux out of any closed surface is q_enclosed/ε₀, which quickly gives E for a long wire (λ/2πε₀r), a plane sheet (σ/2ε₀) and a thin spherical shell (kq/r² outside, 0 inside).
5. E. The Wave Nature of Light
E1 Relating Science to Technology, Society, and the Environment · E2 Developing Skills of Investigation and Communication · E3 Understanding Basic Concepts
- 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.
6. F. Revolutions in Modern Physics: Quantum Mechanics and Special Relativity
F1 Relating Science to Technology, Society, and the Environment · F2 Developing Skills of Investigation and Communication · F3 Understanding Basic Concepts
- Modern Physics: Quantum Theory and Relativity – Modern physics began around 1900, when classical physics failed for the very small and the very fast. Quantum theory says energy comes in packets: a photon has E = hf. The photoelectric effect shows light acts as particles, while interference shows particles such as electrons act as waves (λ = h/p). Special relativity says the speed of light is the same for all observers, so moving clocks run slow (t = γt₀), moving lengths shrink, and mass is energy (E = mc²). These ideas power lasers, solar cells, electron microscopes, GPS and nuclear energy.