Finding a relationship between theta and omega

Ana Leyva, Jonathan, Andrew
4/5/17
lab #9

For this experiment we are trying to find a relationship between theta and omega. We will try to accomplish this by using the free body diagram of our hanging mass and a few calculated values.

In order to find a relationship between theta and omega we first had to come up with a freebody diagram whose equations would allow us to find a relationship between theta and omega. We then had to come up with other equations that would allow us to calculate theta. However, before being able to calculate theta we have to find the measurements of a few object in order to be able to calculate theta.

Our apparatus was an electric motor that was attached to a tripod. We had this motor spin at different rates in order to find different values of omega and theta.

To start this experiment we measured the height (H) of the apparatus, the length of the horizontal bar(R), and the length of the string(L). Then by creating a right triangle with L being the hypotenuse and the H-h being the adjacent side of theta. We then let theta = arccos ((H-h)/L). After this, we created a freebody diagram of the hanging mass in order to try to find a relationship between theta and omega. Then by manipulation the equations we were able to get an equation for omega where the radius(r)= R+Lsin(theta). Finally, in order to test this out we started measuring how long it would take the apparatus to make a certain number of rotations and what the height of the mass was during those rotations. We then calculated omega using that data, and then we calculated it again using the equation that we had came up with.  

Observed data

Calculated data

After plotting a graph of my observed values of omega and calculated values of omega I observed that there was a correlation of 0.9553. Although this is not that great a correlation if it pretty good considering that all of our observed values aren't as accurate as we would want them to be. However, we can still conclude that the equation for omega that we came up with does an adequate job of giving you a value for omega.