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McGill University • Montreal

PHYS 101 Tutor in Montreal, McGill Introductory Mechanics

PHYS 101 is the physics course without calculus, and that is the first thing to get right about it. Almost every physics problem set you find by searching is written for a calculus-based course, so its solutions differentiate where your exam expects a kinematic equation and integrate where it expects an energy balance. Everything on this page is written for PHYS 101 as it is actually examined: algebra, ratios and right-triangle trigonometry, nothing else.

12 chapters, 161 corrected exercises and 12 revision sheets, plus 3 practice papers. Free, no account needed: the full worked solution is on the page.

  1. 1 Units, measurement and vectors Ten exercises built on one idea: a physical quantity is never a bare number, and the direction is the part that cannot be added like one. Part A is the toolkit of the first two weeks, the SI base units and the conversion factor that has to be cubed, a fountain formula tested by its dimensions and a limiting case, the significant figures a measurement actually earns, orders of magnitude and Fermi estimates, the components of a vector read off a right triangle, and the proof that two magnitudes of three and four add to anything between one and seven, then the dot product and the law of cosines of the formula sheet on the two legs of a delivery drone. Part B works at assessment level: three displacements summed component by component with the quadrant of the arctangent restored by hand, unit vectors and subtraction, five statements to correct and a multiple choice question in the midterm format, a laboratory density measured by water displacement and quoted to the digit its uncertainty allows, and a ramp solved on tilted axes. No calculus anywhere, as the course demands: algebra, proportions and right triangle trigonometry only. Sheet
  2. 2 Motion in a straight line The chapter where marks are lost to an axis nobody wrote down. Part A takes the basics: a velocity-time graph that crosses the axis, so that displacement and distance stop being the same number, the two averages and why a speed is never negative, instantaneous velocity read as the slope of a drawn tangent rather than as a limit, the four sign cases that decide whether an object speeds up or slows down, and the four equations chosen by the quantity that is missing, with a cart that climbs a tilted air track and glides back. Part B works at midterm level: a ball thrown up from a balcony, then solved in letters and checked by its dimensions and a limit case, the chain from the acceleration graph to the position, a camera drone whose motors fail mid-climb, followed to the top and back to the altitude of the fault, five statements to correct and a graph to recognise among four, a cyclist catching a runner, and the ruler drop test of reaction time carried through to a stopping distance. Sheet
  3. 3 Projectile motion and relative velocity Ten exercises built on one habit: rule the page into two columns and let nothing but the time cross between them. Part A sets the machinery in place, a ball leaving a bench and the speed it lands with, a launch at an angle and the apex where the velocity is horizontal rather than zero, a strobe photograph read as a laboratory measurement of gravity, the two complementary angles that share a landing point and two ball machines triggered together at complementary angles, whose balls hit one spot almost two seconds apart, then the two splashes of a fountain in letters, and relative velocity from a bush plane in a crosswind to a rainy windshield. Part B works at midterm level: a throw from a cliff, then a shot put released above the ground, its flight time written as a formula first, a river crossing with the heading that cancels the current, five statements to correct including a garden hose tested against its advertised speed, keys dropped in a moving tram as a four option question, a grasshopper filmed at 240 frames per second and then jumping down a 30 degree slope, and a supply drop seen from the ground and from the cockpit. No calculus anywhere, as the course requires. Sheet
  4. 4 Newton's laws and free-body diagrams The chapter where the drawing decides the mark. Part A builds the diagram itself: the inventory rule that gives one arrow per contact and one per field and nothing else, mass against weight and the units that separate them, the action and reaction pair with its two different bodies, a rope pulling at an angle and the normal force that stops being the weight, and the bathroom scale in a lift where the reading changes while the weight does not. Part B works at midterm level: a block released on a frictionless incline with axes tilted along the slope, two blocks joined by a cord over an ideal pulley sharing one acceleration and one tension, then two crates pushed together across a warehouse floor, solved in letters with dimensions and limiting cases before any number, five statements to correct and an exam-style multiple choice on the tension of an Atwood machine, the traction frame of a physiotherapy ward where two cords pull at an angle, and a stretcher winched up an ambulance ramp with the cable parallel to the surface and then horizontal. No calculus anywhere: algebra, components and right-angle trigonometry only. Sheet
  5. 5 Friction, circular motion and gravitation Ten exercises on the chapter where most of the term's marks are lost. Part A builds the two reversals the chapter lives on: static friction is an inequality and not a formula, so it takes whatever value stops the sliding up to a ceiling, and the centripetal force is not an extra arrow but the name of the resultant of the arrows already drawn. It covers the crate on the point of slipping, the incline with friction and its slipping angle, uniform circular motion read through both forms of the acceleration, universal gravitation and surface gravity, then circular orbits and Kepler's third law. Part B works at midterm level: the banked curve and the conical pendulum solved by the same pair of equations, then the same icy ramp taken below its design speed, where friction points up the slope, the bucket at the top of a vertical circle, five statements to correct, a laboratory centrifuge and its relative centrifugal field scaled up to a spinning space habitat with artificial gravity, and a pilot pulling out of a dive at six times her weight. No derivative and no integral anywhere, which is the point of PHYS 101. Sheet
