Measurement techniques that reduce uncertainty

Lengths and heights

• Clamp the metre rule so it cannot move, and check it is vertical using a set square against the bench or floor (say what it is vertical relative to).
• Place the rule close to the object, so you are not reading across a gap.
• Read with your eye level with and perpendicular to the scale, to avoid parallax.
• Use a pointer or marker (a fiducial mark) fixed to the object to make the reading point clear.

Words like 'straight', 'parallel' or 'horizontal' without saying relative to what are not credited.

Times and periods

• Time many oscillations (say 10 or 20) and divide by the number, so the reaction-time uncertainty is shared out.
• Use a timing marker (fiducial mark) at the equilibrium position, where the object moves fastest, so the moment it passes is sharpest.
• Count down '3, 2, 1, 0' and start the stopwatch on 0, so you do not miscount.
• Use a small displacement so the oscillation is regular.

Very small quantities

Measure many identical items together and divide: the thickness of 500 sheets of paper, the diameter of 10 identical ball bearings in a line, or the time for 20 swings. The absolute uncertainty is spread over all the items, so the percentage uncertainty is much smaller.

Technique or modification?

A technique is how you use the apparatus you have (eye level, set square, timing marker). A modification is new apparatus (light gates, a video camera, a data logger). If a question asks for techniques, modifications earn no credit, and the other way round.

Worked example

A student times 20 oscillations as 31.6 s, with an uncertainty of 0.2 s. Find the period and its percentage uncertainty. Compare with timing one oscillation.

1. T = 31.6 / 20 = 1.58 s, with uncertainty 0.2 / 20 = 0.01 s
2. Percentage uncertainty = 0.2 / 31.6 x 100 = 0.63%
3. One oscillation timed directly: 0.2 / 1.58 x 100 = 13%

Answer: T = 1.58 s ± 0.63%, twenty times smaller than timing one swing

Check yourself

1. A stack of 500 sheets of paper is 48 mm thick. Find the thickness of one sheet in mm.
   Show answer

   0.096 mm. 48 / 500 = 0.096 mm.

2. A student times 10 oscillations of a pendulum as 14.2 s. Find the period in s.
   Show answer

   1.42 s. T = 14.2 / 10 = 1.42 s.

3. 20 oscillations take 27.4 s, with an uncertainty of 0.2 s. Find the percentage uncertainty in the period, to 2 s.f.
   Show answer

   0.73 %. The percentage is the same for 20T and T: 0.2 / 27.4 x 100 = 0.73%.

4. Why should a timing marker be placed at the equilibrium position of an oscillation?
   • The object stops there
   • It is where the amplitude is largest
   • The object moves fastest there, so the moment it passes is clearest
   • It reduces the period
   Show answer

   The object moves fastest there, so the moment it passes is clearest. At the ends the object moves slowly and it is hard to judge the exact turning moment.

5. What is a set square used for when measuring a height with a metre rule?
   • Checking the rule is vertical relative to the bench
   • Reading the scale at eye level
   • Measuring the zero error
   • Keeping the object still
   Show answer

   Checking the rule is vertical relative to the bench. A set square against the bench checks the rule is at 90° to it.

6. A question asks for a technique to improve the measurement of a time period with a stopwatch. Which answer is a technique rather than a modification?
   • Use light gates and a data logger
   • Film the oscillations with a video camera
   • Use a timing marker at the equilibrium position
   • Use a motion sensor
   Show answer

   Use a timing marker at the equilibrium position. The other three add new apparatus, which counts as a modification and is not credited for 'technique'.

7. Describe how to measure a single height of about 50 cm as accurately as possible with a metre rule.
   Show answer

   Clamp the metre rule vertically, checking with a set square against the bench, place it close to the object, and read with the eye level with the scale (perpendicular to it) to avoid parallax.. Two creditworthy techniques: a vertical rule checked with a set square, and reading at eye level.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson examiners' report: IAL Physics WPH13/01, January 2024
• Pearson examiners' report: IAL Physics WPH13/01, October 2024
• Pearson examiners' report: IAL Physics WPH16/01, October 2024

Last updated 8 November 2026. Spotted a mistake? Tell us.