Physical quantities & measurement

Measuring time intervals

Measuring time intervals Core 3 min read

Units of time

Time is a fundamental physical quantity. Its SI unit is the second (s).

Unit	Symbol	Conversion
millisecond	ms	1 ms = 0.001 s
second	s	base unit
minute	min	1 min = 60 s
hour	h	1 h = 3600 s

Instruments for measuring time

Different instruments are chosen based on the duration and precision required.

Instrument	Typical precision	Best for
Stopwatch (analogue)	±0.1 s (reaction time dominates)	Durations of seconds to minutes
Stopwatch (digital)	±0.01 s	Durations of seconds to minutes
Light gate + datalogger	±0.001 s or better	Very short intervals (e.g. a card passing through a sensor)
Ticker timer	±0.02 s (50 Hz tape)	Recording motion on a tape

When describing a timing method in an exam, always state (1) the instrument, (2) when you start it, and (3) when you stop it. Each step earns a mark.

Human reaction time and how to reduce error

The main source of error when using a stopwatch is reaction time — the delay between the event occurring and the experimenter pressing the button. Typical human reaction time is 0.1–0.4 s.

Reaction time cannot be eliminated, but it can be reduced:

Use a digital stopwatch rather than a mechanical one (reduces reading error).
Measure many oscillations and divide (see the next subtopic on multiples).
Use electronic timing (light gates) where possible — no human reaction involved.

The period of an oscillation

The period \( T \) of an oscillation is the time for one complete oscillation. Unit: seconds (s).

A simple pendulum is a small mass (the bob) suspended from a fixed point by a light, inextensible string. When displaced and released, it swings back and forth.

A → B → C → B → A = one complete oscillation B = equilibrium (centre)

How to measure the period of a pendulum

Set the pendulum swinging with a small amplitude (<10° from the vertical).
Start the stopwatch as the bob passes through the equilibrium position (centre).
Count 20 complete oscillations (bob returns to the same position moving in the same direction).
Stop the stopwatch after 20 oscillations. Record the total time \( t \).
Calculate the period: \( T = \dfrac{t}{20} \)

A common mistake is starting the timer at the end of the swing (at maximum displacement). It is better to start at the centre because the bob is moving fastest there, making the moment easier to judge precisely.

Worked example — calculating period and frequency

A student counts 20 complete oscillations of a pendulum in 34.0 s. Calculate (a) the period and (b) the frequency of the pendulum.

(a) \( T = \dfrac{t}{n} = \dfrac{34.0}{20} = 1.70 \text{ s} \)

(b) Frequency \( f = \dfrac{1}{T} = \dfrac{1}{1.70} \approx 0.588 \text{ Hz} \)

Note: frequency (Hz) is not on the syllabus for this section, but may appear in Section 3 (Waves).

A "Describe how you would measure the period" question typically awards marks for: (1) using a stopwatch, (2) timing a large number of oscillations (20 or more), (3) dividing by the number of oscillations. Write these three steps explicitly.