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Ontario Grade 12 Physics (SPH4U) lessons and practice
Build SPH4U skills in dynamics, energy and momentum, gravitational and electromagnetic fields, wave optics, quantum mechanics, and special relativity.
Publication status
71 of 71 written lessons published
The topic map covers the course expectations. A topic marked “written lesson not published” remains available for practice and tutoring, but does not have a reviewed written lecture yet.
SPH4U study path
Connect mechanics, fields, light, and modern physics
Two-dimensional forces, reference frames, friction, systems, and circular motion.
Work-energy reasoning, springs, impulse, collisions, explosions, and conservation laws.
Gravitational, electric, and magnetic fields, potentials, forces, and particle motion.
Diffraction, refraction, interference, polarization, colour, and electromagnetic radiation.
Photons, matter waves, quantum evidence, special relativity, and the standard model.
Review the SPH3U prerequisite · Compare Ontario Grade 12 math courses · Connect SPH4U to engineering study
Free published lessons
Start learning SPH4U
These lessons are public, free to read, and connected to the full course map below.
- A1.1 · Form scientific questions, predictions, and testable hypotheses
- A1.2 · Choose suitable equipment, materials, methods, and procedures
- A1.3 · Find appropriate print and electronic research sources
- A1.4 · Plan investigations using safe laboratory practices and WHMIS
- A1.5 · Conduct inquiries safely while controlling relevant variables
- A1.6 · Record and organize accurate data in suitable formats
- A1.7 · Organize research information and document sources
- A1.8 · Analyse evidence, solve quantitative problems, and evaluate error
SPH4U
Topics by strand
Plan, perform, analyse, and communicate advanced physics investigations safely, and explore related careers.
- A1.1 · Form scientific questions, predictions, and testable hypotheses (published written lesson)
- A1.2 · Choose suitable equipment, materials, methods, and procedures (published written lesson)
- A1.3 · Find appropriate print and electronic research sources (published written lesson)
- A1.4 · Plan investigations using safe laboratory practices and WHMIS (published written lesson)
- A1.5 · Conduct inquiries safely while controlling relevant variables (published written lesson)
- A1.6 · Record and organize accurate data in suitable formats (published written lesson)
- A1.7 · Organize research information and document sources (published written lesson)
- A1.8 · Analyse evidence, solve quantitative problems, and evaluate error (published written lesson)
- A1.9 · Evaluate research sources for accuracy, reliability, and bias (published written lesson)
- A1.10 · Draw and justify conclusions from inquiry and research evidence (published written lesson)
- A1.11 · Communicate physics procedures, results, and conclusions clearly (published written lesson)
- A1.12 · Use numeric, symbolic, graphical, and vector representations (published written lesson)
- A1.13 · Report calculations with suitable precision and significant figures (published written lesson)
- A2.1 · Explore advanced physics careers and required education (published written lesson)
- A2.2 · Describe contributions of physicists, including Canadians (published written lesson)
Analyse two-dimensional forces, relative motion, systems of objects, friction, and uniform circular motion.
- B1.1 · Analyse a device that applies linear or circular motion (published written lesson)
- B1.2 · Assess impacts of linear- and circular-motion technologies (published written lesson)
- B2.1 · Use terminology for frames, components, friction, and circular motion (published written lesson)
- B2.2 · Solve projectile and relative-motion problems with two-dimensional vectors (published written lesson)
- B2.3 · Solve two-dimensional force and friction problems (published written lesson)
- B2.4 · Predict and investigate forces acting on systems of objects (published written lesson)
- B2.5 · Relate system motion to its forces using free-body diagrams (published written lesson)
- B2.6 · Solve horizontal and vertical uniform-circular-motion problems (published written lesson)
- B2.7 · Investigate centripetal force, acceleration, radius, period, and speed (published written lesson)
- B3.1 · Distinguish inertial and non-inertial frames and apparent forces (published written lesson)
- B3.2 · Explain benefits and drawbacks of static and kinetic friction (published written lesson)
- B3.3 · Derive course-level uniform-circular-motion relationships (published written lesson)
Apply work, energy, impulse, momentum, and conservation laws in one and two dimensions.
