U of T · Introduction to Physics I · Fall

PHY131H1: motion, force, and conservation.

Classical mechanics from kinematics through waves. The physics is Newton's; the difficulty is translating a paragraph of English into a diagram, then into equations that can be solved — and knowing which conserved quantity makes the problem short.

About this course

The mechanics half of first-year physics.

PHY131H1 "Introduction to Physics I" covers classical kinematics and dynamics, momentum, energy, force, friction, work, power, angular momentum, oscillations, waves and sound. It runs 36 lecture hours and 20 practical hours, so roughly a third of the time is laboratory work, and a lab kit fee of about 53 dollars applies. Calculus is a recommended co-requisite — MAT158H1 qualifies. The sequel is PHY132H1.

Note the exclusion. PHY131H1 excludes PHY151H1, the specialist stream. If a Physical Science specialist is ever under consideration, check which one that program requires before enrolling — they are not interchangeable.

01

Chapters

In course order. Each page has the concept, worked examples, the diagram habits that make problems tractable, pitfalls, and practice.

PHY131H1Physics I · Fall PHY132H1Physics II · Winter (sequel) Co-reqcalculus recommended

1. Units, vectors & estimation

   Dimensional analysis, components, significant figures.

   Open →

2. Kinematics in one dimension

   Position, velocity, acceleration; the constant-$a$ equations.

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3. Motion in two dimensions

   Projectiles and relative motion.

   Open →

4. Newton's laws

   Free-body diagrams and $\sum F = ma$.

   Open →

5. Friction & circular motion

   Static versus kinetic; centripetal acceleration.

   Open →

6. Work, energy & power

   The work-energy theorem and conservation.

   Open →

7. Momentum & collisions

   Impulse, conservation, elastic and inelastic.

   Open →

8. Rotation & angular momentum

   Torque, moment of inertia, rolling.

   Open →

9. Oscillations

   Simple harmonic motion, pendulums, damping.

   Open →

10. Waves & sound

    Wave equation, superposition, standing waves, Doppler.

    Open →

02

Textbook Spine

The calendar lists the topics in the order used here. This guide follows the standard calculus-based introductory sequence — kinematics, dynamics, then the conservation laws — which every major first-year text shares. Check the syllabus on Quercus for the assigned text, edition and problem numbers.

Unit-to-topic alignment

Describing motion

Units 1-3 cover the calendar's "classical kinematics": vectors, one-dimensional motion, projectiles and relative motion. No forces yet — this is only the language for saying where something is and how fast it is going.

Causing motion

Units 4-5 cover "dynamics, force, friction". Newton's laws explain why the motion in Units 1-3 happens. The free-body diagram is introduced here and is used in every later unit.

Conserved quantities

Units 6-8 cover "momentum, energy, work, power, angular momentum". These are shortcuts: problems that would need integrating a force over time collapse to one line of bookkeeping.

Repetitive motion

Units 9-10 cover "oscillations, waves, sound". A wave is an oscillation that travels, so the second follows directly from the first, and both feed the optics in PHY132H1.

DRAW

Diagram before algebra

A labelled sketch with axes, then a free-body diagram, then equations. Most wrong answers in this course are correct algebra applied to a mis-drawn picture.

CHECK

Units every time

Dimensional analysis catches a large share of errors in seconds. If an answer has the wrong units it is wrong, no further checking needed.

CHOOSE

Pick the right law

Forces and time → Newton or impulse. Speeds and distances → energy. Collisions → momentum. Choosing well turns a page of algebra into three lines.

TEST

Check limiting cases

Set a mass to zero, an angle to $0$ or $90$ degrees, friction to zero. If the formula does not reduce to something obvious, it is wrong.

03

Practice Plan

Physics is learned by solving problems, not by reading solutions. The unit pages give worked examples and exercises; use this course-level mix to build exam readiness.

01

Symbols first, numbers last

Solve for the unknown algebraically, then substitute. It is easier to check, easier to mark, and shows whether the answer depends on a quantity at all.

02

One diagram per body

In a multi-body problem draw a separate free-body diagram for each. Combining them on one sketch is the most common source of sign errors.

03

Estimate before computing

Guess the order of magnitude first. If the calculator disagrees by a factor of a thousand, you have found an error for free.

04

Take the lab seriously

A fifth of the course hours are practical. Uncertainty and error analysis are examinable and are the part students most often neglect.

Course-wide challenge bank

These mix the conservation laws in the way the final exam does, where the first difficulty is deciding which tool applies.

Challenge 1 · Which law?

A block slides down a frictionless ramp of height $h$. Find its speed at the bottom, twice: once with Newton's laws and once with energy.

Solution sketch

Energy is one line: $mgh = \tfrac12 mv^2$ gives $v = \sqrt{2gh}$, independent of the ramp angle and of the mass. Newton needs the angle, the acceleration $g\sin\theta$, the ramp length $h/\sin\theta$, and a kinematic equation — three steps to the same answer. That contrast is the argument for energy methods.

Challenge 2 · Collision

Two carts of equal mass collide and stick. One was at rest. What fraction of the kinetic energy survives?

Solution sketch

Momentum gives the final speed $v/2$. Kinetic energy goes from $\tfrac12 mv^2$ to $\tfrac12(2m)(v/2)^2 = \tfrac14 mv^2$ — half is lost. Momentum is conserved in every collision; kinetic energy is not, and that asymmetry is the whole point of Unit 7.

Challenge 3 · Rolling

A solid cylinder and a hoop of the same mass and radius roll from rest down the same incline. Which reaches the bottom first?

Solution sketch

The cylinder. Energy splits between translation and rotation, and the hoop has all its mass at radius $R$ so its moment of inertia is larger. More of its energy goes into spinning and less into moving. Neither mass nor radius appears in the answer — only the shape.

Challenge 4 · Period

A pendulum is taken to the Moon, where $g$ is about a sixth of Earth's. What happens to its period?

Solution sketch

$T = 2\pi \sqrt{L/g}$, so dividing $g$ by six multiplies $T$ by $\sqrt6$, about $2.4$. Note the mass does not appear at all, which is worth checking against intuition.

04

Resources

PHY131H1 — official calendar listing
Department of Physics

The calendar confirms the PHY131H1 topic list, the 36L/20P hours and the lab kit fee, but does not publish a current instructor textbook. Verify the assigned text, edition and problem numbers against the active syllabus each year.