P1: Physical Quantities, Units and Measurement

A physical quantity has a numerical magnitude and a unit. The K323 base quantities used here include mass in kilograms, length in metres, time in seconds, current in amperes, temperature in kelvin, and amount of substance in moles. Derived quantities such as speed and density combine base units.

Convert prefixes before substituting. For example, $\pu{3.2 mm}=3.2 \times 10^{-3}\,\pu{m}$, while $\pu{5.0 Mohm}=5.0 \times 10^6\,\pu{ohm}$. An order-of-magnitude estimate compares powers of ten and can expose an impossible calculator result.

Match the instrument to the size of the object and the precision required. A metre rule suits ordinary lengths, vernier calipers suit internal or external diameters, and a micrometer screw gauge suits small thicknesses. A balance measures mass, while a stopwatch or electronic timer measures time.

Check for zero error, avoid parallax by viewing a scale normally, repeat readings when random variation is expected, and state precision consistently. For a repeated thickness, measure several layers together and divide so the measured total is large compared with the scale division.

A scalar has magnitude only. A vector has magnitude and direction. Distance and speed are scalars, while displacement, velocity and force are vectors. Units alone do not decide whether a quantity is scalar or vector.

To add two vectors graphically, choose a scale, draw the first vector, place the tail of the second at the head of the first, then draw the resultant from the first tail to the final head. Measure both magnitude and direction and show the scale used.