Measuring g with a pendulum · Charlie
The problem says to use simple pendulum (point mass as the bob), so 𝐼 = 𝑚 𝐿 2 I=mL 2 . Substituting, we get Now solve for 𝑔 g: So all we need to do is measure the string’s length 𝐿 L and the period 𝑇 T. Simple, right? The only materials we need are a string, a pendulum bob, and a stopwatch. I didn’t have any ideal object with simple moment of inertia, so I thought I’d first try to just use a longer string and let the 𝑑 d in 𝐼 = 𝐼 𝑐 𝑚 + 𝑚 𝑑 2 I=I cm +md 2 dominate. And for the bob, I needed the densest thing around to remove the effect of string’s mass: my character this lotion bottle. I took 5 trials of 10 periods each (let nature do the summing to reduce uncertainty). I only had the edge of protractor as my ruler, and the bob was already tied up, so it was a real pain to measure 𝐿 L. It came out, after 3 back-to-back measurements, to be ~14 inches or 35.6 cm. Substituting into the equation, we get.. *drumroll* What?? What could be wrong? Time for round two. T