Physical Quantities and Measurement Techniques Notes

A ruler measures length: line up the zero mark with one end and read the other end. Keep your eye level with the scale to avoid parallax error. For small distances, repeat and take the average. A measuring cylinder measures volume: read the bottom of the meniscus with your eye level to the scale. To find the volume of a solid, use displacement.

Clocks and digital timers measure time intervals. A digital timer reads to 0.01 s or better, but a hand-held stopwatch is limited by human reaction time, typically about 0.2 s. Timing one short event, like a single swing of a pendulum, is unreliable. Instead time many oscillations (for example 20) and divide the total time by the number to find the period.

A scalar has magnitude only. A vector has magnitude and direction. Ask: "does this need a direction to be fully described?" If yes, it is a vector. Distance and displacement are the classic pair.

The resultant is the single vector with the same effect as two vectors combined. For vectors of size $a$ and $b$ at 90°, they form a right-angled triangle with the resultant as the hypotenuse, so $R=\sqrt{a^2+b^2}$. This applies to perpendicular forces, and to horizontal and vertical velocity components. A scale drawing gives the same answer and shows direction.

All measurements have uncertainty: from the instrument (scale divisions, reaction time), the environment (temperature changes, friction) or the observer (parallax). Taking several measurements and finding the mean reduces random errors, because individual errors are unlikely to all lie the same way. State the number of readings and show the calculation.