Courses › PHYS 110 + PHYS 110L

About this course

This is a free self-study course outline written by Saving Planets. It is not a university course, it carries no academic credit, and no school is involved.

Its scope follows the first semester of calculus-based college physics (classical mechanics), the course every engineering and physics major takes first. It is modeled on the topics and depth of open materials such as OpenStax University Physics Volume 1 and MIT OpenCourseWare 8.01SC Classical Mechanics, which we link to throughout. Those organizations do not endorse this page.

What we add: every unit is tied to real aerospace and Earth-observation work, every number on the page is re-computed by a checking script before it goes live, and every lab has a home or virtual version so anyone can do it.

Work through it in order. Each unit has goals, key ideas, equations, step-by-step examples, practice with full answers, common mistakes, flashcards and a quiz. Your progress is saved only in this browser.

How this course helps save the planet

Mechanics is the physics of launching, flying and orbiting. The same equations put Earth-observing satellites such as Landsat 9 and GRACE-FO into orbit, keep them pointed, and turn tiny changes in their motion into maps of water, ice and land.

On the ground, the same ideas size wind turbines, make cars and aircraft use less energy, and help engineers plan how to move an asteroid. Each unit ends with a short, sourced section showing how its ideas help both people and nature.

Before you start

Prerequisites

Algebra and trigonometry: solving equations, sine, cosine and tangent, the Pythagorean theorem.
Calculus I, at least at the same time: derivatives as rates of change and integrals as areas. This course uses dv/dt and ∫v dt from Unit 1.
Vectors in two dimensions: components, magnitude and direction.
SI units and scientific notation.

How to study

Read the unit, then close it and try the worked examples yourself before checking each step.
Draw a picture for every problem. For any force problem, draw a free-body diagram before writing an equation.
Solve with symbols first and put numbers in at the end. Then check the units and whether the size of the answer makes sense.
Do every practice problem on paper before opening the answer. Getting it wrong first and fixing it is how the method sticks.
Use the PhET simulations to test your intuition: predict what will happen, then run it.
Retake the quizzes a few days later. Spaced practice beats one long session.
Use g = 9.81 m/s² unless a problem says otherwise, and keep three significant figures.

Lab equipment (for the wet labs)

Meter stick and tape measure; vernier caliper if available.
Stopwatch (a phone works) and, ideally, a phone app or school sensor that records motion or acceleration.
Low-friction cart and track (or a smooth board), a pulley and a set of hanging masses.
A small ball, a ramp, carbon or plain paper for marking landing spots.
String, a dense bob (a fishing weight works) and a protractor.
Spreadsheet software for averages, standard deviations and graphs.

Suggested 15-week schedule

About 6 to 9 hours a week: reading, practice problems and, in lab weeks, the lab.

Week	Unit	Topics	Reading
1	Measurement, Vectors & Motion in One Dimension	Units, uncertainty, vectors; Lab A	OpenStax 1.1–1.7, 2.1–2.2
2	Measurement, Vectors & Motion in One Dimension	Velocity and acceleration as derivatives; constant acceleration; free fall	OpenStax 3.1–3.5
3	Motion in Two Dimensions: Projectiles & Circles	Projectiles, relative motion, circular motion; Lab B	OpenStax 4.1–4.5
4	Newton’s Laws, Friction & Circular Dynamics	Newton’s laws and free-body diagrams	OpenStax 5.1–5.7
5	Newton’s Laws, Friction & Circular Dynamics	Friction, connected bodies, circular dynamics; Labs C and D	OpenStax 6.1–6.4
6	Work, Energy & Power	Work, kinetic energy, power	OpenStax 7.1–7.4
7	Work, Energy & Power	Potential energy and conservation of energy; Lab E	OpenStax 8.1–8.5
8	Momentum, Collisions & Rockets	Momentum, impulse, collisions, center of mass, rockets; Lab F; midterm practice	OpenStax 9.1–9.7
9	Rotation, Torque & Angular Momentum	Rotational kinematics, moment of inertia	OpenStax 10.1–10.5
10	Rotation, Torque & Angular Momentum	Torque, rolling, angular momentum; Lab G	OpenStax 10.6–10.8, 11.1–11.3
11	Gravitation & Orbits	Newton’s law of gravitation, g at altitude, satellites	OpenStax 13.1–13.4
12	Gravitation & Orbits	Kepler’s laws, escape speed, orbital transfers	OpenStax 13.5–13.6
13	Oscillations & Introduction to Fluids	Simple harmonic motion, pendulums, damping, resonance; Lab H	OpenStax 15.1–15.6
14	Oscillations & Introduction to Fluids	Fluids: pressure, buoyancy, continuity, Bernoulli	OpenStax 14.1–14.6
15	Review	Review and final practice set	All units