- C1.1 · Analyse and improve a technology using energy and momentum (published written lesson)
- C1.2 · Assess impacts of energy- and momentum-based technologies (published written lesson)
- C2.1 · Use work, energy, impulse, momentum, and collision terminology (published written lesson)
- C2.2 · Solve one- and two-dimensional work-energy problems (published written lesson)
- C2.3 · Analyse mechanical and thermal energy systems through inquiry (published written lesson)
- C2.4 · Test conservation of energy during transformations (published written lesson)
- C2.5 · Solve momentum, impulse, mass, velocity, and kinetic-energy problems (published written lesson)
- C2.6 · Analyse elastic and inelastic collisions in one and two dimensions (published written lesson)
- C2.7 · Test conservation laws with collisions and explosions (published written lesson)
- C3.1 · Relate Hooke’s law, work, and elastic potential energy (published written lesson)
- C3.2 · Connect simple harmonic motion, Hooke’s law, and circular motion (published written lesson)
- C3.3 · Distinguish elastic and inelastic collisions (published written lesson)
- C3.4 · Explain implications of energy and momentum conservation (published written lesson)
- C3.5 · Explain how conservation laws supported the neutrino prediction (published written lesson)
Compare fields and solve problems involving gravity, charge, electric potential, and magnetic force.
- D1.1 · Analyse a technological system that uses fields (published written lesson)
- D1.2 · Assess impacts of technologies that use fields (published written lesson)
- D2.1 · Use terminology for field forces, potentials, energies, and exchange particles (published written lesson)
- D2.2 · Solve universal-gravitation and circular-orbit problems (published written lesson)
- D2.3 · Solve electric-force, field, energy, and potential problems (published written lesson)
- D2.4 · Solve magnetic-force problems for moving charges and currents (published written lesson)
- D2.5 · Investigate particle behaviour in a field (published written lesson)
- D3.1 · Compare fundamental forces in major physics models (published written lesson)
- D3.2 · Compare gravitational, electric, and magnetic fields (published written lesson)
- D3.3 · Use diagrams to compare field sources and directions (published written lesson)
Investigate diffraction, refraction, interference, polarization, colour, and electromagnetic radiation.
- E1.1 · Analyse a technology that uses the wave nature of light (published written lesson)
- E1.2 · Assess impacts of wave-optics technologies (published written lesson)
- E2.1 · Use terminology for diffraction, interference, polarization, and radiation (published written lesson)
- E2.2 · Investigate wave diffraction and interference (published written lesson)
- E2.3 · Investigate diffraction, refraction, polarization, and interference of light (published written lesson)
- E2.4 · Analyse and solve diffraction and interference problems (published written lesson)
- E3.1 · Explain two-dimensional diffraction and interference of water waves (published written lesson)
- E3.2 · Explain diffraction, refraction, polarization, and interference of light (published written lesson)
- E3.3 · Explain colour separation using wave-optics concepts (published written lesson)
- E3.4 · Describe electromagnetic radiation from an oscillating electric dipole (published written lesson)
Study evidence and course-level calculations for quantum mechanics, particle models, and special relativity.
- F1.1 · Analyse how quantum mechanics and relativity changed scientific thought (published written lesson)
- F1.2 · Assess the importance of modern physics to technology (published written lesson)
- F2.1 · Use quantum-mechanics and special-relativity terminology (published written lesson)
- F2.2 · Solve photoelectric, Compton-effect, and matter-wave problems (published written lesson)
- F2.3 · Calculate course-level time, length, and mass effects in special relativity (published written lesson)
- F2.4 · Analyse data supporting relativity or quantum theory (published written lesson)
- F3.1 · Describe evidence for the particle model of light (published written lesson)
- F3.2 · Describe evidence for the wave model of matter (published written lesson)
- F3.3 · Explain Einstein’s postulates and evidence for special relativity (published written lesson)
- F3.4 · Describe quarks, hadrons, and field particles in the standard model (published written lesson)
Worked examples
Start with worked Grade 12 examples
These original examples introduce selected SPH4U expectations. The full expectation map is not a complete set of published written lessons or a substitute for official course materials and assignments. The strand-prefixed labels below identify the matching Ontario specific expectations; titles are concise study-guide paraphrases.
A car travels at 10.0 m/s around a level circular curve of radius 50.0 m. Find its centripetal acceleration.
Worked method: The acceleration points toward the centre. ac = v²/r = (10.0 m/s)²/(50.0 m) = 2.00 m/s² inward.
فارسی · توضیح مثال
خودرویی با سرعت ۱۰٫۰ متر بر ثانیه در مسیر دایرهای افقی با شعاع ۵۰٫۰ متر حرکت میکند. شتاب مرکزگرا را بیابید. شتاب به سوی مرکز است. ac = v²/r = (10.0 m/s)²/(50.0 m) = 2.00 m/s² به سمت مرکز.
A 0.200 kg ball moving at +6.0 m/s rebounds at −4.0 m/s. Find the impulse on the ball.
