Physics · Ch 1 — Units and Measurement

Summary

Physical quantities are expressed as a product of a numerical value and a unit: $Q = n \times u$ .
Fundamental quantities (mass, length, time, etc.) have base SI units (kg, m, s, A, K, mol, cd). Derived quantities are expressed in terms of these.
Dimensions are powers of fundamental quantities in a derived unit, e.g., velocity has dimensions $[L T^{-1}]$ .
Dimensional formula uses square brackets: $[M^a L^b T^c]$ . Only quantities with same dimensions can be added/subtracted.
Principle of homogeneity: In a valid equation, dimensions of each term must be identical.
Dimensional analysis checks formula correctness, derives relations, and converts units (e.g., $1 \, \text{N} = 10^5 \, \text{dyn}$ ).
Limitations: Dimensional analysis cannot determine dimensionless constants, nor apply to trigonometric/exponential/logarithmic functions. …