To determine the relationship between the centripetal acceleration and angular frequency.
Set-up:
1. We first place the accelerometer on the disk and make sure that the accelerometer reads 0 in the x and y-directions and -9.8m/s2 in the z-direction.
2. Spin the disk at some speed corresponding to 4.4 Volts, 6.4 Volts, 8.6 Volts, 9.6 Volts, and 12.8 Volts
3. Using Logger Pro to record the acceleration as a function of time and also time the number of rotations with a stopwatch.
4. To make it easy, the apparatus of the experiment includes a photo-gate and a bit of tape sticking out from the edge of the disk to determine how long it takes to make one rotation.
5. Plotting acceleration vs. angular speed and compare the slope to the theoretical value.
Below is the apparatus of the experiment.
Figure 1: The apparatus of the experiment.
Data collecting.
For each time we spin the disk with different electrical power, we record how many rotations, total time to finish those rotations, and the acceleration. Below is an example how we collected the data.
First, we started to spin the disk with 4.4 Volts. We collected the rotations and the total time to finish those rotations.
Figure 2: Rotations and total time for the disk to finish these rotations.
Then we used the Logger Pro to record the value of acceleration as a function of time.
Figure 3: The value of acceleration corresponding to the rotations and total time above.
We continued doing the same process with an increasing amount of electrical power in order of 6.4 Volts, 8.6 Volts, 9.6 Volts, and lastly 12.8 Volts. Figure 4 shows the data we got after recording all the data.
Figure 4: The data we collected for the rotations, total time, and the acceleration.
Data Analysis:
Since we have the data, we need to figure out the value of angular speed which is the product of 2∏ and the number of rotations, then divide by the total time that the disk needs to spin these rotations. Calculation is shown in figure 5:
Figure 5: Calculating the angular speed
After calculating the value of angular speed, we then enter the data into the Logger Pro and plot acceleration vs. angular speed to check the relationship. And below is our results.
Figure 6: The centripetal acceleration vs. angular speed graph.
As we notice from the graph, the centripetal acceleration has a positive relationship with angular speed which is shown as the value of the slope of the graph m = 0.1378.
From the lecture, we know that centripetal acceleration is related to angular speed through an equation:
a = rw2
After doing this experiment, we can verify that the value showing the relationship between centripetal acceleration and angular speed is the radius of the accelerometer. We then measure the radius of the accelerometer and then compare it with the value we got from the graph. The percent error would show us how well we do in predicting the relationship between centripetal and angular speed. The smaller the percent error is, the more accurately we did in determining the relationship.
Measuring the radius of accelerometer:
r = 13.8cm
The slope of the acceleration vs. angular speed graph gives us m = 0.1378 which is the experimental value of radius.
r = 0.1378m = 13.78cm
Calculating the percent error:
Figure 7: The percent error of the radius of the accelerometer.
%error = +0.145%
Conclusion:
Through this experiment, we tried to determine the relationship between centripetal acceleration and angular speed. The result we got after plotting the data is that the centripetal acceleration is positively related to the angular speed through an equation:
a = rw2
We also calculate the percent error to check how well we did in determining the relationship. Our percent error is % error = +0.145% which is very good. It shows that our experimental value is so close to the theoretical value and we did get the correct equation as the one shown in lecture. The percent error is not equal 0 maybe because of the human error in measuring the radius of the accelerometer or rounding number. 
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