Foundations Of Physics.pdf

Physical quantities have a numerical value and a unit, with examples including mass, length, temperature, and time. The Systeme Internationale (S.I.) units provide a set of base units to express the magnitudes of quantities, reducing confusion and increasing efficiency in scientific data exchange. The base quantities and units to learn are mass (kg), length (m), time (s), current (A), temperature (K), and amount of substance (mol). Derived units are expressed in terms of base units using mathematical symbols.

Homogeneity of physical equations requires both sides to simplify to the same base unit, indicating correctness if no numerical errors are made. Unit prefixes are used to form decimal multiples and submultiples of S.I. units. Measurements and uncertainties involve accuracy, precision, systematic error, and random error. Systematic errors can be reduced or eliminated using better techniques and instruments, while random errors can be reduced by improving techniques, making multiple measurements, or using more precise instruments.

Resolution, or the smallest change an instrument can measure, affects precision. Reliable measurements give consistent results, while unreliable experiments yield different results or large scatter. Uncertainties include absolute uncertainties, which are the size of the range of values in which the true value probably lies, and percentage uncertainties, calculated as (uncertainty/average value) x 100. Rules for determining percentage uncertainties in quantities involve adding uncertainties for multiplication and division, and multiplying uncertainties by the exponent for powers. The uncertainty in the gradient of a line can be determined using maximum and minimum gradients or error bars.