Measurement techniques, errors & uncertainties
Every experiment you will ever do rests on one skill: making a careful measurement and knowing how much to trust it. In this AS-level lesson we choose the right instrument for a quantity — rule, vernier calipers, micrometer screw gauge, balance, protractor, stopwatch, cathode-ray oscilloscope, thermometer, ammeter, voltmeter and galvanometer — and we learn to read a vernier to a tenth of a millimetre and a micrometer to a hundredth. Then we meet the heart of AS physics: the difference between precision and accuracy, the two families of error (systematic, including zero errors, and random), and how to attach an honest uncertainty to a result. We learn absolute, fractional and percentage uncertainty, how to estimate an uncertainty from a set of repeated readings, and the three golden rules for combining uncertainties — add absolute uncertainties when adding or subtracting, add percentage uncertainties when multiplying or dividing, and multiply the percentage by the power when raising to a power.
By the end you should be able to (NSSCAS Physics (AS) 1.2):
- Choose and use appropriate instruments for length, mass, angle, time, temperature and electrical quantities (rule, vernier calipers, micrometer, balance, protractor, stopwatch, c.r.o. time-base, thermometer, ammeter, voltmeter, galvanometer, oscilloscope)
- Read a length from vernier calipers to 0.1 mm and from a micrometer screw gauge to 0.01 mm
- Read both analogue scales and digital displays, avoiding parallax, and use a calibration curve
- Distinguish between precision (readings close to one another) and accuracy (close to the true value)
- Explain the effects of systematic errors, including zero errors, and of random errors, and how each may be reduced
- Estimate the uncertainty in a quantity from a set of repeated readings using the mean and half the range
- Define and calculate absolute, fractional and percentage uncertainty, and express a result as value plus or minus its absolute uncertainty
- Combine uncertainties: add absolute uncertainties for addition/subtraction, add percentage (fractional) uncertainties for multiplication/division, and multiply the percentage uncertainty by the power