Walter Lewin uses a ±0.5 cm uncertainty because it is a standard level of precision commonly used in scientific experiments. It is also considered a reasonable level of uncertainty for measurements taken in laboratory settings.
An uncertainty is important because it accounts for the potential error in a measurement and provides a range within which the true value is likely to fall. Without an uncertainty, the accuracy and reliability of the measurement may be called into question.
Uncertainty is determined by considering the limitations of the measuring instrument, the precision of the measurement, and any potential sources of error. It is typically expressed as a range, such as ±0.5 cm, to indicate the level of uncertainty.
In most cases, it is not possible to reduce the uncertainty in a measurement to ±0.1 cm. This would require extremely precise measuring instruments and control over all potential sources of error, which is not always feasible. However, scientists strive to minimize uncertainty as much as possible through careful experimental design and data analysis.
Yes, the uncertainty in a measurement does affect the accuracy of the result. A larger uncertainty means there is a greater range within which the true value may fall, making the result less precise. To improve accuracy, scientists may use more precise measuring instruments or reduce potential sources of error.