Physics

Why does a snowball thrown from a cliff land so far out, how does a pilot hold a straight track in a crosswind, why does a toolbox slide off a fast-starting truck, and what keeps a roller-coaster rider in the seat upside down? This unit answers with dynamics in two dimensions.

You will sharpen your vector skills (including vector subtraction and change in velocity) and use them for projectiles launched at any angle and height and for relative velocity. You will apply Newton's laws in two dimensions with free-body diagrams, analyse static and kinetic friction, inclined planes and connected systems (pulleys, a counterweighted dumbwaiter, ramp-and-pulley systems, stacked blocks and loads on accelerating vehicles), and compare inertial and non-inertial frames of reference and the fictitious forces felt in accelerating frames. You will derive the equations of uniform circular motion and use them for flat and banked curves, conical pendulums, rotor rides and vertical loops, then test them in a whirling-stopper investigation. The unit ends by analysing technologies such as seat-belt retractors, centrifuges and runaway truck ramps, their social and environmental impacts, and careers that use dynamics.

This unit builds on the SPH3U units Kinematics and Forces (and the trigonometry of MCR3U). Scientific investigation skills and career exploration (strand A) are woven through the lessons. It leads into Work, Energy and Simple Harmonic Motion, Momentum and Collisions, and Gravitational, Electric and Magnetic Fields, where circular motion returns in satellite orbits. Use g = 9.8 m/s² throughout.

In this unit you will extend the energy ideas of Grade 11 to the full Grade 12 toolkit. You will define work for a force at any angle (W = FΔd cos θ) and for a changing force (the area under a force–displacement graph), and use the work–energy theorem in two dimensions, on inclines and on curved paths. You will connect gravitational potential energy to the work done by gravity, learn what makes a force conservative, and apply the law of conservation of energy to roller coasters, pendulums, loops and toboggan runs, with and without friction.

Next come springs. You will use Hooke's law (F = −kx), derive elastic potential energy (Ee = ½kx²), and solve launcher, spring-drop and bungee problems. Springs lead to simple harmonic motion: the period of a mass on a spring (T = 2π√(m/k)), its link to uniform circular motion through the reference circle, energy in SHM, and the simple pendulum (T = 2π√(L/g)). You will test conservation of energy with a bouncing ball, a pendulum and a bungee investigation, explain damped motion in shock absorbers and why perpetual motion is impossible, and finish with power, efficiency and an analysis of energy technologies such as regenerative braking, elevator counterweights and pumped storage, including their social and environmental impacts.

Remember from Grade 11: SPH3U (Work, Energy and Power) introduced W = FΔd, Ek = ½mv², Eg = mgh, conservation of energy, power and efficiency; SPH3U Waves and Sound introduced period, frequency and amplitude. This unit also uses vectors, inclines and circular motion from the sibling unit Dynamics: Forces and Motion in a Plane, and connects to MHF4U (radians, exponential decay) and MCV4U (dot products and derivatives of sinusoidal functions). Use g = 9.8 N/kg and a scientific calculator. Every lesson has worked examples, a safe hands-on activity, plenty of practice with full answers and a short quiz.

Coming next: momentum, impulse and collisions in one and two dimensions are taught in the sibling unit Momentum and Collisions.

Curriculum: The Ontario Curriculum, Grades 11 and 12: Science (2008, revised), Physics, Grade 12, University Preparation (SPH4U), strand C. Energy and Momentum: overall expectation C1 and specific expectation C1.2 (technologies and their impact), C2.1 to C2.4 (work, energy, the work–energy theorem, conservation of energy and its investigation), and C3.1, C3.2 and C3.4 (Hooke's law and elastic potential energy, simple harmonic motion, and the implications of conservation laws for damped motion and perpetual motion). Expectations C2.5 to C2.7, C3.3 and C3.5, and the momentum parts of C1 and C2.1, are taught in Momentum and Collisions. Scientific investigation skills and career exploration (strand A) are woven through the lessons.

