01Introduction to Physics
Explore physics as a science: measurement systems, SI units, significant figures, dimensional analysis, and the scientific method.
Physics is the foundation of all natural sciences. Mastering measurement, SI units, and the scientific method gives you the analytical tools you'll use throughout every unit — from forces to quantum mechanics.
Essential Question: How do scientists use measurement, units, and systematic reasoning to describe and understand the physical world?
Lesson Overview
Physics is the fundamental science that studies matter, energy, and the interactions between them — from subatomic particles to the large-scale structure of the universe. Before we can describe any physical phenomenon quantitatively, we need a shared language of measurement: the International System of Units (SI), rules for expressing precision through significant figures, and the powerful tool of dimensional analysis that lets us convert between units and check whether equations make physical sense. Layered on top of all measurement is the scientific method — the cycle of observation, hypothesis, experiment, and conclusion that drives every discovery in physics.
Key Concepts
Branches of Physics
Mechanics
Motion, forces, energy
Thermodynamics
Heat and temperature
Electromagnetism
Electric & magnetic fields
Optics
Light and wave behavior
Quantum Mechanics
Subatomic phenomena
Relativity
Space, time, gravity
SI Base Units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | Meter | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Electric current | Ampere | A |
| Temperature | Kelvin | K |
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
Common SI Prefixes
| Prefix | Symbol | Factor | Scientific Notation |
|---|---|---|---|
| Giga | G | 1,000,000,000 | 10⁹ |
| Mega | M | 1,000,000 | 10⁶ |
| Kilo | k | 1,000 | 10³ |
| Centi | c | 0.01 | 10⁻² |
| Milli | m | 0.001 | 10⁻³ |
| Micro | μ | 0.000001 | 10⁻⁶ |
| Nano | n | 0.000000001 | 10⁻⁹ |
Significant Figures Rules
All non-zero digits are significant.
e.g. 3.14 → 3 sig figs
Zeros between non-zero digits are significant.
e.g. 1,002 → 4 sig figs
Leading zeros are NOT significant.
e.g. 0.0042 → 2 sig figs
Trailing zeros after a decimal point ARE significant.
e.g. 3.500 → 4 sig figs
Trailing zeros in a whole number are ambiguous; use scientific notation.
e.g. 1200 → ambiguous; 1.20 × 10³ → 3 sig figs
For addition/subtraction: round to the fewest decimal places.
e.g. 12.3 + 4.56 = 16.9 (tenths)
For multiplication/division: round to the fewest sig figs.
e.g. 4.5 × 2.31 = 10. (2 sig figs)
The Scientific Method
1. Observation
Notice a phenomenon
2. Hypothesis
Propose a testable explanation
3. Experiment
Design a controlled test
4. Analysis
Interpret data & results
5. Conclusion
Support, revise, or reject hypothesis
Worked Examples
Convert 5.2 km to meters using dimensional analysis.
Write the given value: 5.2 km
Set up the conversion factor: 1 km = 1,000 m → (1,000 m / 1 km)
5.2 km × (1,000 m / 1 km)
Cancel the km units: km / km = 1
= 5.2 × 1,000 m
Express 3,500,000 Hz in megahertz (MHz) using scientific notation.
Write in scientific notation: 3,500,000 Hz = 3.5 × 10⁶ Hz
Recall: 1 MHz = 10⁶ Hz → conversion factor: (1 MHz / 10⁶ Hz)
3.5 × 10⁶ Hz × (1 MHz / 10⁶ Hz)
Cancel 10⁶ Hz: = 3.5 × (10⁶ / 10⁶) MHz
= 3.5 × 1 MHz
How many significant figures are in 0.00420?
Identify leading zeros: 0.00 — these are placeholders, NOT significant.
Identify the digits 4, 2, 0 after the leading zeros.
4 → significant (non-zero digit)
2 → significant (non-zero digit)
0 → significant (trailing zero after a decimal point)
Add 12.3 m + 4.56 m + 0.789 m with the correct number of significant figures.
Perform the addition: 12.3 + 4.56 + 0.789 = 17.649 m
For addition, round to the fewest decimal places among the addends.
12.3 m has 1 decimal place (tenths) — the fewest.
Round 17.649 to the tenths place: look at the hundredths digit (4) → round down.
A car travels at 90 km/h. Convert this speed to m/s using dimensional analysis.
Write the given: 90 km/h
Conversion 1 — km to m: multiply by (1,000 m / 1 km)
Conversion 2 — hours to seconds: multiply by (1 h / 3,600 s)
90 km/h × (1,000 m / 1 km) × (1 h / 3,600 s)
= 90 × 1,000 / 3,600 m/s
= 90,000 / 3,600 m/s
= 25 m/s [equivalently: divide km/h by 3.6]
Guided Problems
Convert 250 cm to meters.
