Overview
This lecture covers unit conversions between SI and English systems, use of prefixes, significant figures, scientific notation, and solves related physics problems.
Physical Quantities and SI Units
- Physical quantities are measurable and used to express laws of physics (e.g., length, mass, time).
- The International System of Units (SI) standardizes measurements globally.
- SI base units: meter (m) for length, kilogram (kg) for mass, second (s) for time.
- Meter is defined by the distance light travels in vacuum in 1/299,792,458 second.
- Second is defined by 9,192,631,770 cycles of radiation from cesium atom.
- Kilogram is defined by a platinum-iridium cylinder standard.
Unit Conversion
- The United States uses the British (English) system; conversions between systems are standardized.
- To convert units, multiply by a conversion factor so that unwanted units cancel, leaving desired units.
- Example: 28 oz × (28.3 g / 1 oz) = 792.4 g.
- For multi-step conversions, convert each unit step separately (e.g., kg → g → oz).
Prefixes in the Metric System
- Prefixes indicate multiples or subdivisions of units (e.g., kilo-, mega-, milli-).
- Combine prefixes with units to express large or small quantities (e.g., 12 Mm = 12 megameters = 12 × 10⁶ m).
Significant Figures
- Significant figures show the precision of a measurement.
- All non-zero digits are significant (24 has 2 sig figs; 3.56 has 3).
- Leading zeros are not significant (0.0025 has 2).
- Captive (between non-zeros) zeros are significant (1502 has 4).
- Trailing zeros are significant if there’s a decimal point (100 has 1; 2306.0 has 5).
Scientific Notation
- Used to express very large or small numbers as a coefficient (1≤|a|<10) times a power of ten.
- Move decimal left for positive exponent; right for negative exponent.
- Example: 4567.89 = 4.56789 × 10³; 0.004567 = 4.567 × 10⁻³.
Sample Conversion Problems
- Example: 1 cm/20 s × (1 in / 2.54 cm) = 0.0196 in/s = 1.9 × 10⁻² in/s.
- Example: 40 km/h converted to ft/s requires sequential conversion of length and time units.
- Multi-step problems require converting each unit one at a time.
Key Terms & Definitions
- Physical Quantity — A measurable property used to describe physical phenomena.
- SI Units — The International System of Units, standard metric units for science.
- Conversion Factor — A ratio expressing how many of one unit equals another.
- Prefix — A symbol added to a unit's name to indicate multiples or subdivisions.
- Significant Figures — Digits in a number that express its precision.
- Scientific Notation — A method to write numbers as a product of a coefficient and a power of ten.
Action Items / Next Steps
- Solve the problems on pages 3-4 of the physics module.
- Write solutions clearly, box the final answers.