25-Mar-2015 Centripetal Acceleration Demonstration

Purpose
The purpose of this demonstration was to find out what the relationship between centripetal acceleration and angular speed was. This was done with using and accelerometer, photogate, heavy rotating disk, and a modified scooter motor

Experiment
For the demonstration the accelerometer is taped down to the edge of the rotating disk pointing inwards, then a piece of tape is then taped to the accelerometer so that it will pass though the accelerometer once ever rotation. We then used the modified scooter motor to spin the dick at different speeds to determine what the acceleration is and how long it took for the disk to make ten rotations.



This experiment was done at six different speeds which gave us all different accelerations, which was each found by taking the average from the graph that was generated during the experiment. The average was taken by looking at the data and taking the first ten rotations, and we know when each rotation occurred by looking at the data and seeing that a one represents a rotation and a zero is not.





Once we have all the acceleration and times where the first rotation starts and the tenth rotation ends we enter it all into logger a new logger pro file so we can calculate the centripetal acceleration and angular speed. The angular speed was calculated by taking 2π/t (the time was found by taking the (final time - initial time)/ 10), and then in the column next to it we then square the angular speed.



We then graph the centripetal acceleration and angular speed squared against each other which will give us a graph whose slope would be the radius of the disk. It was decided to use angular speed squared because we know that centripetal acceleration is a_c= (V^2)/r and that V= Wr; therefore, when we substitute the V we get a_c = (W^2)r. So if we solve for r we then get    
r = a_c/(W^2) which is the same as the slope in the case.

When we compare our results with the actual radius of the disk we can see that they are very close to each other meaning that this our model for centripetal acceleration and angular speed works.