Units and Measurement Basics

Units and Measurement

• A physical quantity is a quantity that can be measured and expressed in terms of a number and a unit.
• Measurement is the process of comparing an unknown quantity with a known standard (unit).

Fundamental and Derived Units

• Fundamental units are basic units for fundamental quantities, such as meter for length, kilogram for mass, and second for time.
• Derived units are units derived from fundamental units, such as m/s for velocity and N for force.

System of Units

• The International System of Units (SI) is the modern form of the metric system and the most widely used system of measurement.
• SI units include:
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
  • Ampere (A) for electric current
  • Kelvin (K) for temperature
  • Mole (mol) for amount of substance
  • Candela (cd) for luminous intensity

Accuracy, Precision, and Errors in Measurement

• Accuracy refers to the closeness of a measured value to the true value.
• Precision refers to the closeness of repeated measurements to each other.
• Errors can be classified into two types:
  • Systematic errors: consistent and predictable errors due to faulty equipment or bias.
  • Random errors: errors due to unknown and unpredictable variations.

Significant Figures

• Significant figures are digits in a measurement that are known reliably plus one last digit that is estimated.
• Rules for significant figures:
  • All non-zero digits are significant.
  • Zeros between significant figures are significant.
  • Leading zeros are not significant.
  • Trailing zeros are significant if there is a decimal point.

Dimensional Analysis

• Dimension is the nature of a physical quantity expressed in terms of fundamental quantities, such as [L] for length and [M] for mass.
• Dimensional formula is an expression showing how and which of the fundamental units are involved, such as [M L T^-2] for force.
• Applications of dimensional analysis:
  • Checking the correctness of equations.
  • Converting units from one system to another.

Standard Units and Measurements

• Meter is defined as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 seconds.
• Kilogram is defined by the Planck constant, where h = 6.62607015 × 10^-34 Js.
• Second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

Measuring Instruments

• Vernier calipers measure length with a least count of 0.01 cm.
• Micrometer screw gauge measures small lengths with a least count of 0.01 mm.

Errors in Measurements

• Absolute error is the difference between the true value and the measured value.
• Relative error is the absolute error divided by the true value.
• Percentage error is the relative error expressed in percentage.