Why does a rifle kick back, how can a curler know where both stones will go, why do air bags and helmets save lives, and how did physicists predict a particle that no one could see? This unit answers with momentum, one of the most powerful conservation laws in physics.

You will define linear momentum (p = mv) and impulse (J = FΔt), use the impulse–momentum theorem, and find impulse as the area under a force–time graph. You will apply the law of conservation of momentum to collisions and to explosions and recoil in one dimension, then sort collisions into elastic and inelastic by tracking kinetic energy, and derive the results of head-on elastic collisions (including how a CANDU reactor's moderator slows neutrons). Combining momentum with energy lets you solve ballistic pendulum, spring-release and crash reconstruction problems. With vector components you will extend everything to two dimensions and glancing collisions, then test the conservation laws in a home investigation of collisions and explosions. The unit finishes with applications and their impacts: rockets and propulsion, vehicle safety, helmets and sports equipment, building implosion, fireworks and forensic crash analysis, and the conservation-law detective story that predicted the neutrino, later studied at the Sudbury Neutrino Observatory.

Remember from Grade 11: SPH3U (Kinematics: Motion in One and Two Dimensions and Forces) introduced velocity, acceleration, Newton's laws and F = mΔv ÷ Δt; SPH3U (Work, Energy and Power) introduced kinetic and gravitational energy; SPH3U (Thermal and Nuclear Energy) introduced alpha and beta decay. This unit also uses vector components from the sibling unit Dynamics: Forces and Motion in a Plane and the energy ideas (work, springs, conservation of energy, damping) from Work, Energy and Simple Harmonic Motion, which it builds on rather than re-teaching. Use g = 9.8 N/kg and a scientific calculator. Every lesson has worked examples, a safe hands-on activity, plenty of practice with full answers and a short quiz.

Coming next: the sibling units Gravitational, Electric and Magnetic Fields, The Wave Nature of Light, Quantum Mechanics and Special Relativity use momentum again, for example for charged particles, photons and objects moving near the speed of light.

Curriculum: The Ontario Curriculum, Grades 11 and 12: Science (2008, revised), Physics, Grade 12, University Preparation (SPH4U), strand C. Energy and Momentum: specific expectations C1.1 and C1.2 (analysing and assessing momentum technologies such as rockets, protective equipment, crumple zones, building implosion and crash analysis), C2.1 (momentum terminology), C2.5 to C2.7 (momentum, impulse and kinetic energy in one and two dimensions, elastic and inelastic collisions, and investigations of collisions and explosions), and C3.3 to C3.5 (elastic and inelastic collisions, the implications of the conservation laws, and the prediction of the neutrino). Expectations C2.2 to C2.4, C3.1 and C3.2, and the energy parts of C1 and C2.1, are taught in Work, Energy and Simple Harmonic Motion. Scientific investigation skills and career exploration (strand A) are woven through the lessons.

This unit is about fields: the invisible "maps of force" that let masses, charges and currents push and pull each other across empty space. You will start with Newton's law of universal gravitation and the gravitational field, then use them to explain satellite orbits, Kepler's laws, escape speed, black holes and the evidence for dark matter. Real missions run through the unit, from GPS and Canada's RADARSAT Constellation Mission to the Artemis II flight around the Moon in April 2026, with Canadian astronaut Jeremy Hansen on board.

Next you will move to electricity: Coulomb's law, electric fields and field lines, electric potential energy and electric potential, and the uniform field between parallel plates. You will follow charged particles as they are accelerated and deflected, and repeat the reasoning of Millikan's oil drop experiment to show that charge comes in packages of 1.60 × 10⁻¹⁹ C. Then you will add magnetism: the fields of wires and solenoids, the force on a current-carrying conductor, and the force on a moving charge, which bends particles into circles.

Finally, you will analyse field technologies (mass spectrometers, cyclotrons and synchrotrons, MRI, magnetic storage), compare the three fields and the four fundamental forces, and weigh the social and environmental effects of GPS, Earth-observation and internet satellites, space debris and medical accelerators.

