Overview
This lecture introduces fundamental concepts in measurements for General Physics 1, including unit conversions, fundamental and derived units, significant figures, scientific notation, and dimensional analysis.
Measurement and Physical Quantities
- Measurement assigns numerical values, with units, to physical properties (dimensions) of objects.
- Physical quantity = numerical value + unit (e.g., 9 meters).
- Units communicate the magnitude and type of a physical property.
Fundamental and Derived Units
- Seven fundamental quantities: length, mass, time, temperature, electric current, luminous intensity, amount of substance.
- Fundamental units (base units): cannot be broken into simpler units; examples include meter (m), kilogram (kg), second (s).
- Derived units: combinations of fundamental units (e.g., speed = meters/second, force = kg·m/s²).
Systems of Measurement
- Two main systems: Metric (SI) and English (Imperial).
- Metric system uses prefixes (kilo-, centi-, milli-, etc.) for ease of conversion (multiples of 10).
- English system uses irregular conversion factors (e.g., 1 mile = 5280 feet).
Unit Conversion and Dimensional Analysis
- Dimensional analysis uses conversion factors (ratios) to change units.
- Steps: Identify value to convert, find conversion factor, multiply and cancel units, write the answer with correct units.
- Use conversion tables for English-Metric conversions (e.g., 1 inch = 2.54 cm).
- For derived or compound units, convert each part separately as needed.
Significant Figures
- Significant figures reflect measurement precision.
- Rules:
- All nonzero digits are significant.
- Zeros between nonzero digits are significant.
- Leading zeros are not significant.
- Trailing zeros after a decimal are significant.
- In calculations, the result should not have more significant digits than the least precise value.
Scientific Notation
- Expresses large/small numbers as n × 10^k, where 1 ≤ n < 10.
- Positive exponent for numbers >1, negative for numbers <1.
- Move decimal left/right for conversion to/from scientific notation.
Dimensional Analysis and Checking Equations
- Dimensions are physical properties that must be consistent in equations.
- An equation is dimensionally correct if both sides have the same dimensions.
- Dimensional analysis can check equation correctness and guide unit conversions.
Key Terms & Definitions
- Measurement — Assignment of numerical value and unit to a physical property.
- Physical Quantity — Value describing a physical property; includes number and unit.
- Fundamental Unit — Basic unit of measurement (e.g., meter, kilogram).
- Derived Unit — Results from combining fundamental units (e.g., Newton).
- Dimensional Analysis — Method of converting units and checking equation consistency using dimensions.
- Significant Figures — Digits in a value that reflect measurement certainty.
- Scientific Notation — Method of writing numbers as n × 10^k for simplicity.
Action Items / Next Steps
- Review the table of SI units and conversion prefixes.
- Practice unit conversions and applying dimensional analysis to word problems.
- Complete concept builders and exercises on significant figures and scientific notation as assigned in your module.