Hint: Use the conversion factor 1 m = 100 cm. Set up the fraction so that cm cancels.
Write 0.000056 kg in scientific notation.
Hint: Move the decimal point to the right until you have one non-zero digit before the decimal. Count the moves — that becomes a negative exponent.
How many significant figures are in 40,500?
Hint: Trailing zeros in a whole number without a decimal point are ambiguous. Consider which zeros are definitely significant and which are not.
Multiply 3.2 m × 4.15 m and express the answer with the correct number of significant figures.
Hint: For multiplication, the result should have the same number of sig figs as the factor with the fewest sig figs. How many sig figs does each factor have?
A scientist observes that plants near a window grow taller than those in a dark corner. Write a testable hypothesis for this observation.
Hint: A good hypothesis follows the format: 'If [independent variable], then [dependent variable] because [reasoning].' Make sure it can be tested experimentally.
Key Vocabulary
Physics
The branch of science that studies matter, energy, and the fundamental forces and interactions of the universe.
Example: Physics explains why a ball falls when dropped and how electricity flows through a wire.
SI Unit
A unit belonging to the International System of Units (Système International), the globally agreed standard for scientific measurement.
Example: The meter (m) is the SI unit of length; the kilogram (kg) is the SI unit of mass.
Meter
The SI base unit of length, defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
Example: A standard doorway is about 2 meters tall.
Kilogram
The SI base unit of mass, defined by fixing the numerical value of Planck's constant.
Example: A liter of water has a mass of approximately 1 kilogram.
Significant Figures
The digits in a measurement that carry meaningful information about its precision, including all certain digits plus one estimated digit.
Example: 0.00420 has 3 significant figures: 4, 2, and the trailing zero.
Scientific Notation
A way of expressing very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of ten.
Example: 3,500,000 Hz = 3.5 × 10⁶ Hz
Dimensional Analysis
A problem-solving technique that uses conversion factors to change units while keeping the physical quantity the same.
Example: 5.2 km × (1,000 m / 1 km) = 5,200 m
Hypothesis
A testable, falsifiable prediction or explanation for an observed phenomenon, proposed before conducting an experiment.
Example: 'If light intensity increases, then plant growth rate will increase.'
Workbook Check — Interactive Quiz
Interactive Practice — 5 Questions
Which of the following is NOT one of the seven SI base units?
How many significant figures are in the measurement 0.00420 m?
A speed of 72 km/h is equivalent to how many m/s?
In the scientific method, what immediately follows forming a hypothesis?
The prefix "micro-" (μ) represents which power of ten?
Independent Practice
A student records a mass of 2,450 g. Convert this measurement to kilograms using dimensional analysis, showing all conversion factors.
Express the speed of light (299,792,458 m/s) in scientific notation, rounded to 3 significant figures.
Identify the number of significant figures in each measurement: (a) 0.00340 km (b) 5,200 g (c) 1.0 × 10⁴ s
A room is 4.8 m long and 3.5 m wide. Calculate the area in m² with the correct number of significant figures.
★ A scientist claims: "I heated water 10 times and it always boiled at 100°C, so water always boils at exactly 100°C." Identify two weaknesses in this conclusion and describe how a more rigorous experiment would address them.
ChallengeCommon Mistakes
Confusing mass (kg) and weight (N) — treating them as the same quantity
Mass is the amount of matter (kg); weight is the gravitational force on that mass (W = mg, in Newtons)
Rounding intermediate calculation results, causing accumulated error
Keep full precision through all steps; round only the final answer to the correct significant figures
Forgetting to convert units before substituting into equations (e.g., cm instead of m)
Always convert all quantities to SI base units (m, kg, s) before plugging into any formula
Adding vectors algebraically like scalars (e.g., 3 m/s + 4 m/s = 7 m/s at any angle)
Vectors must be added using components or the triangle/parallelogram rule; magnitude depends on direction
Math Tips
Dimensional analysis: write units as fractions and cancel them like algebra — if the units of your answer don't match the expected unit, the setup is wrong
Significant figures rule: the result of multiplication/division has as many sig figs as the factor with the fewest; for addition/subtraction, match the least precise decimal place
SI prefixes to memorize: nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), centi (10⁻²), kilo (10³), mega (10⁶)
Scientific notation check: 6.02 × 10²³ means the decimal moves 23 places right. Always express answers in scientific notation when the value is very large or very small