  6. 6 Work, energy and power Ten exercises on the chapter that stops being about forces and starts being about accounting. Part A builds the tools: the angle in the work formula and the two forces that do no work at all, work read as an area under a force against position graph, then a buffer spring that stops a parcel at the foot of a rough chute, solved in letters and checked by its dimensions and a limit case, the work-energy theorem used on a problem that never mentions time, the reference level you have to write down before any potential energy means anything, and the pendulum whose height is not its sideways displacement. Part B works at midterm level: a roller coaster whose measured speed reveals what friction took, average and instantaneous power with an efficiency and the launch of a roller coaster by electric motors, five statements to correct, an exercise bike converted into food Calories, and the landing that explains why you bend your knees. No calculus anywhere, as the course requires. Sheet
  7. 7 Momentum, impulse and collisions The chapter where one equation is always true and the other one has to be earned. Part A builds the vector habit: momentum with its sign, the change of momentum on a bounce against a stop, the impulse momentum theorem and the airbag that divides the force by five without touching the impulse, the impulse read as an area of triangles and rectangles under a force time graph, then the perfectly inelastic collision with its energy audit and the three endings of one and the same collision, elastic, in between and stuck together, then the elastic collision of the formula sheet solved in letters, with its dimensions, its three limit cases and its energy check. Part B works at midterm level: explosions and recoil, where the light piece takes five hundred times the energy of the heavy one, the ballistic pendulum with its two stages and the height of thirty metres that a single misplaced energy line produces, five statements to sort out and an exam style choice on two sleds given the same impulse, a two dimensional collision on an air table audited against a suspect laboratory reading, and the centre of mass that crosses a collision without changing speed. Every solution is written for PHYS 101, with no derivative and no integral anywhere. Sheet
  8. 8 Torque, rotation and equilibrium Ten exercises built on one idea: in rotation a force counts by its lever arm and a mass counts by its distance from the axis, never by its own size. Part A: angular kinematics and the radian, torque read as a lever arm, a plank whose reaction turns negative, Newton's second law for rotation with a pulley that has mass, the moment of inertia of a four-weight mobile about two axes, and rolling, with a hoop, a disk and a sphere racing down a ramp and a cable spool solved in letters against a sliding crate. Part B: a ladder against a smooth wall, the forearm as a lever built to lose, five statements and a ranking question to settle, a laboratory flywheel from spin-up to coast-down, and a playground carousel where angular momentum survives and kinetic energy does not. Sheet
  9. 9 Oscillations and simple harmonic motion Ten exercises on one uncomfortable fact: the period of an oscillator does not depend on how you launch it. Part A is the toolkit, reading amplitude and period off a graph, Hooke's law recognised as the condition for simple harmonic motion, where the maximum speed and the maximum acceleration happen and why never at the same place, recovered from the reference circle of a turntable, the energy traded between kinetic and elastic, a launch with a push and the phase constant of the formula sheet's A sin(ωt + φ), and the same spring hung vertically. Part B works at midterm level: springs side by side and end to end, the pendulum and the small-angle approximation, five statements to correct with an exam-style multiple-choice question, an astronaut weighed in orbit by an inertial balance, and a damped trace followed by the resonance curve of the same system driven by a motor. Sheet
  10. 10 Waves and sound Ten exercises built on one hierarchy: the source chooses the frequency, the medium chooses the speed, and the wavelength is only the quotient of the two. Part A is the mechanics of it, reading a snapshot against reading the history of one point, the speed of a wave on a string and of sound in air, ocean swell refracted toward a beach, path difference counted in wavelengths, standing waves on a clamped string, and why a pipe closed at one end drops half of its harmonics. Part B works at midterm level: intensity and the decibel scale, from an intensity or a microphone amplitude, with the inverse square law, beats and the Doppler effect kept apart, five statements to correct and a four-option question, a sonometer with its systematic errors, and medical ultrasound from the echo time to the Doppler shift of flowing blood. No calculus anywhere, as the course requires. Sheet
  11. 11 Refraction and dispersion, with a look ahead to lenses Ten exercises on light for PHYS 101, starting with what the course formula sheet gives. Snell's law and the speed of light in a medium, rewritten in the sheet's speed form and followed through the acrylic wall of an aquarium (exercise 2), total internal reflection from the pool to the optical fibre, with the critical angle derived in letters from the two speeds and checked by its dimensions and a limit case (exercise 3), dispersion in a prism and the rainbow, with an exam format question on speed, colour and frequency (exercise 7). Mirrors, thin lenses, the eye and the optical bench (exercises 1, 4, 5, 6, 9 and 10) are kept as a look ahead to PHYS 102, where geometric optics is taught: the PHYS 101 formula sheet does not give their equations, and the set says so. Five statements to correct, and no calculus anywhere, as the course requires. Sheet
  12. 12 Wave optics, interference and diffraction The chapter where light stops being a ray. Part A builds the one question the whole subject reduces to, namely how many wavelengths separate two paths that arrive at the same point: Huygens and the ratio of wavelength to opening, the path difference of Young's two slits, the fringe positions on a screen with the small angle approximation and the price of using it too far, the proportional reasoning that answers a change of colour, of spacing or of medium without recomputing anything, and the single wide slit whose condition looks exactly like the double slit one and means the opposite. Part B works at exam level: a grating and the sodium doublet with the resolving power that decides whether two lines are separated, thin films counted by their reflection flips, soap, oil and an anti-reflection coating, five statements to correct, polarized sunglasses on a lake with the Brewster angle and Malus's law, and the Rayleigh criterion that explains why no light microscope will ever resolve a virus. Three questions follow the formula sheet: refraction written with the wave speeds and derived from Huygens, a single slit under water solved in letters with its limit checks, and a multiple choice question on the fringes of an immersed double slit. No calculus anywhere: algebra, proportions and right triangle trigonometry only, as PHYS 101 requires. Sheet

