1.2 Units and Standards - University Physics Volume 1

Learning Objectives

• Define SI base units.
• Describe the creation of derived units from base units.
• Express quantities in SI units with metric prefixes.

Importance of Units in Physics

• Physics studies a wide range of phenomena, from the very small to the cosmic scale.
• Numerical values and equations enhance the understanding of nature.
• Standard units are necessary for expressing and comparing measurements effectively.

Major Systems of Units

• SI Units (Metric System): Used globally in science and mathematics.
• English Units: Historically used in the British Empire and still in use in the USA.
• SAE Units: Refers to measurements in inches, often used in automotive contexts.

SI Units: Base and Derived Units

• Base Quantities and Units:

  • Length (meter, m)
  • Mass (kilogram, kg)
  • Time (second, s)
  • Electrical current (ampere, A)
  • Thermodynamic temperature (kelvin, K)
  • Amount of substance (mole, mol)
  • Luminous intensity (candela, cd)

• Derived Quantities: Expressed as combinations of base units, e.g.,

  • Area (square meters, m²)
  • Volume (cubic meters, m³)
  • Speed (meters per second, m/s)
  • Density (kilograms per cubic meter, kg/m³)

Units of Time, Length, and Mass

The Second

• Defined as the time for 9,192,631,770 vibrations of cesium atoms.
• Essential for technologies like GPS that rely on precise time measurements.

The Meter

• Current definition: Distance light travels in 1/299,792,458 of a second in a vacuum.
• Previous definitions were based on Earth's dimensions and later light wavelengths.

The Kilogram

• New definition (since 2019) based on the Planck constant.
• Measurement via a Kibble balance.

Metric Prefixes

• Useful for expressing SI units as powers of ten.

• Examples:

  • Centimeter (1 cm = 10⁻² m)
  • Kilometer (1 km = 10³ m)
  • Megagram (1 Mg = 10⁶ g)

• Prefix Table:

  • Yotta (Y, 10²⁴) to Yocto (y, 10⁻²⁴)
  • Common prefixes: kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹), etc.

• Rules: Metric prefixes cannot be doubled up, e.g., 1000 kg is a megagram (Mg), not a kilokilogram.

Example of Using Metric Prefixes

• Restate masses using appropriate prefixes to ensure the numerical value is between one and 1000.
• Check calculations by ensuring powers of ten add up correctly.

Additional Notes

• Metric systems simplify unit conversions and allow easy scaling with prefixes.
• Non-SI units are sometimes used, with conversions provided where necessary.