Remember from Grade 11: in SPH3U Forces you used Fg = mg with g = 9.8 N/kg and Newton's three laws; in SPH3U Electricity and Magnetism you met charge, current and potential difference, magnetic field lines, Oersted's principle, the right-hand rules (and left-hand rules for electron flow) and the motor principle. This unit turns those ideas into equations that work anywhere in the universe. You will also use circular motion (centripetal acceleration v²/r) from the SPH4U unit Dynamics, and energy conservation from Work, Energy and Simple Harmonic Motion.

Constants used in this unit:

• G = 6.67 × 10⁻¹¹ N·m²/kg², k = 8.99 × 10⁹ N·m²/C², μ₀ = 4π × 10⁻⁷ T·m/A
• e = 1.60 × 10⁻¹⁹ C, c = 3.00 × 10⁸ m/s
• electron mass 9.11 × 10⁻³¹ kg, proton mass 1.67 × 10⁻²⁷ kg, 1 u = 1.66 × 10⁻²⁷ kg
• Earth: mass 5.97 × 10²⁴ kg, radius 6.37 × 10⁶ m, g = 9.8 N/kg
• Moon: mass 7.35 × 10²² kg, radius 1.74 × 10⁶ m, mean distance from Earth 3.84 × 10⁸ m
• Sun: mass 1.99 × 10³⁰ kg, mean distance from Earth 1.50 × 10¹¹ m (1 AU)

Safety first: investigations use balloons, small magnets, everyday devices and free online simulations. Never open anything that plugs into the wall, keep magnets away from young children and medical devices, and do any cloud-chamber or dry-ice work only with an adult or at a science centre.

Curriculum expectations covered: D1.1, D1.2, D2.1 to D2.5 and D3.1 to D3.3 (The Ontario Curriculum, Grades 11 and 12: Science, 2008, SPH4U Strand D, Gravitational, Electric, and Magnetic Fields). Scientific investigation skills from Strand A are woven into the activities. Related SPH4U units: Dynamics; Work, Energy and Simple Harmonic Motion; Momentum and Collisions; Wave Nature of Light; Quantum Mechanics; Special Relativity.

Is light a wave or a stream of particles? In this unit you will follow the evidence that settled that question in the 1800s, and learn to use the wave model to explain and calculate what light does. You will start with wavefronts, rays and refraction, explain dispersion (why a prism makes a rainbow), and study diffraction and Huygens' principle in a ripple tank. You will analyse the two-point-source interference pattern of water waves, then trace the historical debate between Newton's particle model and Huygens' wave model.

With those tools you will tackle the classic experiments: Young's double slit (d sin θ = mλ and Δx = Lλ/d), single-slit diffraction (w sin θ = nλ), and diffraction gratings and spectroscopy. You will explain the colours of soap bubbles and oil slicks with thin-film interference, design anti-reflective coatings, measure tiny thicknesses with air wedges, and use polarization (including Malus's law and Brewster's angle) to show that light is a transverse wave. You will see how diffraction limits the resolution of eyes, telescopes and disc players, and describe how oscillating electric dipoles produce electromagnetic waves, from radio to X-rays. The unit ends by analysing technologies such as holograms, CDs, DVDs and Blu-ray discs, anti-reflective coatings, spectroscopes, polarizing lenses, night vision and wireless networks, and assessing their effects on society and the environment.

Remember from earlier grades: in Grade 10 (Light and Geometric Optics) you used the ray model, the index of refraction and Snell's law. In Grade 11 (Waves and Sound) you used v = fλ, superposition, path difference and the reflection of waves at boundaries. In this course, Gravitational, Electric and Magnetic Fields gives the field ideas behind electromagnetic waves.

Safety first: several activities can use a low-power laser pointer. Read the laser-safety box with a grown-up each time: never look into a beam or point it at anyone. Never look at the Sun, with or without a filter, grating or lens. You will need a scientific calculator (in degree mode, except for the radian answers in the resolution lesson).