Your progress

Tick units and labs as you finish them, and take the quizzes. Progress and quiz scores are saved only in this browser, never sent to us.

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The lab (PHYS 110L)

The lab is the hands-on part of the course, a 1-credit component in a typical college schedule. Here it is free and for practice only.

Each lab tests one idea from lecture against real measurements, and each one asks you to state an uncertainty. A result without an uncertainty cannot be compared with a prediction. Every lab also has a home or PhET version.

Safety reference: OSHA: workplace safety

Lab A: Measurement and uncertainty (measuring g)

Week 1

Goal: Time a ball dropped from a measured height, find g, and state a proper uncertainty.

g=\frac{2h}{t^2},\quad \frac{\delta g}{g}=\sqrt{\left(\frac{\delta h}{h}\right)^2+\left(2\frac{\delta t}{t}\right)^2}

Propagate relative uncertainties in quadrature; time is squared, so its relative uncertainty counts twice

Procedure

Measure the drop height h from the bottom of the ball to the floor; estimate δh (for a tape, about ±2 mm).
Drop a dense ball from rest and time the fall. A phone slow-motion video or a sound-trigger app beats a hand stopwatch.
Repeat at least five times.
Find the mean time, the sample standard deviation s and the standard error s/√N; use the standard error as δt.
Compute g and δg, and compare with 9.81 m/s².

Data table

Trial	Fall time (s)
1	0.55
2	0.56
3	0.54
4	0.55
5	0.56
Mean	0.552
Std. deviation s	0.0084
Standard error s/√5	0.0037

Sample data for practice only. h = 1.500 ± 0.002 m.

Sample calculation

g = 2h/t² = 2 × 1.500 ÷ 0.552² = 9.85 m/s².
Relative uncertainty from time: 2 × 0.0037 ÷ 0.552 = 1.36%. From height: 0.002 ÷ 1.500 = 0.13%.
Combined: √(1.36² + 0.13²) = 1.36%, so δg = 0.0136 × 9.85 = 0.13 m/s².
Result: g = 9.85 ± 0.13 m/s². The accepted 9.81 m/s² lies inside the range, so the two agree. Timing dominates the uncertainty.

Safety

Drop the ball only where nobody is underneath, and keep the floor clear.
Stand on a sturdy surface, not a chair, to reach the release height.

Home or virtual alternative

Do it exactly as written at home with a phone slow-motion video.
Or use the PhET Projectile Motion sim with launch speed 0 to check timing.

PhET: Projectile Motion · JCGM uncertainty guide (GUM)

Planet link: GRACE-FO’s science only works because its team knows the uncertainty of every distance it measures; a change counts only when it beats that uncertainty. NASA JPL: GRACE-FO

I completed this lab (wet or virtual)

Lab B: Projectile motion

Week 3

Goal: Measure a launcher’s speed from a horizontal shot, then predict and test where an angled shot lands.

v_0=\frac{x}{\sqrt{2h/g}},\quad R=\frac{v_0^2\sin2\theta}{g}

Launch speed from a horizontal shot, then the predicted range

Procedure

Fire a ball horizontally from a launcher (or roll it off a ramp) at table height h.
Tape carbon paper over plain paper where it lands; do five shots and measure each landing distance x.
Find the mean x and compute v₀.
Predict the range for a 30° launch from floor level, mark the spot, and test it with five shots.
Compare prediction and result; list sources of error (air drag, launch height, angle reading).

