Physical Quantities & Measurement
Section: Motion, Forces & Energy | Syllabus: Cambridge IGCSE Physics (0625)
Measuring Length
A ruler looks like the simplest instrument in the lab, but the marks on its scale have width and your eye can view them from the wrong angle. Both effects shift the reading unless you control for them.
- Lay the object straight and closely alongside the ruler
- A bent wire must be straightened first
- Check the ends of the object — ragged ends make it hard to judge exactly where it begins and ends
- Ruler markings are typically 1 mm apart, but the marks themselves have width, which affects where you line up the zero end
- Align one end of the object with the zero mark, not the physical edge of the ruler
- Read the other end at eye level, looking perpendicular to the scale
- This avoids parallax error — viewing the scale at an angle makes the reading appear shifted
A ruler lying flat with a piece of wire placed alongside it. The left end of the wire aligns with the 0 cm mark. At the right end, two eye positions are shown: (1) correct - eye level with the scale, looking straight down, giving a reading of 6.4 cm; (2) incorrect - eye at an angle above or below the scale, giving a different apparent reading due to parallax. The correct reading position is labelled "Eye at scale level - no parallax error". The incorrect position is labelled with a cross "Parallax error".
Measuring Volume
A regular solid's volume can be calculated from a few ruler measurements. Most real objects, though, are not regular — a stone or a key has no formula, so its volume has to be measured by the water it pushes aside.
Regular Shapes
- For a cuboid (rectangular block), measure the length, width and height with a ruler and multiply them together
- V = l × w × h
- For other regular shapes (e.g. a sphere or cylinder), measure the relevant dimensions and use the appropriate equation for the volume of that shape
A measuring cylinder containing water. The water surface is curved (meniscus), dipping downward in the centre. The eye of the observer is shown level with the bottom of the meniscus. A horizontal dashed line marks the correct reading point at the base of the curve. A label reads "Read at the bottom of the meniscus". A second inset shows the wrong technique - eye above the meniscus level, reading the top of the curve - labelled "Wrong: parallax error gives reading that is too high".
Irregularly Shaped Solids - Displacement Method
- Most objects do not have a regular shape - to find their volume, use the displacement method
- Select a measuring cylinder about three or four times larger than the object
- Partially fill it with water - enough to cover the object - and note the initial volume
- Carefully immerse the object in the water (lower it on a thread if needed), without letting it touch the sides
- The water level rises because the object displaces (pushes aside) the water
- Volume of object = V_final - V_initial
Measuring Time
- Every experiment depends on measuring time accurately.
- A stopwatch is suitable for events lasting several seconds, but very short time intervals require electronic timers that start and stop automatically.
- Choosing the correct instrument reduces measurement error and improves the reliability of your results.
- A stopwatch may display hundredths of a second, but your reaction time (about 0.2 s) is usually much larger than the last digit shown on the display.
Measuring Multiples to Find Averages
When a single distance or time interval is too small to measure accurately on its own, measure many multiples of it together and divide to find the average value of one.
Small Distances
- A single sheet of paper is far too thin to measure with a ruler - instead, take a stack of 500 sheets and measure its total thickness.
- Any inaccuracy in the total measurement is spread across all 500 sheets, so the error per sheet is very small
Short Time Intervals - The Pendulum
- A simple pendulum consists of a mass (called a plumb bob) hanging on a string clamped at the top - when pulled gently to one side and released, it swings back and forth at a steady rate
- A single period is usually too short to time accurately with a stopwatch
Instead:- Use a stopwatch to time 20 complete oscillations
- Divide by 20 to find the period of one oscillation
- T = (total time/20)
- Any inaccuracy in starting or stopping the stopwatch is much less significant when spread across 20 oscillations
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