Lab 8 - March 28, 2015 - Centripetal Acceleration vs. Angular Frequency

Lab 8:
March 28, 2015
Brandon Elder

Centripetal Acceleration vs. Angular Frequency

Fig. 1 Apparatus used to measure centripetal
 acceleration and time of rotations.

Purpose: Using an accelerometer to measure the amount of time and acceleration of a rotating disk in order to determine the relationship between centripetal acceleration and angular speed.

Set-Up: The apparatus was set up in the front of the classroom and the experiment was performed by the instructor. We recorded all the data as a class so we all have the same numbers. This lab was very short and not much to it other than a few calculations. See Fig. 1 below for a picture of the set-up and apparatus.

The wheel was spun around at various speeds and the amount of time that it took to complete 10 different rotations was recorded. The accelerometer reading corresponding to each rotational speed was also recorded. Lastly, the distance of the accelerometer from the center of the rotating disk was calculated.

Calculations: Six different trials were performed at various speeds set by voltages from the source causing the wheel to spin the disk. See Fig. 2 for all of the data saved and used in the calculations.

Fig. 2 All calculations and data taken for this lab. Each highlighted voltage represents a
different trial of data recorded. The t(0) represents the time the photogate on the first rotation
was passed and the t(10) represents the time the tenth pass took place. The difference of the two
represents the amount of time it took for 10 rotations around the axis and is recorded
next to each trial. The "a = acceleration" which is the centripetal acceleration recorded. The 

The formula used in calculating the centripetal acceleration is written at the top of Fig. 2. It is "a=r*omega^2.  Omega is equal to "2*pi radians / time for 1 rotation". The omegas are all calculated and displayed as well above for each speed.  During the lab, acceleration was calculated for us as well as the time for one rotation. We rearranged the formula to solve for the radius. Each calculation was performed and the radius was recorded above as well. The average was taken and determined to be .13685 meters or 13.685 centimeters. We were told by the pro-FESS-OR that the acceptable range was between 13.8 and 14 centimeters.

Lastly, we inputted all our data into a data table in LoggerPro to create a graph of data with acceleration on one axis and the omega value on the other side (see Fig. 3). The data table underneath it (Fig. 4) are the same numbers that were calculated on paper above. The only slight variance is that the best fit line of the graph, which displays the average r value is off by a few thousandths from the calculated r average value.

Fig. 3 Graph of acceleration vs. Omega squared. The average value for the radius is displayed here on the best-fit line.
The value is 0.1372 or 13.72 centimeters. This varies slightly from the value of 13.685 calculated in the notes above.

Fig. 4 Data table with calculated values inputted. The R values are in purple to the right.

Conclusion:

There are a few reasons why the values of R do not add up to what we were told is the acceptable range of R values. Perhaps the tape for the photogate apparatus caused a fluctuation in the acceleration values or the time values. There could have been friction inputted into the system on the wheel causing a force to slow down the wheel more than was expected.