1.1.3 — Determine an average value for a small distance and for a short interval of time by measuring multiples (including the period of oscillation of a pendulum)
When distances or times are very small, measuring once is unreliable. Instead, measure many repetitions.
Examples:
1. Measuring a very small distance
Suppose you want the thickness of one sheet of paper:
- Measure the thickness of 100 sheets.
- Divide by 100.
This reduces error by averaging out tiny uncertainties.
2. Measuring a short time: the period of a pendulum
A pendulum swings too quickly to time one oscillation accurately.
Steps:
- Time 20 oscillations using a stopwatch.
- Divide total time by 20 → period, T.
Real-world example:
Scientists measuring microscopic distances or tiny time intervals always measure multiples — the same principle used by astronomers timing pulsars or engineers measuring vibration frequencies.