9/23/2014 Relationship of angular velocity and the angle of a conical pendulum

Purpose:
The purpose of this lab is to find a relation between angular velocity of a conical pendulum and the angle which the conical pendulum makes with is string and the ground.

Experiment:
To accomplish this lab we had a very large conical pendulum hooked up to a power source so our rotations where almost uniform. The first data we collected was the measurements of the concial pendulum which included the height, radius of the stick which spun around, the length of the string which held the weight, and later we measure the height on which the weight was above the ground during it rotations. Next we would calculate the period on which the pendulum was moving by timing a couple of rotations and finding the average of this time for one rotation. We repeated the task of increaseing the angular speed and find the the height of the weight from the ground during its rotation and the period of rotation for seven data collections.

Here is a picture of the setup:

Next we had to create a formula that is our predicton for the relationship betwewen the angle between the ground and the string with the angular velcotity. Here is our formula for the model of angular velocity and the the angle between the gournd and the wire. Here is the forumula.

Now with the height on which the weight would hit during its rotations we could use trigonometry to find the angle created with the ground in string. With this data we plugged in a table of possible useful data we would need to prove our relationship is correct shown below is our data table.

Now with this data was much more then we needed, but we decided to show our formula is correct by comparing it the formula of w = 2PI / T. We made a graph of our model for the model w = 2PI / T.

Even though our graph is not that great I think our model is still right and our collection of time is what make our data bad. The slope of this graph should be very close to one which our is and isn't.

Update: I re did the formula which is shown above and I realized our original formula was the one crossed out which is wrong. Which explains why our graph is so bad.