Coming next: in Quantum Mechanics you will meet evidence that light also behaves like particles (photons) and that matter behaves like waves, and in Special Relativity you will see what follows from the constant speed of light.

Curriculum: The Ontario Curriculum, Grades 11 and 12: Science (2008, revised), Physics, Grade 12, University Preparation (SPH4U), strand E. The Wave Nature of Light: E1.1 and E1.2 (relating science to technology, society and the environment), E2.1 to E2.4 (developing skills of investigation and communication) and E3.1 to E3.4 (understanding basic concepts). Strand A (scientific investigation skills and career exploration) is woven through the lessons.

Around 1900, physics seemed almost complete. Then a handful of experiments that classical physics could not explain started a revolution. In this unit you will follow it step by step: blackbody radiation and Planck's idea that energy comes in quanta (E = hf); Einstein's photons and the photoelectric effect (E(k,max) = hf − W), including analysing real-style data to measure Planck's constant; photon momentum and the Compton effect; wave-particle duality, pair production and PET scans; de Broglie's matter waves (λ = h/p) and the electron diffraction experiments that confirmed them; the Bohr model and atomic line spectra; and Heisenberg's uncertainty principle and the probability interpretation.

You will also see how quantum ideas power everyday and cutting-edge technology (solar cells, digital camera sensors, LEDs, lasers, electron microscopes and quantum computers), weigh their effects on society, meet Canadian contributors from Willard Boyle and Donna Strickland to Arthur McDonald at SNOLAB, and finish with the Standard Model of elementary particles.

The other revolution of modern physics, Einstein's theory of relativity, has its own unit: Special Relativity. You will use ideas from The Wave Nature of Light (diffraction, interference, c = fλ), Gravitational, Electric and Magnetic Fields (work done on charges, magnetic forces) and Momentum and Collisions (conservation of momentum) throughout.

In 1905 a 26-year-old patent clerk named Albert Einstein published a paper that rewrote the rules of space and time. In this unit you will follow that revolution step by step. You will start with frames of reference and the "common sense" physics of Galileo and Newton, see why the speed of light caused a crisis, and study the Michelson–Morley experiment, which looked for the "ether" and found nothing. Then you will meet Einstein's two postulates and follow his thought experiments to their surprising consequences: the relativity of simultaneity, time dilation, length contraction, the twin paradox and the cosmic speed limit.

You will solve real problems with the Lorentz factor γ: how long a moving clock's tick lasts, how far a muon can travel, how short a spacecraft becomes, how velocities add near the speed of light, and how relativistic momentum and E = mc² describe particles in accelerators and nuclear reactors. You will analyse the evidence: muons from cosmic rays, atomic clocks flown on jets, particle lifetimes in accelerators. You will finish by assessing how relativity made possible technologies such as GPS, particle accelerators, PET scanners and nuclear power, and what they mean for society.

Remember from Grade 11: in Physics (SPH3U) you added relative velocities (Kinematics: Motion in One and Two Dimensions), met E = mc² and mass defect in fusion (Work, Energy and Power) and learned how fission, fusion and CANDU reactors work (Thermal and Nuclear Energy). In this course, the Dynamics: Forces and Motion in a Plane unit introduced inertial and non-inertial frames of reference. This unit builds on all of these. The quantum half of strand F (photons, the photoelectric effect, matter waves and the Standard Model) is taught in the sibling unit Quantum Mechanics.

You will need a scientific calculator with scientific-notation keys. Use c = 3.00 × 10⁸ m/s unless a question says otherwise. Every lesson has worked examples, diagrams, a hands-on activity, plenty of practice with full answers and a short quiz.

Curriculum: The Ontario Curriculum, Grades 11 and 12: Science (2008, revised), Physics, Grade 12, University Preparation (SPH4U), strand F. Revolutions in Modern Physics: Quantum Mechanics and Special Relativity, the special-relativity part: specific expectations F1.1, F1.2, F2.1, F2.3 and F2.4, and overall expectation F3 (the evidence for special relativity). Scientific investigation skills (strand A) are practised throughout.