25-Mar-2015: Centripetal Acceleration vs. Angular Frequency

Purpose: To determine the relationship between centripetal acceleration and angular speed using an accelerometer and a photo-gate.

Disk with accelerometer being rotated through photo-gate by scooter tire.

Procedure: A scooter wheel rigged to a motor is used to rotate a disk with an accelerometer mounted flat on top. The accelerometer passes through a photo-gate in order to measure the seconds it takes to make one rotation.  Measurements we made include how long it takes the disk to make some number of rotations at a range of rotational speed, the accelerometer reading corresponding to the rotational speed, and the distance of the accelerometer from the center of the disk. Using six different speeds from six different voltages, we were able to measure the acceleration (a) of the disk between the time (t) of 10 rotations and the time t0(beginning of first rotation) to t10(end of tenth rotation) it took for the disk to make 10 rotations.

Data table for voltage, acceleration, time t0 and t10.

Using a=v^2/r, where v=rω (linear speed relation to angular speed), we get a=rω^2. Solving for r, we should be between 13.8 - 14.0 cm. We then solved for our omega using ω = 2π rad*10/(time for 10 rotations). We used a calculated column in logger pro to quickly solve for omega and omega^2. After recording all our data in the data table, we plotted an acceleration vs. angular speed^2 graph.

Data table and graph of a over ω^2.

Results: The slope of the graph gives us the radius, which came out to 0.1371 m or 13.71 cm. Not exactly within our measured range but still pretty accurate.

Conclusion/Uncertainty: As the theory predicted, we were able to show that centripetal acceleration and angular speed are directly affected by the radius of the disk or object rotating. During the course of this experiment, there were a few uncertainties that we became aware of. First there could be many points of friction that can alter the speed of the disk, and secondly the accelerometer's distance from the center is not perfect, which is why we had a range from 13.8 to 14 cm. The readings from the devices should be fairly accurate.