Data table

Quantity	Value
Table height h	1.00 m
Mean landing distance x	2.26 m
Fall time √(2h/g)	0.452 s
Launch speed v₀	5.01 m/s
Predicted range at 30°	2.21 m

Sample data for practice only.

Sample calculation

t = √(2 × 1.00 ÷ 9.81) = 0.452 s.
v₀ = 2.26 ÷ 0.452 = 5.01 m/s.
R(30°) = 5.01² × sin 60° ÷ 9.81 = 25.1 × 0.866 ÷ 9.81 = 2.21 m.
Percent difference = |measured − predicted| ÷ predicted × 100%.

Safety

Wear eye protection with any spring launcher, and never aim it at a person.
Keep the landing zone clear.

Home or virtual alternative

Roll a marble off a table and measure x; skip the angled part or use the PhET sim for it.

PhET: Projectile Motion

Planet link: The same prediction-then-test method is used to forecast where a reentering rocket stage could land.

I completed this lab (wet or virtual)

Lab C: Newton’s second law

Week 5

Goal: Show that acceleration is proportional to net force and inversely proportional to mass.

a=\frac{m_hg}{m_c+m_h}

Cart pulled by a hanging mass over a pulley, ignoring friction

Procedure

Level a track. Attach a cart (mass m_c) by string over a pulley to a hanging mass m_h.
Release from rest and record the motion with a sensor, video or by timing a known distance (a = 2d/t²).
Repeat for five hanging masses, moving mass from the cart to the hanger so the total stays fixed.
Graph a against m_h g. The slope should be 1/(m_c + m_h).
Repeat with extra mass on the cart to test the mass dependence.

Data table

Quantity	Value
Cart mass m_c	0.500 kg
Hanging mass m_h	0.050 kg
Predicted a	0.892 m/s²
Measured a	0.86 m/s²

Sample data for practice only.

Sample calculation

Predicted a = 0.050 × 9.81 ÷ 0.550 = 0.892 m/s².
Measured 0.86 m/s² is 3.6% lower.
Friction force needed to explain the gap: (0.892 − 0.86) × 0.550 = 0.018 N, a reasonable rolling friction.

Safety

Put a soft stop at the end of the track and keep fingers clear of the pulley.

Home or virtual alternative

Use PhET Forces and Motion: Basics (Acceleration screen) to vary force and mass.

PhET: Forces and Motion: Basics

Planet link: F = ma is why lighter vehicles need less energy to speed up: every kilogram saved cuts the force, and the fuel, needed.

I completed this lab (wet or virtual)

Lab D: Friction

Week 5

Goal: Measure static and kinetic friction coefficients with a tilting ramp.

\mu_s=\tan\theta_{slip},\quad \mu_k=\tan\theta_{steady}

On a ramp, friction balances mg sin θ when N = mg cos θ

Procedure

Place a block on a board and slowly raise one end until the block just starts to slide; record the angle θ_slip. Repeat five times.
Find the angle at which the block, given a tap, slides down at a steady speed: θ_steady.
Compute μₛ and μₖ. Repeat on a second surface (felt, rubber).

Data table

Quantity	Value
Block mass	0.250 kg
Mean slip angle	31°
Mean steady-slide angle	24°
μₛ	0.60
μₖ	0.45

Sample data for practice only.

Sample calculation

μₛ = tan 31° = 0.601.
μₖ = tan 24° = 0.445.
As expected, μₖ < μₛ. The mass does not appear: it cancels.

Safety

Keep the ramp low and stable; catch the block at the bottom.

