Investigating gravitational acceleration via a pendulum experiment: A student-centered approach to measurement uncertainty

To improve the understanding of uncertainty analysis and method comparison by first-year physics students, gravitational acceleration was investigated via a simple pendulum experiment using a hands-on, student-centered approach. By measuring the periods of pendulums of different lengths, the students calculated gravitational acceleration with an error of 1.29–4.27%, factoring in measurement uncertainties from equipment limitations and human reaction time. The study emphasized the importance of increasing measurement repetitions to reduce reaction-time errors and improve accuracy. Manual stopwatch measurements resulted in a gravitational acceleration of 9.65 m/s² (error: 1.39%; s.d.: 0.01 m/s²), while an electronic photogate recorded 9.50 m/s² (error: 2.90%; s.d.: 0.001 m/s²). Despite the photogate’s higher error percentage, its lower s.d. highlights its ability to minimize systematic errors and provide more-consistent measurements across trials. While the stopwatch yielded higher variability due to human reaction time, the photogate demonstrated superior precision in reducing measurement inconsistencies. Although the students had not yet mastered complex uncertainty models, the experiment developed foundational skills essential for future experimental physics. These findings underscore the value of precise measurement techniques and technology in fostering scientific understanding.