Chapter Summary: Units and Measurements

  • Physical Quantities are quantities that can be measured and expressed numerically. They are classified as fundamental (like mass, length, time) or derived (like speed, force).

  • A unit is a standard of measurement. The International System of Units (SI) is a globally accepted system with 7 base units:

  • Length (m), Mass (kg), Time (s), Electric current (A), Temperature (K), Luminous intensity (cd), Amount of substance (mol).

  • SI also includes supplementary units:

  • Plane angle (radian), Solid angle (steradian)

  • Significant Figures indicate the precision of a measurement. They include all known digits plus the first doubtful digit. Rules are applied to determine how many are significant.

  • Rounding off and scientific notation are used for representing measured values correctly.

  • Dimensions express physical quantities in terms of base quantities. Examples:

  • Speed: [M0L1T−1][M^0 L^1 T^{-1}], Force: [M1L1T−2][M^1 L^1 T^{-2}]

  • Dimensional Equations relate physical quantities with their dimensional formulae. They are used to:

  • Check equation consistency

  • Convert units

  • Derive relations among physical quantities (up to constants)

  • The principle of homogeneity states that all terms in a valid physical equation must have the same dimensions.

  • Dimensional analysis is limited—it cannot determine dimensionless constants (like π\pi or 22).

Mastering these basics helps in understanding and verifying physical equations and their correctness across all topics in physics.