01-Apr-2015: Centripetal Force With a Motor

Purpose: Using our knowledge of centripetal force, we had to come up with a relationship between theta and omega.

Lab Apparatus

Procedure: The lab apparatus consisted of an electric motor mounted to a surveying tripod, connected to a vertical rod which spun a horizontal rod around the tripod. Tied at the end of the horizontal rod was a string with a rubber stopper attached to the opposite end so that as the angular speed (omega) increased, the radius from the rubber stopper to the center of the tripod and angle theta also increased. A ring stand with a horizontal piece of paper sticking out was placed just outside the radius of the stopper and the tripod in order to measure the height (h) of the stopper from the ground.

Measurements of height (H), radius (R) and length (L) from lab apparatus. 

In order to find a relationship between theta and omega, we first had to make a few measurements, including total height (H), radius of horizontal rod (R), and length of string (L). Using Newtons second law, we were able to derive an equation for omega that we used later. We then found the height of the stopper from the ground using 6 different angular speeds and found the angle theta by looking at the right triangle with height (H-h), and hypotenuse L.

Newton's second law to derive equation for omega, right triangle to solve for theta

Measurements of heigh (h) from 6 runs, each at different sec/10 rev.

Next, we went onto logger pro in order to create a data chart and use a calculated column in order to easily find omega for each respected run. We were able to find omega using the derived equation of omega = sqrt( g*tan(theta)/ r) and test the model by measuring omega using 2pi*10/t(10 rev).

data set of modeled omega

Using the data of modeled omega and measured omega, we were able to create a graph in order to see just how similar the two results were. If our model is correct, then the measured and modeled omega graph should have a slope of about 1.

Measured over modeled omega graph with slope.

Results: Our results show that the linear fit slope of the measured vs. modeled graph was 0.9892, pretty close to 1 which is what we were looking for.

Conclusion/Uncertainty: The results showed us that the model for omega was very consistent with what we got through our measurements from the lab. It proves that the model is an excellent way of solving for angular velocity. We were able to derive a equation for omega that fits the model and figured out that as the angular velocity of the system increases, so does the radius from the mass to the center. The few uncertainties in the lab include the period T having an uncertainty of +/- .01 seconds and h having an uncertainty of +/- .5 cm. Having six runs is better than just plotting a couple runs, but maybe having a few more runs would have put the slope of the measured and modeled omega closer to 1. Human error in our stopwatch measurements and the paper technique to measure height (h) also could have affected our final results.