Video ANALYSIS

Video 2: Pendulum 1

GOAL:

Overall: To calculate the inertia of the fidget spinner, so that I can calculate the angular momentum and rotational kinetic energy of the fidget spinner.
Specific: To use this first pendulum to help calculate a relationship between T²MgL/4π² and L²

Set Up:

Using the video of the pendulum, I tracked the center of the fidget spinner as the physical pendulum went through simple harmonic motion.
Then, I used the ruler tool to measure the length from the top of the stick to the fidget spinner.
Afterwards, I used the data collected to determine the time it takes for the pendulum to return back to its position.

video plotting

Using the Video Analysis feature in Logger Pro, I analyzed 56 frames and manually marked the edge of the center of the fidget spinner as the physical pendulum went through simple harmonic motion. Every blue dot is one frame.

Data Collected

At time 6.721 (the time I first release the stick), the X coordinate is 21.62 cm. It begins to travel to the right (positive x), then moves back and travels to the left (negative x).

The pendulum returns back to this position for the first time at around 7.587 seconds, however, at this time, the pendulum hasn't complete an entire cycle yet. (It still has to go a bit more to the left and then back to this position). To calculate the period we need to figure out when it completes an entire run, thus we take the time when it returns to this position FROM the left.

In this case, the time it returns is 7.654 sec, where the x position is exactly 21.62 cm again.

Thus the period can be determined by finding the difference between these two values. (See Equations Section)

Graphical Representation

We can see from this graph that the X coordinate in this pendulum follows an upside down cosine graph, further supporting the fact that this pendulum follow simple harmonic motion.

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