Daniel Guzman
Lab#8 (Centripetal acceleration vs angular speed)
Physics 4A.
The purpose of this particular experiment is to determine the relationship that exists between the force that makes an object spin and the angular speed of the object that is rotating.
Summary of the apparatus and experimental procedure.
The apparatus in this particular experiment consisted of a big wooden disc that was placed on top of two scooter wheels, which were connected to a motor that would make the wheels spin in different direction so the big wooden disk could spin with respect to its center. this apparatus also consisted of different weights, a wireless motion sensor, a photo gate and a laptop were all the measurements were being recorded in logger pro.
The experimental procedure for this experiment consisted first, on taping or securing a mass to the rotational disc some distance r in inches from the center of the circle, so we would know what was the radius when the mass was rotating, after the mass was secured on the rotational disc, the professor secured the wireless motion sensor so the computer would record the centripetal force when the disc was rotating; also a piece of paper had to be taped to the disc, so when the disc was rotating a photo gate could count or measure the frequency of the disc and the mass that was put on it. Once this was all set up the entire class proceeded and observed the data, which was being recorded in real time by the force sensor and the photo gate. Once the measurements were collected the professor repeated the same process, but moved the mass that was attached to the disc so it would have a different radius than the last trial.
Multiple trials were done where the same mass was kept but the radii changed, the same mass and same radius but different rotational speeds, the same radius and same rotational speed, but different masses.
The same exactly process was repeated for all the other masses which were 50, 100, 200 and 300 grams. a total of 11 trials were done in this lab.
Data Table
Data collected of the eleven trials
Calculations for the Frequency and Angular Frequency
Calculations and graphs of the data
These calculations were done in the spreadsheets in excel
Data table repeated to show the frequencies calculated based on the data collected.
Graphs of data
For trials 6,7 and 8 we plotted force vs mass , then set a liner trend through the points and force the line to go through zero to obtain a better correlation, the slope that we obtained for this plot is the radius times angular velocity raised to second power. the slope that we obtained was 9.4956, nevertheless the slope obtained in this particular graph does not model the system very well due that the apparatus was not able to sustain a constant angular velocity, which makes the results nor precise.
For trials 1,2 and 3 we plotted force vs radius and forced the trend line through zero to obtain a better correlation the slope of the line is mw^2 , which is 5.092, the value obtained in the graph can be compared to the values in the data table for the specific trial recorded. when force vs radius is plotted the slope that one would obtain is mass times angular velocity raised to the second power. This particular model of the system also fails to give accurate data, due to the same reason as the previous plot, the apparatus used in this experiment was not able to keep the same angular speed therefore the information one obtains in this graph is not precise as one would like; therefore this model fails at providing accurate results or close results to what one would like.
For the third graph, we plotted force vs the angular velocity, the slope of this particular graph is mass times radius, the slope for this graph was the only slope that was constant for all the graphs plotted. This particular slope was constant because the only value changing was the angular velocity, which is a correct model for the system because as explained before the apparatus was not able to keep the same angular speed, so when one compared the slope of this particular graph one would find that it matches perfectly the value that one is expecting, this model is more accurate due that keeping the mass and radius constant for the trials is possible, not like in the other trials were more than one variable was not constant,
Conclusion
For this particular experiment, not all the models attempted were accurate or precise, due that for two of the models two variables were not constant, in the first model the angular speed and the mass varied and in the second model the angular speed and the radius varied, reason why the information obtained in the graphs were not accurate. On the other hand the information obtained in the third graph was very accurate because there was only one variable changing and it was the angular speed, the radius and the mass were held constant reason why the graph provided very accurate results. The sources of error for this experiment basically come from the apparatus used in this experiment because the apparatus could not spin uniformly which brings error to the calculations and models that one is trying to do, nevertheless, when the angular velocity was the only changing variable the results were very accurate and precise.
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