Home or virtual alternative

A book, a phone inclinometer app and a hardcover board work fine.
PhET The Ramp lets you set friction and watch the forces.

PhET: The Ramp

Planet link: Rolling friction in tires is one of the forces a vehicle burns energy against at every speed; lower-friction designs save fuel. U.S. DOE: Vehicle Technologies Office

I completed this lab (wet or virtual)

Lab E: Conservation of energy

Week 7

Goal: Compare a cart’s measured speed at the bottom of a ramp with the speed energy conservation predicts.

v=\sqrt{2gh},\quad \text{fraction kept}=\frac{v_{meas}^2}{2gh}

Ideal speed from a drop h, and how much mechanical energy survived

Procedure

Measure the vertical drop h of a ramp.
Release a low-friction cart from rest and measure its speed at the bottom (photogate, or video over a short known distance).
Repeat five times and average.
Compute the predicted speed and the fraction of energy kept; explain where the rest went.

Data table

Quantity	Value
Drop height h	0.300 m
Predicted speed	2.43 m/s
Measured speed (mean)	2.35 m/s
Energy kept	93.8%

Sample data for practice only.

Sample calculation

v = √(2 × 9.81 × 0.300) = 2.43 m/s.
Fraction kept = 2.35² ÷ (2 × 9.81 × 0.300) = 5.52 ÷ 5.89 = 0.938.
About 6.2% of the mechanical energy became heat and sound through friction and drag.

Safety

Clamp the ramp and stop the cart at the bottom.

Home or virtual alternative

Roll a ball down a book-ramp and time it over a measured flat run.
PhET Energy Skate Park shows the same energy bar charts.

PhET: Energy Skate Park

Planet link: Tracking where energy goes is how engineers find savings, from regenerative braking to pumped-storage hydro. U.S. DOE: Electric vehicle basics

I completed this lab (wet or virtual)

Lab F: Momentum and collisions

Week 8

Goal: Test conservation of momentum in elastic and sticky collisions, and measure how much kinetic energy is lost.

m_1v_1+m_2v_2=(m_1+m_2)v_f

Perfectly inelastic collision

Procedure

On a level track, send cart 1 into cart 2 at rest with Velcro facing so they stick.
Measure speeds just before and after (sensor or video).
Repeat with magnets or springs facing for a nearly elastic bounce.
For each run, compare total momentum and total kinetic energy before and after.

Data table

Quantity	Value
m₁ = m₂	0.50 kg
v₁ before	0.80 m/s
Predicted v after (stuck)	0.40 m/s
Measured v after	0.39 m/s

Sample data for practice only.

Sample calculation

p before = 0.50 × 0.80 = 0.40 kg·m/s. p after = 1.00 × 0.39 = 0.39 kg·m/s, a 2.5% difference (friction during the run).
K before = ½ × 0.50 × 0.80² = 0.160 J. K after = ½ × 1.00 × 0.39² = 0.076 J.
About half the kinetic energy was lost, as theory predicts for equal masses sticking (exactly 50% ideally).

Safety

Keep speeds low and stop carts before the track ends.

Home or virtual alternative

PhET Collision Lab lets you set elasticity from 0% to 100%.

PhET: Collision Lab

Planet link: DART used exactly this physics on an asteroid: a planned, measured collision to change a moonlet’s orbit. NASA: DART mission

I completed this lab (wet or virtual)

Lab G: Rotational inertia

Week 10

Goal: Measure a disk’s moment of inertia with a falling mass and compare it with ½MR².

I=mr^2\left(\frac{g}{a}-1\right),\quad a=\frac{2d}{t^2}

Hanging mass m on a string wound around an axle of radius r

Procedure

Wind a string around the disk’s axle (radius r) and hang a mass m from it.
Release from rest and time the fall through a height d; repeat five times.
Compute a, then I. Measure the disk’s mass M and radius R and compute ½MR².
Compare. Then add a ring and see how much I grows.

