Measuring Length and Time

Accurate measurement of length and time is the foundation of experimental physics. Choosing the correct instrument and technique reduces both systematic and random errors.

Which instrument should you use?

Instrument	Typical range	Precision	Use for
Ruler	0 to 1 m	1 mm	Length of a bench, width of a block
Vernier caliper	0 to 15 cm	0.1 mm (0.01 cm)	Diameter of a tube, thickness of a coin
Micrometer screw gauge	0 to 25 mm	0.01 mm	Diameter of a wire, thickness of a sheet
Stopwatch	up to hours	0.01 s (digital)	Timing oscillations, races

For very short distances, use calipers or micrometers. For very short time intervals, light gates connected to a data logger eliminate human reaction time.

How do you reduce timing errors?

Human reaction time is roughly 0.2 to 0.3 s. For a pendulum with a period of about 1 s, this error is significant. The standard technique is to time many oscillations and divide:

$T = \frac{t_{\text{total}}}{n}$

Timing 20 complete swings and dividing by 20 reduces the reaction time error by a factor of 20.

Worked example

A student times 25 complete oscillations of a pendulum and records 32.5 s. Calculate the period. [2]

Step 1. $T = \frac{32.5}{25}$

Step 2. $T = 1.30\ \text{s}$

Marking points: M1 for dividing total time by number of oscillations. A1 for 1.30 s (or 1.3 s) with unit.

These marking points are for this original example and are not an official Cambridge mark scheme.

Common errors and how to correct them

• Starting the count at one instead of zero. The count begins at zero when the pendulum passes the reference point, then one after the first complete swing. Starting at one gives n − 1 oscillations, not n.
• Measuring from the wrong point on a ruler. Always measure from the zero mark, not the end of the ruler (which may be worn). Alternatively, measure from a known mark and subtract.
• Not repeating measurements. Take at least three readings and calculate the mean. This reduces the effect of random errors.

How to apply this in an exam

Paper 6 (Alternative to Practical) often asks you to describe how to measure a quantity. State the instrument, the technique (multiple readings, eye level for ruler), and how you process the raw data. Always name a specific instrument rather than writing “measure the length”.