25-Mar-2015: Centripetal acceleration vs angular speed

PURPOSE

The purpose of this experiment was to extend our theoretical knowledge of the relationship between centripetal acceleration and angular speed to a real-life experiment.

PROCEDURES

Figure 1: Set-up consisting of a disk, accelerometer, photogate, and power supply

This experiment was conducted by the professor as a demonstration to the entire class. The set-up shown in Figure 1 consisted of an accelerometer (circled in blue) confined to a rotating disk that was powered by a voltage supply (circled in purple). A piece of tape (circled in green) was protruding out of the disk to enable the photogate (circled in red) record the time of the disk's rotations. The professor varied the power supply six times, increasing it each time. We took note of the time it took the disk to rotate ten times for each voltage. In addition, the accelerometer measured the centripetal acceleration of the disk during each trial.

Figure 2: Data table

The data we gathered from the experiment is displayed in Columns 2, 3, and 7, of the data table shown in Figure 2. We found the time it took for the disk to rotate once by subtracting the second column from the the third column and dividing the resulting value by ten. Then, we found the angular speed by dividing 2π by the value we found in the previous step. Finally, we squared the angular speed and recorded the values in Column 6.

Figure 3: Centripetal acceleration vs angular speed squared

After recording our data, we graphed centripetal acceleration with respect to the square of angular speed (Figure 3). Since centripetal acceleration equals the radius times the square of the angular speed (refer to the formula below), we concluded that the slope of this graph must equal the distance between the center of the disk and the location of the accelerometer. We measured this distance to be somewhere between 13.8 cm to 14.0 cm. Since the slope of the graph is in terms of meters, it can be seen that the experimental value was very close to the expected value.

ac = ω²r

=> r = ac/ω²

CONCLUSION

In this experiment, we implemented our knowledge on centripetal acceleration and angular speed. The experiment was successful since the experimental value was very close to the expected value. In fact, the percent error was only 1.4 percent (assuming the measured radius to be 13.9 cm). Since the percent error is well below 5 percent, we can conclude that we executed the lab correctly.

There may have been a few sources of error since the experimental value was not a hundred percent accurate. First, the distance between the center of the disk and the accelerometer may have been measured incorrectly. Since we used a ruler to measured the distance, we were limited in our ability to be accurate. Another possible source of error was the measurements taken by the photogate. There is no guarantee that the measurements made by the photogate was a hundred percent accurate.