Week 1 — Building the foundation of physics
Physics is the study of how the universe works. From the smallest subatomic particles to the largest galaxies, physics seeks to understand the fundamental laws of nature through careful observation and mathematical description.
Physics builds knowledge through a systematic process:
If it disagrees with experiment, it's wrong. That's the basic idea.
— Richard Feynman
The International System of Units (SI) is the standard for all scientific measurement.
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Current | ampere | A |
| Temperature | kelvin | K |
| Amount | mole | mol |
| Light | candela | cd |
| Quantity | Unit | In Base Units |
|---|---|---|
| Velocity | meter/second | m/s |
| Acceleration | meter/second² | m/s² |
| Force | newton (N) | kg·m/s² |
| Energy | joule (J) | kg·m²/s² |
| Pressure | pascal (Pa) | kg/(m·s²) |
Every physical quantity has dimensions — the basic types of measurement it represents. The three fundamental dimensions are:
Key rule: Both sides of any equation must have the same dimensions.
Is the equation v² = 2ax dimensionally consistent?
Left side: [v²] = (L/T)² = L²/T²
Right side: [2ax] = [L] × [L/T²] = L²/T² (the "2" is dimensionless)
✅ Both sides have dimensions L²/T² — the equation passes!
Significant figures are the digits in a measurement that carry meaningful information about its precision.
Scientific notation expresses numbers compactly:
NASA lost the Mars Climate Orbiter in 1999 because one team used imperial units (pounds-force) while another used SI units (newtons). Dimensional analysis isn't just math — it can save million-dollar missions!
The key technique is multiplying by 1 in the form of a conversion factor:
Convert 60 miles/hour to meters/second.
Known: 1 mile = 1609.34 meters, 1 hour = 3600 seconds
✅ Answer: 26.8 m/s
Try these on your own. Scroll down for solutions.
Problem 1: A car travels 120 km in 2 hours. What is its average speed in m/s?
Problem 2: How many significant figures are in 0.003040?
Problem 3: Is the equation d = vt + ½at² dimensionally consistent? (d = distance, v = velocity, t = time, a = acceleration)
Problem 4: Convert 5.0 m/s² to km/h².
Answer these questions before moving on:
Q1: What are the dimensions of power (P = energy / time)?
Energy has dimensions [M][L]²/[T]² = M·L²·T⁻²
Power = energy/time → [M][L]²/[T]³ = M·L²·T⁻³
Q2: A ball is thrown upward. At the very top of its path, what is its velocity? Its acceleration?
Velocity: 0 m/s (it momentarily stops)
Acceleration: 9.8 m/s² downward (gravity never stops!) This is why it falls back down.
Q3 (mini-problem): You walk 3 meters east, then 4 meters north. What is your displacement (straight-line distance from start)?
Use the Pythagorean theorem: d = √(3² + 4²) = √(9 + 16) = √25 = 5 meters
Displacement is different from distance (which would be 7 m). Displacement is the straight-line change in position.