Apparatus: Large metal disk on a central shaft, a cart, ramp, and a camera. We must find the Moment of inertia of this apparatus.
What we did: First we took the measurement of all the desired pieces. We got the diameter of the large metal disk which equaled 20.04 cm, the length of the two small rods were 5.15 cm each, and the thickness of the large disk was 1.56 cm wide.Next we set up a camera to obtain a video capture of the disk as it decelerated. We made sure to give the disk a push soft enough for it to spin 2 revolutions. We captured the video and opened it into logger pro. We first set an axis. Then we plotted the points as it revolved around in circles until it came to a complete stop. Finally we scaled the disk and made the diameter of the disk our scale of 20.04 cm.
What we did with this info: This video capture and points gave us a graph and we were able to get the velocities in the x and y direction. This enabled us to get the final velocity which equaled (Vy^2 +Vx^2)^.5. Then we made a linear fit which gave us a slope that turned our to be our acceleration. In this case our deceleration. It was equal to - 2.385 . We were able to find alpha with this since we now had an acceleration and the radius. Alpha=AxR This allowed us to come up with the formulas below to find the moment of inertia. With the calculations below we were also able to predict how long it would take for the cart to travel 1 meter.
Conclusion: Our Pridiction was that it would take 7.83 seconds.
This is a picture of three different times it took for our cart to travel 1 meter. The Average was 7.84 seconds. This gave us an error of less tan .128%.
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