How to calculate the uncertainty in a time measurement using a stopwatch?

To calculate the uncertainty in a time measurement using a stopwatch, you need to consider the stopwatch's resolution and your reaction time.

The resolution of a stopwatch is the smallest time interval it can measure. For example, if the stopwatch has a resolution of 0.01 seconds, the smallest time interval it can measure is 0.01 seconds. This means that any time measurement you make with the stopwatch will have an uncertainty of ±0.01 seconds.

Your reaction time is the time it takes you to react to the start and stop signals on the stopwatch. This can introduce an additional uncertainty in your time measurement. To estimate your reaction time, you can perform a simple experiment where you measure the time it takes you to react to a visual or auditory signal. Once you have an estimate of your reaction time, you can add this to the uncertainty due to the stopwatch's resolution.

For example, if the stopwatch has a resolution of 0.01 seconds and your reaction time is 0.2 seconds, the total uncertainty in your time measurement would be ±0.21 seconds. It's important to note that this uncertainty is only an estimate and may vary depending on the specific experiment and conditions.