For this lab, our professor had setup a rotating apparatus and conducted the experiment while the groups recorded data. To record the height of the swinging stopper, our professor attached a piece of paper to a ring stand and slowly raised the paper until the top of the paper was barely grazed by the bottom of the stopper. It is also important to mention that there was a meter stick at the top of the rotating apparatus which the rubber stopper was attached to the end. This created a distance from the apparatus that would form an angle with the vertical when swung. We then proceeded to measure the distance of the string to the apparatus, height of the apparatus, and length of the string.
Our group collected six trials with our periods consisting of ten rotations. Our group members individually timed the ten rotations with our cell phones and our periods generally agreed to a hundredth of a second.
From there, we drew a free body diagram of the rubber stopper and divided the forces into their x and y components. From the x and y components we were able to derive a relationship between the angle the string makes with the vertical and its angular speed (shown below).
Using our measured heights, we were able to find the angles of each trial (shown below).
Next we calculated our angular speed using our trial periods (shown below).
Using our equation relating angular speed and the angle, we found values for calculated angular speed (seen below).
Here is a table with all our data for convenience.
Here is the error in our calculated rotational speed compared to our experimental rotational speed.
Where our error most likely comes from in this lab are our measurements taken with the meter stick and our period times taken with our phones.
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