Centripetal Acceleration vs. Angular Frequency

The focus of this lab was to determine a relationship between centripetal acceleration and angular speed from measurements.

Our professor set up and collected data for the class in a demonstration using a Heavy Rotating Disk, accelerometer, a photo gate, and an electric motor off of a scooter.  He attached a small piece of tape to the edge of the disk that would pass through the photo gate to count the number of times it passed through that point in a period of time.  He then used the scooter motor to rotate the disk at a certain number of volts and used Logger Pro to record data.

Our professor ran five trials and collected the acceleration and times for a number of rotations that  could be used to find the angular speed of the disk.  For example, in the first trial our professor set the voltage to 4.4v.  He used the photo gate to count the number of times the tape passed through it in a time period and Logger Pro to get the acceleration.

With this information, we are able to first get the period for the trial by dividing a set of time by the number of full rotations that happened in the time set.  After that, we can find the angular speed by dividing 2pi by the period for the trial.  Lastly, we are able to see the relationship between acceleration and the angular speed by the equation a=rw^2 which would be the radius of the point we are using to take data.  Our professor had previously measured the radius to be 13.8cm.  Below is a table with the trials and their data.

Here is an example of my calculations.















According to the equation, acceleration and the angular speed squared are related by the radius of the circle.  Taking my data and plotting it in a graph, we can see this to be true as the radius acts like the slope of a line equation.

Here we can see the slope of the equation to be 0.1388m or 13.88cm.

For this lab, the error would come out of the measuring of the radius using a ruler.  Everything else was measured by the accelerometer and photo gate.