Data table

Quantity	Value
Hanging mass m	0.050 kg
Axle radius r	0.025 m
Fall distance d	0.800 m
Mean fall time t	4.00 s
Disk M, R	1.50 kg, 0.064 m

Sample data for practice only.

Sample calculation

a = 2 × 0.800 ÷ 4.00² = 0.100 m/s².
I = 0.050 × 0.025² × (9.81 ÷ 0.100 − 1) = 0.050 × 0.000625 × 97.1 = 3.03 × 10⁻³ kg·m².
½MR² = ½ × 1.50 × 0.064² = 3.07 × 10⁻³ kg·m².
Difference 1.2%, within the uncertainty of the radius and timing.

Safety

Keep the hanging mass low over a soft landing pad.

Home or virtual alternative

Roll a full can of soup and an empty can down the same ramp and compare times; explain the result with K = ½mv² + ½Iω².

OpenStax 10.4 Moment of Inertia

Planet link: Reaction wheels that point Earth-observing satellites are designed around exactly this quantity.

I completed this lab (wet or virtual)

Lab H: Pendulum and simple harmonic motion

Week 13

Goal: Test T = 2π√(L/g), show the period does not depend on mass or small amplitude, and measure g a second way.

g=\frac{4\pi^2L}{T^2}

Rearranged pendulum equation

Procedure

Hang a dense bob on a string; measure L from the pivot to the bob’s center.
Pull it back less than 10° and time 20 full swings; divide by 20 for T.
Repeat for five lengths. Graph T² against L: the slope is 4π²/g.
Change the bob mass and the amplitude (still small) and check that T stays the same.
Optional: time a mass bouncing on a spring and test T = 2π√(m/k).

Data table

Quantity	Value
Length L	0.800 m
Time for 20 swings	35.9 s
Period T	1.795 s
g	9.80 m/s²

Sample data for practice only.

Sample calculation

T = 35.9 ÷ 20 = 1.795 s. Timing 20 swings divides the reaction-time error by 20.
g = 4π² × 0.800 ÷ 1.795² = 31.58 ÷ 3.222 = 9.80 m/s².
Compare with Lab A: two independent methods, and the pendulum is far more precise.

Safety

Use a secure pivot and swing the bob away from faces.

Home or virtual alternative

A key on a shoelace works; time it with a phone.

PhET: Pendulum Lab · PhET: Masses and Springs

Planet link: Precise knowledge of g, and of its tiny changes from place to place, is what gravity missions such as GRACE-FO turn into maps of water and ice. NASA JPL: GRACE-FO

I completed this lab (wet or virtual)

Exam prep practice sets

Time yourself: about 10 minutes per problem. Then compare with the full solutions.

Midterm practice set (Units 1–4)

A rocket accelerates straight up from rest at 5.0 m/s² for 20 s, then its engine stops. What is the maximum height it reaches?
Show full solution
1. At burnout: v = 5.0 × 20 = 100 m/s; height = ½ × 5.0 × 20² = 1,000 m.
2. Coasting up: extra height = v²/2g = 100² ÷ 19.62 = 510 m.
Answer: 1,510 m, ignoring drag.
A ball is kicked at 25 m/s at 40° above level ground. Find its range and time of flight.
Show full solution
1. v_y = 25 sin 40° = 16.1 m/s; t = 2 × 16.1 ÷ 9.81 = 3.28 s.
2. R = 25² × sin 80° ÷ 9.81 = 625 × 0.985 ÷ 9.81 = 62.7 m.
Answer: 62.7 m in 3.28 s.
A 20 kg sled is pulled at constant speed across snow (μₖ = 0.10) by a horizontal rope. Find the rope tension and the work done over 50 m.
Show full solution
1. Constant speed: T = μₖmg = 0.10 × 20 × 9.81 = 19.6 N.
2. W = 19.6 × 50 = 981 J.
Answer: 19.6 N; 981 J, all turned into heat by friction.
A 2.0 kg block slides from rest down a frictionless curved track from 5.0 m high and then compresses a spring (k = 400 N/m) on level ground. Find the maximum compression.
Show full solution
1. mgh = ½kx².
2. x = √(2 × 2.0 × 9.81 × 5.0 ÷ 400) = √0.4905 = 0.700 m.
Answer: 0.700 m.