When the chapters are done

Papers to sit under exam conditions, fully corrected on the page: in real time, with the formula sheet and nothing else. The midterm paper covers the first five chapters; the finals are cumulative, like the real one in December.

Practice exam

Practice midterm, PHYS 101 at McGill

A two hour practice midterm for PHYS 101, twelve questions and one hundred points, with the full solution under every question. Part A asks eight conceptual questions in the format of the real paper, each with four or five choices: the sum and the difference of two vectors, the farthest point read on a velocity graph, two falling drops, three kicks of the same height, a round trip in the wind, two cords of unequal slope, static friction on a wall and a Ferris wheel. Part B asks four problems: a hoop and a ball that meet in mid-air, a life buoy thrown from a moving boat, a pallet held on a roof by a bucket of gravel, and the balance point between the Earth and the Moon with Newton's Moon test.

  • 12 questions
  • 100 points
  • 120 minutes
Sit the paper

Practice exam

Practice final exam, PHYS 101 at McGill

A three hour practice final for PHYS 101, twelve questions and one hundred points, with the whole solution written out under every question. Part A weighs motion and forces: an aircraft takeoff roll that mixes a unit conversion, a uniform acceleration and a climb angle, a volleyball serve that clears the net and still lands out, and three short scenes on friction, a car cresting a hill and the mass of Jupiter read off the orbit of Io. Part B weighs energy, momentum and rotation: a spring plunger firing a block up a rough ramp with the full energy audit, an accident reconstructed backwards from a skid mark, and a hinged beam whose cable snaps. Part C weighs oscillations, waves and sound: a pendulum clock that loses two minutes a day when it changes city, a resonance tube measured over water, and a wave given as a formula next to two trains passing. Part D weighs optics: two lenses in series on a bench as a look ahead to PHYS 102, a double slit read inside its single slit envelope, and a closing synthesis question that makes three chapters talk to each other.

  • 12 questions
  • 100 points
  • 180 minutes
Sit the paper

Practice exam

Second practice final, PHYS 101 at McGill

A second three hour practice final for PHYS 101, in the format of the real paper: ten conceptual questions, then seven problems, one hundred points, with the full solution under every question. The conceptual part tests the angle in the formula that adds two vectors, two stones thrown from a bridge, the third law, Kepler's third law, the sign of work, the centre of mass of a canoe, the angular momentum of a diver, oscillators on the Moon, decibels and the Rayleigh criterion. The problems: two tugboats and a barge, a snowboarder on a rough slope, a toy car on a loop, a fireworks shell that bursts, a cue ball that slides then rolls, a tuning fork walked toward a wall, and an insect wing, a CD and a polarized screen.

