Ontario Grade 12 Physics Study Guide (SPH4U): Mechanics, Fields, Waves, and Modern Physics

Ontario Grade 12 Physics (SPH4U) is the most mathematically demanding science course in the Ontario secondary curriculum. It requires strong vector algebra, algebraic manipulation, and the ability to set up multi-step problems from physical principles. Students who have taken SPH3U (Grade 11 Physics) and MCR3U (Grade 11 Functions) will have most of the mathematical prerequisites; those who found Grade 11 Physics challenging should expect to invest significantly more time in the mechanics units.

The primary value of SPH4U for students continuing to university is the preparation it provides for first-year university physics courses, which are among the most common first-year fail points for students in engineering and physical science programs.

Kinematics: vectors in two dimensions

Vector components: Every 2D vector can be resolved into x and y components using trigonometry: Fₓ = F cosθ, F_y = F sinθ (where θ is measured from the x-axis or from a specified reference). To find the resultant of multiple vectors: add all x-components, add all y-components, then find the resultant: R = √(Rₓ² + R_y²), θ = arctan(R_y/Rₓ).

Relative motion: The velocity of A relative to B is v_A|B = v_A − v_B (vector subtraction). For a swimmer crossing a current, for example: the swimmer's velocity relative to the water and the water's velocity relative to the ground add vectorially to give the swimmer's actual path.

Projectile motion: Horizontal: uniform velocity, xₓ = v₀ₓ × t. Vertical: uniformly accelerated, y = v₀_y t − ½gt². These equations hold simultaneously — the time parameter links the two equations for a given projectile.

Dynamics: Newton's laws in 2D

Setting up a 2D free body diagram: (1) Draw the object isolated from its surroundings; (2) Draw every force acting on it (gravity always, normal force if in contact with surface, tension if connected by a string, friction if surface contact with relative motion or tendency for it, applied forces); (3) Set up a coordinate system — usually horizontal and vertical, but choose incline-parallel and perpendicular for objects on inclines; (4) Resolve all forces into components; (5) Apply ΣFₓ = maₓ and ΣF_y = ma_y separately.

Friction: Static friction: fₛ ≤ μₛN (can be anywhere from zero to maximum). Kinetic friction: fₖ = μₖN (constant once moving). Always determine first whether the object is moving or stationary to know which friction applies.

Circular motion: The net force toward the centre of the circle = mv²/r (centripetal force). This is not a new type of force — it is the net inward force from tension, gravity, normal force, or friction. For a car turning on a flat road: friction provides the centripetal force. For a car turning on a banked curve: the horizontal component of normal force plus friction (or minus, if the car tends to slide down) provides it.

Gravitation: Universal gravitation: F = Gm₁m₂/r². Gravitational field strength g = GM/r². For circular orbit: set F_gravity = F_centripetal: GM/r² = v²/r → v = √(GM/r). Period: T = 2πr/v = 2πr√(r/(GM)).

Energy and momentum

Conservation of energy: Total mechanical energy = KE + PE (constant when no non-conservative forces). When friction or air resistance acts: ΔKE + ΔPE + Ethermal = 0 (energy is conserved overall, but mechanical energy decreases by the work done against friction).

Conservation of momentum: Total momentum is conserved in all collisions (no external forces). For 2D collisions: momentum is conserved separately in each direction. p_x,before = p_x,after AND p_y,before = p_y,after. For elastic collisions, additionally: KE_before = KE_after.

Impulse-momentum theorem: Impulse J = F·Δt = Δp. Area under a force-time graph = impulse = change in momentum.

The wave nature of light

Snell's Law: n₁sinθ₁ = n₂sinθ₂ where n is the index of refraction (n = c/v). Total internal reflection occurs when light travels from a denser medium to a less dense medium and the angle of incidence exceeds the critical angle θ_c = arcsin(n₂/n₁).

Thin film interference: Light reflecting off the top and bottom surfaces of a thin film creates path length difference of 2t (for normal incidence, where t = film thickness). Phase shift of π (half wavelength) occurs when light reflects off a surface with higher refractive index. For constructive interference (bright): 2t = mλ/n (when both reflections have phase shift or neither does) or 2t = (m + ½)λ/n (when only one reflection has phase shift). For destructive interference: the other case.

Double-slit experiment: Path length difference Δx = dsinθ ≈ dy/L (for small angles) where d = slit separation, y = fringe position, L = screen distance. Constructive: Δx = mλ. Destructive: Δx = (m + ½)λ.

Modern physics

Photoelectric effect: Maximum KE = hf − φ (work function). If f < f₀ = φ/h, no electrons ejected regardless of intensity. Einstein's photon model explains all observations that the classical wave model cannot.

de Broglie wavelength: λ = h/p = h/(mv). All matter has an associated wavelength. For everyday objects, λ is negligibly small — quantum effects are only observable at atomic scales.

Bohr model: Electrons occupy quantised circular orbits. Energy of orbit: Eₙ = −13.6 eV/n². Photon emitted when electron transitions: E_photon = hf = Eᵢ − E_f.

Special relativity: As covered in the FAQ above — time dilation (t = γt₀), length contraction (L = L₀/γ), relativistic momentum (p = γmv), mass-energy (E = mc²).

The Spaced Repetition Flashcard Tool is excellent for formula recall under pressure. Build cards for every formula with the variables labelled and a note about when to apply it. The Pomodoro Timer helps structure problem-solving practice — 25 minutes of focused problems per topic, working through every question in released past exams. See the Ontario Grade 12 Chemistry study guide for the parallel study strategy for SCH4U.