PURPOSE: To determine the relationship between centripetal acceleration and angular speed.
MATERIALS:
As a class, we did an experiment in which we placed an accelerometer on a heavy rotating disk, making sure it was flat with the axis pointing toward the center. We also set up a motion detector, counting the number of rotations the accelerometer made at a corresponding time.
The accelerometer measured centripetal acceleration, and the motion detector measured every time the rotating disk made one full rotation. We took the measurement of centripetal acceleration, the time at one rotation (t0), and the time at 10 rotations (t10) for 6 different trials using 6 voltage powers to make the disk spin faster each time.
MATERIALS:
- Accelerometer
- Heavy rotating disk
- Motion detector
As a class, we did an experiment in which we placed an accelerometer on a heavy rotating disk, making sure it was flat with the axis pointing toward the center. We also set up a motion detector, counting the number of rotations the accelerometer made at a corresponding time.
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| (Fig. 1) Set up to measure centripetal acceleration. |
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| (Fig 2) Data collected from 6 trials. |
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| (Fig 3) Graphs of acceleration collected from 5 out of the 6 trials. |
We plotted the data in excel for each trial. We found the time for 1 rotation (column E) by subtracting the time at 1 rotation from the time at 10 rotations and dividing by 10. We then found angular speed using the formula ω = 2π rad / time for one rotation. In the last column we squared
angular speed.
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| (Fig. 4) |
The equation for centripetal acceleration is acentripetal = rω^2, or r = acentripetal / ω^2. This equation can be shown by the graph of acceleration vs. angular speed^2, as shown in the graph of (Fig. 4). The slope of this line should be equal to the radius of the rotating disk. We were told the radius of the disk was between 13.8 and 14.0 cm, and the slope gives us a value of 0.1371. This value is in meters, so if we convert that to cm it becomes 13.71, This is really close to the value of the radius.
CONCLUSION:
This lab proved that we were able to come up with a relationship between centripetal acceleration and angular speed. By knowing centripetal acceleration and calculating angular speed based on number of rotations in a given time, we found the relationship and was able to verify with the known dimensions of the radius of the disk.
Uncertainty in this lab could have come from errors in the tools. The tools used to measure acceleration or rotation could have lagged. In addition, we used masking tape to mark a rotation, and it may have moved a little while it was spinning. If we look at the graph of acceleration vs. time, we can see that the acceleration fluctuates differently for each trial.
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