To do well in Ontario SPH4U, master vectors first — they appear in every unit, and the students who lose marks are those who work with magnitudes instead of resolving forces into x and y components before applying Newton's second law. Practise a wide range of multi-step mechanics problems (watching for the common traps with friction, circular motion, and collisions), and for the modern-physics unit prioritise conceptual understanding — why the photoelectric effect breaks the wave model, and identifying proper time and proper length — over memorising the relativity formulas.
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.
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Frequently asked questions
What are the units covered in Ontario Grade 12 Physics (SPH4U)?
Ontario Grade 12 Physics (SPH4U) covers five units: Unit 1 — Kinematics (vectors in 2D, displacement, velocity and acceleration vectors, projectile motion, relative motion); Unit 2 — Dynamics (Newton's laws applied to 2D problems, free body diagrams, friction, circular motion, gravitational force and fields, centripetal acceleration); Unit 3 — Energy and Momentum (work, kinetic and potential energy, conservation of energy, elastic and inelastic collisions, impulse-momentum theorem, conservation of momentum); Unit 4 — The Wave Nature of Light (electromagnetic waves, reflection, refraction, Snell's law, total internal reflection, thin film interference, diffraction, the double-slit experiment and single slit, polarisation); Unit 5 — Revolutions in Modern Physics (special relativity — time dilation, length contraction, mass-energy equivalence; photoelectric effect; Compton effect; de Broglie hypothesis; Bohr model; wave-particle duality; nuclear fission and fusion). SPH4U is explicitly designed as preparation for first-year university physics.
How important are vectors in SPH4U, and how do I work with them?
Vectors are fundamental to SPH4U and appear in every unit. A vector quantity has both magnitude and direction; a scalar has magnitude only. Force, velocity, acceleration, displacement, and momentum are vectors; speed, distance, mass, energy, and work are scalars. Vector addition: use components (resolve each vector into x and y components using trigonometry, add components separately, find resultant magnitude and direction). For free body diagram problems, always set up a coordinate system and resolve all forces into components before applying Newton's Second Law (ΣF = ma) in each direction separately. Students who try to work with magnitudes only without resolving into components consistently lose marks on multi-force problems.
What are the most common errors in SPH4U mechanics problems?
The most common errors in SPH4U mechanics: (1) Omitting friction — always check whether friction is present and whether it is static (object not moving) or kinetic (object in motion); static friction can range from zero to μₛN, kinetic friction is exactly μₖN; (2) In circular motion, treating centripetal force as a separate force to add to the free body diagram rather than identifying which combination of real forces provides the centripetal force; (3) In energy problems, forgetting that friction converts mechanical energy to thermal energy (not conserved — use work-energy theorem with work done by friction as negative); (4) In projectile motion, confusing the velocity at the highest point (horizontal component only, vertical = 0) with zero velocity (the object is still moving horizontally); (5) In collision problems, forgetting to check whether the collision is elastic (KE conserved) or inelastic (KE not conserved) before applying conservation of energy.
How do I approach the special relativity unit in SPH4U?
Special relativity in SPH4U introduces two concepts that contradict everyday experience: time dilation (moving clocks run slow) and length contraction (moving objects are shorter). The key is accepting these as physically real, not as measurement errors. The Lorentz factor γ = 1/√(1 − v²/c²) appears in both formulas: time dilation: Δt = γΔt₀ (where Δt₀ is proper time measured in the rest frame of the event); length contraction: L = L₀/γ (where L₀ is proper length measured in the rest frame of the object). For SPH4U problems: identify which time interval is the proper time (measured at the same location in one frame) or which length is the proper length (measured in the rest frame of the object). Relativistic momentum: p = γmv. Mass-energy: E₀ = mc² (rest energy); total energy E = γmc².
How should I prepare for the SPH4U final examination?
SPH4U preparation should balance conceptual understanding with problem-solving practice. For the mechanics units (kinematics, dynamics, energy): practice a wide variety of multi-step problems including 2D force situations, circular motion in various orientations, and collisions. For waves: practice calculations involving Snell's law, thin film interference path length conditions, and the double-slit equation. For modern physics: focus on conceptual understanding alongside formula application — understanding why the photoelectric effect disproves the classical wave model is more important than memorising the photoelectric equation. For special relativity: practice identifying proper time and proper length in scenarios before applying the Lorentz transformations. Most schools provide a formula sheet for the final exam — familiarise yourself with what is and is not included.
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