Worked method: Choose the initial direction as positive. J = Δp = m(vf − vi) = 0.200(−4.0 − 6.0) = −2.0 N·s. The negative sign means the impulse is opposite the initial motion.
فارسی · توضیح مثال
توپی ۰٫۲۰۰ کیلوگرمی با سرعت +۶٫۰ متر بر ثانیه حرکت میکند و با سرعت −۴٫۰ متر بر ثانیه برمیگردد. ضربه وارد بر توپ را بیابید. جهت اولیه را مثبت میگیریم. J = Δp = m(vf − vi) = 0.200(−4.0 − 6.0) = −2.0 N·s. علامت منفی یعنی ضربه خلاف جهت حرکت اولیه است.
Find the energy of a 500 nm photon using h = 6.626 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s.
Worked method: Convert 500 nm to 5.00 × 10⁻⁷ m. E = hc/λ = 3.98 × 10⁻¹⁹ J to three significant figures.
فارسی · توضیح مثال
انرژی فوتونی با طول موج ۵۰۰ نانومتر را با h = 6.626 × 10⁻³⁴ J·s و c = 3.00 × 10⁸ m/s بیابید. ۵۰۰ نانومتر برابر 5.00 × 10⁻⁷ متر است. E = hc/λ = 3.98 × 10⁻¹⁹ J با سه رقم معنادار.
Try independently, then check
Write your own solution before opening each answer. If a step is unclear, review the matching expectation or a Grade 11 prerequisite.
A 2.0 kg cart moving at 3.0 m/s sticks to a stationary 1.0 kg cart. Find their common velocity.
Show worked answer
Conserve momentum: (2.0)(3.0) = (2.0 + 1.0)vf, so vf = 2.0 m/s in the original direction.
فارسی · تمرین و پاسخ
ارابه ۲٫۰ کیلوگرمی با سرعت ۳٫۰ متر بر ثانیه به ارابه ساکن ۱٫۰ کیلوگرمی میچسبد. سرعت مشترک را بیابید. پایستگی تکانه: (2.0)(3.0) = (2.0 + 1.0)vf، پس vf = 2.0 m/s در جهت اولیه.
Light of wavelength 600 nm passes through two slits separated by 0.30 mm onto a screen 2.0 m away. Find the first-order fringe distance from the centre.
Show worked answer
For small angles, y = mλL/d = (1)(600 × 10⁻⁹ m)(2.0 m)/(0.30 × 10⁻³ m) = 4.0 × 10⁻³ m = 4.0 mm.
فارسی · تمرین و پاسخ
نور با طول موج ۶۰۰ نانومتر از دو شکاف با فاصله ۰٫۳۰ میلیمتر عبور میکند و به پردهای در فاصله ۲٫۰ متر میرسد. فاصله نوار مرتبه اول از مرکز را بیابید. برای زاویه کوچک، y = mλL/d = (1)(600 × 10⁻⁹ m)(2.0 m)/(0.30 × 10⁻³ m) = 4.0 × 10⁻³ m = 4.0 mm.
Scientific investigation processes across expectations
These processes are practised throughout the course, rather than listed as separate lessons.
- Initiating and planning: ask testable questions, predict, identify variables, and select safe procedures (آغاز و برنامهریزی: طرح پرسش آزمونپذیر، پیشبینی، تشخیص متغیرها و انتخاب روش ایمن)
- Performing and recording: measure carefully, control variables, and organize observations and data (اجرا و ثبت: اندازهگیری دقیق، کنترل متغیرها و سازماندهی مشاهدهها و دادهها)
- Analysing and interpreting: use equations and graphs, evaluate uncertainty, and justify conclusions (تحلیل و تفسیر: استفاده از معادله و نمودار، ارزیابی عدمقطعیت و توجیه نتیجه)
- Communicating: use SI units, significant figures, vectors, free-body diagrams, graphs, and clear explanations (ارتباط علمی: استفاده از یکاهای SI، ارقام معنادار، بردار، نمودار جسم آزاد، نمودار و توضیح روشن)
Source and coverage
Prerequisite: Physics, Grade 11, University Preparation (SPH3U). Confirm your current school timetable and admission requirements.
The expectation map follows the official Ontario physics curriculum. Titles are concise study-guide paraphrases; consult the official source for exact requirements. Browse all courses.
Sources and editorial process
Curriculum-aligned and reviewed before publication
This independent study guide follows the official course source. It is not an official government, school, or university publication.
Lesson drafts are AI-assisted, checked for structure, notation, calculations, course boundaries, and readability, and made public only after administrator approval. Because corrections can still be necessary, readers can report a problem.