Final practice set (all units)

A 3.0 kg cart at 4.0 m/s collides with a 1.0 kg cart at rest and they stick. Find the final speed and the fraction of kinetic energy lost.
Show full solution
1. v = 3.0 × 4.0 ÷ 4.0 = 3.0 m/s.
2. K before = 24 J; after = ½ × 4.0 × 9.0 = 18 J.
Answer: 3.0 m/s; 25% of the kinetic energy is lost.
A hollow ring and a solid disk of equal mass and radius roll from rest down a ramp 1.0 m high. Find each speed at the bottom.
Show full solution
1. Ring (I = mr²): mgh = mv², so v = √(gh) = 3.13 m/s.
2. Disk (I = ½mr²): mgh = ¾mv², so v = √(4gh/3) = 3.62 m/s.
Answer: Ring 3.13 m/s, disk 3.62 m/s; the disk wins.
Find the orbital period of a satellite in a circular orbit 1,336 km above Earth.
Show full solution
1. r = 6,371 + 1,336 = 7,707 km.
2. T = 2π√(r³/GM) = 2π√((7.707 × 10⁶)³ ÷ 3.986 × 10¹⁴) = 6,733 s.
Answer: About 112 minutes.
A 0.20 kg mass on a spring oscillates with a period of 0.50 s and amplitude 0.10 m. Find k and the maximum speed.
Show full solution
1. ω = 2π ÷ 0.50 = 12.57 rad/s.
2. k = mω² = 0.20 × 158.0 = 31.6 N/m.
3. v_max = Aω = 0.10 × 12.57 = 1.26 m/s.
Answer: k = 31.6 N/m; v_max = 1.26 m/s.
A 1.0 m³ buoy of mass 400 kg is held fully under seawater (ρ = 1,025 kg/m³) by a cable to the seabed. Find the cable tension.
Show full solution
1. Buoyant force = 1,025 × 1.0 × 9.81 = 10,060 N.
2. Weight = 400 × 9.81 = 3,920 N.
3. Tension = 10,060 − 3,920 = 6,130 N.
Answer: About 6,130 N.

Formula sheet

v=dx/dt,\ a=dv/dt

x=x_0+v_0t+\tfrac12at^2

v^2=v_0^2+2a\Delta x

R=v_0^2\sin2\theta/g

a_c=v^2/r=\omega^2r

\sum\vec F=m\vec a

f_k=\mu_kN

W=\int\vec F\cdot d\vec x

K=\tfrac12mv^2,\ U_g=mgh,\ U_s=\tfrac12kx^2

P=dW/dt=Fv

\vec p=m\vec v,\ \vec J=\Delta\vec p

\Delta v=v_e\ln(m_0/m_f)

\tau=rF\sin\theta=I\alpha

L=I\omega,\ K_{rot}=\tfrac12I\omega^2

F=Gm_1m_2/r^2

v_{orb}=\sqrt{GM/r},\ v_{esc}=\sqrt{2GM/R}

T^2=4\pi^2a^3/GM

T_{spring}=2\pi\sqrt{m/k},\ T_{pend}=2\pi\sqrt{L/g}

P=P_0+\rho gh,\ F_B=\rho Vg

A_1v_1=A_2v_2,\ P+\tfrac12\rho v^2+\rho gh=\text{const}

Constants

Constant	Value
Gravitational constant, G	6.674 × 10⁻¹¹ N·m²/kg²
Standard gravity, g	9.81 m/s² (9.80665 m/s² by definition)
Mass of Earth	5.972 × 10²⁴ kg (NASA Earth fact sheet)
Mean radius of Earth	6,371 km (NASA Earth fact sheet)
GM of Earth	3.986 × 10¹⁴ m³/s²
Sidereal day	86,164 s
Density of fresh water	1,000 kg/m³; seawater about 1,025 kg/m³
Density of air at sea level, 15 °C	1.225 kg/m³

Source: NIST: Fundamental physical constants

Reference data

Use these free, official data sources alongside the course.