  • 17 questions
  • 100 points
  • 180 minutes
Sit the paper

What PHYS 101 covers

The official description is short: an introductory course in physics without calculus, covering mechanics, that is kinematics, dynamics, energy and rotational motion, then oscillations and waves, sound, light and wave optics. It is a four-credit course, taken mostly by students heading into the life sciences, and it is closed to anyone holding PHYS 131 or CEGEP objective 00UR. In practice that last restriction tells you who is in the room: not CEGEP graduates, but students arriving from the French baccalaureate, from Ontario, from the United States and from abroad. Many of them have met part of this material before, in another language and with another method, which is precisely where the marks go.

That is also why the course is harder than its title suggests. It runs from the definition of velocity to double-slit interference in a single term, which is a wider sweep than the two-course calculus sequence covers in the same time. Nothing is deep, everything arrives quickly, and a chapter missed in week three is still missing in week eleven, because forces feed energy, energy feeds oscillations and oscillations feed waves.

The chapters above follow that order. Each one has a corrected exercise set, with the full solution written out on the page, and a revision sheet that answers a different question: not what the chapter says, but what loses marks on it.

Your formula sheet, and what it leaves out

PHYS 101 hands you an official formula sheet, which you may annotate on both sides and bring to the exam. That changes what is worth memorising: not the equations, which are printed, but when each one applies and what it silently assumes.

Where PHYS 101 marks are actually lost

Setting up before drawing

The single most expensive habit in the course. A free-body diagram drawn after the equations have been written is a diagram drawn to match them, so a missing force stays missing. Draw first, axes included, then write one equation per axis.

Treating a vector equation as a number equation

Adding magnitudes, carrying a minus sign that belonged to a chosen direction, or reporting a negative speed. Every sign in mechanics answers one question, which way did you point the axis, and the answer has to be written down before it is used.

Reaching for the wrong tool

Kinematics, energy and momentum can all reach the same answer, but only one of them reaches it in three lines. Energy when speed and distance appear and time does not, momentum whenever two objects touch, kinematics when the acceleration is constant and named.

Borrowing calculus-based solutions

A solution that starts by differentiating a position function is not a PHYS 101 solution, even when its final number is right. A marker follows the method, and a method the course has not taught cannot be given the method marks.

Frequently asked questions

What is PHYS 101 at McGill?

PHYS 101, Introductory Physics - Mechanics, is McGill University's four-credit introductory physics course taught without calculus. It covers mechanics (kinematics, dynamics, energy, momentum and rotational motion), oscillations and waves, sound, light and wave optics. It is taken mostly by students heading into the life sciences, and it is not open to students who have taken PHYS 131 or CEGEP objective 00UR.

Is PHYS 101 calculus-based?

No. PHYS 101 is the algebra-based and trigonometry-based course, which is exactly what separates it from PHYS 131. Every result you need is reached with algebra, ratios and right-triangle trigonometry. This matters when you look for practice online: most physics problem sets found by searching are written for a calculus-based course, and their solutions differentiate and integrate where PHYS 101 expects a kinematic equation or an energy balance.

What is the difference between PHYS 101 and PHYS 131 at McGill?

PHYS 131, Mechanics and Waves, is the calculus-based course taken by students continuing in physics, chemistry and engineering. PHYS 101 covers similar ground without calculus and is intended for the life sciences. The two courses are mutually exclusive: you cannot take PHYS 101 if you have credit for PHYS 131 or for CEGEP objective 00UR.

Do you offer PHYS 101 tutoring in Montreal?

Yes. I tutor PHYS 101 and the other first-year physics courses in Montreal, in person and online. I am a McGill graduate and I work on your own course outline, your assignments and your past midterms rather than on a generic syllabus.

Is geometric optics part of PHYS 101?

Only its first step. PHYS 101 treats light through its speed in a medium, refraction written with speeds, interference and diffraction. Mirrors, lenses and the thin-lens equation are not on the PHYS 101 formula sheet: they belong to PHYS 102, the winter course on electromagnetism and geometrical optics.

Can I bring a formula sheet to the PHYS 101 exams?

Yes. The course provides an official formula sheet that you may annotate on both sides and bring to the exam. The equations are printed for you; what earns the marks is knowing when each one applies, so annotate every line with its conditions.

Other first-year courses

The same free corrected material exists for other courses, some of it in English and the rest in French.

COMP 202, Foundations of Programming (McGill)MATH 133, Linear Algebra and Geometry (McGill)MATH 140, Calculus 1 (McGill)MATH 141, Calculus 2 (McGill)MATH 203, Calculus I (Concordia) Physics tutoring in Montreal All revision sheets in English Higher education, in French
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