Units and Measurement
A complete treatment of physical quantities, the SI system of units, measurement precision through significant figures and rounding, dimensions and dimensional analysis including consistency checks and deriving relations among physical quantities
Topics
Introduction and the International System of Units
What measurement means, the concept of base and derived units, the evolution from CGS/FPS/MKS to the modern SI system, the seven SI base quantities with their definitions, supplementary units (radian and steradian), and commonly retained non-SI units
Significant Figures
What significant figures are, why they matter for reporting measurement precision, the complete set of rules for counting them, how scientific notation eliminates ambiguity, and how exact numbers are handled
Arithmetic Operations with Significant Figures
How to determine the correct number of significant figures or decimal places in the result of multiplication, division, addition, and subtraction, ensuring the final answer reflects the precision of the input measurements
Rounding Off the Uncertain Digits
How to round computed results to the correct number of significant figures, the standard rounding rules including the even-odd convention for the borderline digit 5, and handling multi-step calculations and exact constants
Uncertainty in Arithmetic Calculations
How measurement errors propagate through arithmetic operations including products, quotients, sums, and differences, with rules for combining percentage errors, understanding relative error, and preserving accuracy in multi-step calculations
Dimensions of Physical Quantities
Understanding how every physical quantity can be expressed as powers of seven base quantities, the concept of dimensions in mechanics using mass, length, and time, and how dimensions capture the nature of a quantity rather than its numerical value
Dimensional Formulae and Dimensional Equations
How to write the dimensional formula of any physical quantity, what dimensional equations are, how to derive them from known physical relationships, and the foundational principle that only quantities sharing the same dimensions can be combined
Checking Dimensional Consistency of Equations
The principle of homogeneity of dimensions, how to use it to verify the correctness of physical equations term by term, what dimensionless quantities and special functions mean for this test, and the important limitations of dimensional checks
Deducing Relations among Physical Quantities
How to use the method of dimensions to derive relationships between physical quantities, the product-type assumption, a fully worked derivation of the time period of a simple pendulum, and the important limitations that bound this technique