Physics Measurements and Units

SI Units

• International System of Units (SI) is a modern metric system used to express measurements
• Based on seven fundamental units:
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
  • Ampere (A) for electric current
  • Kelvin (K) for thermodynamic temperature
  • Mole (mol) for amount of substance
  • Candela (cd) for luminous intensity
• Derived units are formed by combining fundamental units, e.g., velocity (m/s), force (N = kg m/s²)

Significant Figures

• Significant figures (sig figs) represent the number of digits in a measurement that are known with some degree of reliability
• Rules for determining sig figs:
  • Non-zero digits are always significant
  • Zeros between non-zero digits are significant
  • Leading zeros are not significant
  • Trailing zeros are only significant if the number contains a decimal point
• Operations with sig figs:
  • Addition and subtraction: result has the same number of sig figs as the number with the fewest sig figs
  • Multiplication and division: result has the same number of sig figs as the number with the fewest sig figs

Dimensional Analysis

• Dimensional analysis is a method for converting between units by using conversion factors
• Conversion factors are ratios of equivalent quantities, e.g., 1 inch = 2.54 centimeters
• Steps for dimensional analysis:
  1. Identify the given quantity and the desired unit
  2. Write a conversion factor that relates the given unit to the desired unit
  3. Multiply the given quantity by the conversion factor
  4. Cancel out units and simplify the result

Errors in Measurement

• Errors in measurement can arise from:
  • Instrumental errors (e.g., faulty equipment)
  • Human errors (e.g., reading mistakes)
  • Methodological errors (e.g., incorrect procedure)
• Types of errors:
  • Systematic errors: consistent errors in the same direction
  • Random errors: unpredictable errors in either direction
• Ways to minimize errors:
  • Use precise instruments and techniques
  • Repeat measurements and take averages
  • Calibrate instruments regularly

Conversion of Units

• Unit conversion involves changing a measurement from one unit to another
• Conversion methods:
  • Using conversion factors (e.g., 1 mile = 1609.34 meters)
  • Using equivalent ratios (e.g., 1 hour = 60 minutes)
  • Using dimensional analysis (see above)
• Common unit conversions:
  • Length: inches to feet, meters to kilometers
  • Volume: liters to milliliters, gallons to liters
  • Time: hours to minutes, seconds to hours