NASA Earth fact sheet: Mass, radius, gravity and orbit data for Earth (and links to other planets).
NIST SI units: The seven SI base units and how they are defined.
JCGM publications (GUM): The international guide to expressing measurement uncertainty.

Glossary

Acceleration: Rate of change of velocity, dv/dt.
Amplitude: Maximum displacement from equilibrium in an oscillation.
Angular momentum: L = Iω; conserved without external torque.
Buoyant force: Upward force from a fluid, equal to the weight of fluid displaced.
Center of mass: Mass-weighted average position of a system.
Conservative force: A force whose work does not depend on path, such as gravity or a spring.
Displacement: Change in position, a vector.
Elastic collision: A collision that conserves kinetic energy.
Escape speed: Minimum speed to leave a body’s gravity without further thrust.
Free-body diagram: Diagram of all forces on one object.
Frequency: Cycles per second (Hz); f = 1/T.
Geostationary orbit: An equatorial orbit with a one-sidereal-day period.
Impulse: Force integrated over time; equals change in momentum.
Inertia: Resistance to change in motion; measured by mass.
Kinetic energy: Energy of motion, ½mv².
Moment of inertia: Rotational inertia, Σmr².
Momentum: p = mv.
Newton: SI unit of force, kg·m/s².
Period: Time for one cycle or one orbit.
Power: Rate of energy transfer, in watts.
Pressure: Force per unit area, in pascals.
Resonance: Large oscillation when driven at a natural frequency.
Standard error: Standard deviation of the mean, s/√N.
Sun-synchronous orbit: A near-polar orbit that passes over each place at about the same local solar time.
Torque: Turning effect of a force, rF sin θ.
Uncertainty: Estimated range around a measured value that probably contains the true value.
Vector: A quantity with size and direction.
Weight: Gravitational force on a mass, mg.
Work: Energy transferred by a force over a displacement.

Self-assessment rubric

No grade or credit is given. Use this to judge honestly where you are in each unit.

Level	What it looks like
4 · Mastery	Solves new, unseen problems correctly, starts from a diagram and a principle (Newton, energy or momentum), and checks units and limits.
3 · Proficient	Solves the practice problems with correct units and sensible significant figures; occasional slips.
2 · Developing	Follows worked examples but struggles to choose a method for new problems, or mixes up vectors and scalars.
1 · Beginning	Plugs numbers into formulas without a diagram; needs to revisit the unit.

Suggested weighting if you want a score

Part	Weight
Practice problems	30%
Lab write-ups (or virtual labs)	20%
Midterm practice set	20%
Final practice set	30%

Aim for level 3 or better in every unit before moving to the next course.

Physics I + Lab

About this course

How this course helps save the planet

Before you start

Prerequisites

How to study

Lab equipment (for the wet labs)

Suggested 15-week schedule

Your progress

Measurement, Vectors & Motion in One Dimension

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Motion in Two Dimensions: Projectiles & Circles

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Newton’s Laws, Friction & Circular Dynamics

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Work, Energy & Power

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Momentum, Collisions & Rockets

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Rotation, Torque & Angular Momentum

Learning objectives

Key concepts

Key equations

Worked examples, step by step

Practice problems

Common misconceptions

Flashcards

Self-check quiz

How this helps save the planet

Free learning resources

Gravitation & Orbits

Learning objectives

Key concepts

Key equations

Worked examples, step by step