Grade 12 · University
SPH4U Grade 12 Physics, worked through with a live AI tutor
SPH4U takes the Grade 11 tools and turns them two-dimensional: forces at angles, momentum in a glancing collision, projectiles from a height. Then it moves on to fields, where the diagrams matter as much as the equations, and finishes with special relativity and the photoelectric effect, which are the first physics most students have met that contradicts everyday intuition. The tutor works each of those on the whiteboard from your own problem set.
Prerequisite: SPH3U (Grade 11 Physics, university preparation)
What SPH4U covers
The strands of SPH4U Physics, in our words rather than the Ministry’s. Your teacher’s course outline decides the order and the weight.
Dynamics
Kinematics and forces in two dimensions, inclines and pulleys with friction, uniform circular motion and centripetal force, and frames of reference.
Energy and momentum
Work and energy with variable forces, springs and simple harmonic motion, conservation of momentum in one and two dimensions, and elastic and inelastic collisions.
Gravitational, electric and magnetic fields
Newton's law of gravitation and orbits, Coulomb's law, electric fields and potential, the motion of charges in electric and magnetic fields, and the field concept itself.
The wave nature of light
Interference and diffraction, Young's double-slit experiment, thin films and polarisation, and the evidence that light behaves as a wave.
Revolutions in modern physics: quantum mechanics and special relativity
Einstein's postulates, time dilation and length contraction, mass-energy equivalence, the photoelectric effect, and the particle and wave models of matter and light.
Curriculum reference: Ontario Ministry course page, checked .
Where students get stuck
Centripetal force is not a new force
It is the name for whatever real force points toward the centre: tension in a string, friction on a turning car, gravity for a satellite, the normal force at the bottom of a loop. Draw the free-body diagram with the real forces only, set their inward component equal to mass times speed squared over radius, and never add a separate centripetal arrow.
Two-dimensional collisions
Momentum is conserved in each direction separately, so write one equation for x and one for y. Resolve every velocity into components before and after, using the angles given. Kinetic energy is a third equation only if the collision is stated to be elastic; if it is not, you do not have that equation and the problem must give you something else.
Electric potential versus electric field
The field is a vector that tells a charge which way to accelerate; the potential is a scalar that tells you how much energy per charge a position holds. Field points from high potential to low. A question with a distance and a force is about the field; a question with energy or voltage is about potential, and the two are related by how fast potential changes with distance.
Double-slit fringe spacing
Bright fringes appear where the path difference from the two slits is a whole number of wavelengths. For small angles, the spacing between fringes is the wavelength times the distance to the screen divided by the slit separation. Narrower slits spread the fringes; longer wavelengths spread them. Check the direction of each effect against that formula before substituting.
Time dilation: whose clock is proper
The proper time is measured by the observer who sees both events at the same place, typically the one moving with the clock. Every other observer measures a longer interval. Decide who the proper observer is before touching the formula, because the factor only goes one way and picking the wrong frame flips the answer.
How a session on SPH4U works
- 1
Bring the actual problem
Share your screen, upload the page, or hold it up to the camera. The tutor reads the SPH4U question itself instead of your retyped version of it.
- 2
Talk it through on the whiteboard
You explain where you got to, out loud. The tutor writes the next step on a shared board while it talks, and asks you to take the one after that.
- 3
Try the next one yourself
Generate a practice set on the same topic, with full worked solutions that show the method rather than only the answer.
It starts in Learn mode: concepts first, the answer as a last resort. The tutor is not a Ministry resource and does not replace your teacher’s course outline.
SPH4U questions
Does the tutor follow the Ontario SPH4U curriculum?
It works from your textbook, your notes and your assignment, and from the five SPH4U strands: dynamics, energy and momentum, fields, the wave nature of light, and modern physics. It is not an official Ministry resource.
Do I need MCV4U for SPH4U?
Not as a prerequisite. SPH4U uses trigonometry, vector components and algebra rather than calculus. Taking MHF4U alongside helps with the trigonometry, and MCV4U's vectors unit overlaps with the fields work.
Stuck on SPH4U tonight
Bring the question from your own textbook or assignment. Talk it through out loud and watch it worked out step by step on a whiteboard.
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