Unit Conversion and Measurement in Physics

Jul 28, 2024

Mindmap

Unit Conversion and Measurement in Physics

Learning Objectives

  • Convert units between SI and English systems
  • Recall rounding off of numbers
  • Designate multiples and subdivisions of units using prefixes
  • Identify significant figures
  • Express numbers in scientific notation

Key Concepts in Physics

  • Physics: Experimental science involving measurements to test hypotheses
  • Physical Quantity: Numbers used to describe measurements; must be measured compared to a reference standard

Physical Quantities

  • Length, mass, time, electric current, temperature, luminous intensity, amount of substance

SI Units (International System of Units)

  • Adopted in 1960 for global consistency
  • Common units: meters (length), kilograms (mass), seconds (time)

Definitions

  • Meter: Distance traveled by light in a vacuum in 1/299,792,458 second
  • Second: 9,192,631,770 cycles of microwave radiation due to cesium atom transition
  • Kilogram: Mass of a platinum-iridium cylinder at the International Bureau of Weights and Measures

Unit Conversion

English to Metric Conversions

  • Length and weight conversions provided in tables (e.g., 1 oz = 28.3 g, 1 foot = 30.5 cm)

Conversion Example Steps

  1. Write the given value and multiply by the conversion factor
  2. Ensure the denominator matches the unit you're converting from, and the numerator matches the unit you're converting to
  3. Cancel out similar units and perform the multiplication

Examples

  • 28 oz to grams: 28 oz x 28.3 g/oz = 792.4 g
  • 3 feet to cm: 3 feet x 30.5 cm/foot = 91.5 cm
  • 2 kg to oz: Convert kg to g, then g to oz (2 kg x 1000 g/kg x 0.0353 oz/g = 70.6 oz)

Multiples and Subdivisions using Prefixes

  • Use prefixes for larger and smaller quantities by powers of 10 (e.g., mega for 10^6)
  • Example: 12 x 10^6 meters = 12 megameters (Mm)

Significant Figures

  • Indicate precision in measurements

Rules

  1. All non-zero digits are significant (e.g., 24 has 2 SFs, 3.56 has 3 SFs)
  2. Leading zeros are not significant (e.g., 0.0025 has 2 SFs)
  3. Captive zeros are significant (e.g., 1502 has 4 SFs)
  4. Trailing zeros are significant if there's a decimal (e.g., 100.0 has 4 SFs)

Scientific Notation

  • Useful for expressing large or small numbers
  • Written as a coefficient (between 1 and 10) multiplied by 10 raised to an exponent

Steps to Express in Scientific Notation

  1. Move the decimal point until one non-zero digit is to the left
  2. Count places moved; left adds positive exponent, right adds negative
  3. Example: 4567.89 → 4.56789 x 10^3, 0.004567 → 4.567 x 10^-3

Example Problems and Solutions

Sample Problem 1

  • Snail moves 1 cm every 20 seconds → Convert to inches/second
    • 1 cm / 20 s x 1 in / 2.54 cm = 0.01968 in/s or 1.9 x 10^-2 in/s after rounding

Sample Problem 2

  • Jeepney moves at 40 km/h → Convert to feet/second
    • 40 km/h x 1000 m/km x 1 ft/0.3048 m x 1 h/3600 s = 36.444 ft/s

Sample Problem 3

  • Distance from Sun to Earth
    • Light travels in 8 minutes at speed 299,792,458 m/s
    • 8 min x 60 s/min x 299,792,458 m/s = 1.44 x 10^11 meters

Additional Problems

  • Converting liters to milliliters, kg to tons, hectares to yield

Homework

  • Solve problems on pages 3-4 of the physics module and enclose final answers in a box.

Conclusion

  • Understanding unit conversion, significant figures, and scientific notation is crucial in solving physics problems effectively.