Chapter 1-7: Units and Measurements - Vocabulary Flashcards

SI Units Basics

• Measurement requires a unit; SI is the internationally recognized system.
• Basic SI quantities: time, length (distance), mass.
• SI base units: $\text{time} = \text{s}, \quad \text{length/distance} = \text{m}, \quad \text{mass} = \text{kg}.$
• Derived quantities (e.g., speed/velocity) use combinations like $\frac{\text{m}}{\text{s}}$.

Prefixes and Base Units

• Prefixes to denote powers of ten:
  • kilo, $k$: $10^3$
  • mega, $M$: $10^6$
  • micro, $\mu$: $10^{-6}$
• Examples:
  • $1\ \text{km} = 10^3\ \text{m}$
  • $1\ \text{MW} = 10^6\ \text{W}$
  • $1\ \mu\text{W} = 10^{-6}\ \text{W}$
• Important: quantities with prefixes are usually converted to base SI units (seconds, meters, kilograms) before calculations.
• The kilogram is already a base SI unit.

Base Quantities and Units

• Time: $\text{s}$
• Length/Distance: $\text{m}$
• Mass: $\text{kg}$
• Speed/velocity: $\frac{\text{m}}{\text{s}}$

Unit Conversions (SI ↔ English)

• Common conversions:
  • 1 inch = $2.54\ \text{cm}$
  • 1 ft = $0.305\ \text{m}$
  • 1 mile = $1.609\ \text{km}$
  • 1 mph = $0.447\ \text{m/s}$
  • 1 m = $39.37\ \text{in}$
  • 1 km = $0.621\ \text{mi}$
  • 1 m/s = $2.24\ \text{mph}$
• Note: 1 mile ≈ 1.6 km; the ratio of miles to kilometers is a conversion factor of 1 when expressed with matching units.

How to Do a Unit Conversion (Step-by-Step)

• Start with the quantity to convert.
• Multiply by a conversion factor that equals 1; value stays the same, units change.
• Cancel the original unit across numerator and denominator.
• Compute the result in the desired units; report with proper significant figures.
• For complex conversions, use several successive conversion factors.

Example: Bike Speed (ft/s → mph)

• Given: $20\ \text{ft/s}$
• Factors: $1\ \text{mile} = 5280\ \text{ft}, \quad 1\ \text{h} = 3600\ \text{s}$
• Calculation:$20\ \text{ft/s} \times \frac{1\ \text{mile}}{5280\ \text{ft}} \times \frac{3600\ \text{s}}{1\ \text{h}} = 13.6\ \text{mph} \approx 14\ \text{mph}$

Reasonableness Checks and Estimations

• Not all problems require precision; use order-of-magnitude estimates when appropriate.
• Order-of-magnitude estimate symbol: $v \sim 20\ \text{mph}$ (two squiggly lines indicate lower precision).
• Walking speed example (rough): walk 1 mile in about 0.5 h → speed
  • $\frac{1\ \text{mile}}{0.5\ \text{h}} = 2\ \text{mph}$
  • Convert to m/s using approximate factor: $1\ \text{mph} \approx 0.5\ \text{m/s}$ → $2\ \text{mph} \approx 1.0\ \text{m/s}$
• A rough pace: stride ≈ 1 m, ~1 step/s → ≈ 1 m/s
• Exact SI-to-English checks: $1\ \text{m/s} = 2.24\ \text{mph}$

Quick Tips for Last-Minute Review

• Always convert to base SI units before performing calculations (except when you’re intentionally staying in the base units).
• Use conversion factors to cancel units; always verify the final units match what you’re solving for.
• For quick sanity checks, convert speeds to familiar units (e.g., mph to check plausibility of bicycle speeds).
• Use order-of-magnitude estimates to judge reasonableness of results; report with the appropriate level of precision.