Daniel Guzman
Physics 4A
Angular Acceleration Part #1
The Purpose for the part one of the experiment was to analyze how the different variations affect the angular acceleration of an object (Disk) that is rotating around its central axis while torque is being exerted, and from the analysis of these different variations determine the moment of inertia of the apparatus or body that is rotating.
Theory introduction: The theory behind this experiment is very interesting because, it will allow one to determine the moment of inertia of a body that is rotating by knowing the angular acceleration and the dimensions of it. Due that is quite hard to determine the moment of inertia of an object just by looking at it. Therefore in this experiment we had to make different measurements of different values to be able to determine the moment of inertia of the apparatus, for example, we measured the dimensions of the apparatus, which were the diameter, and mass of the discs that were rotating, due that is important to know the radius at which the object is rotating and the mass of the object, we also measured the angular acceleration of the rotating bodies; this is key in the experiment due that we are affecting the angular accelerations by different variations, to be able to determine what is the moment of inertia of the apparatus by a derived equation in the class, which heavily depends on the average acceleration found by making the variations in the experiment.
Description of the apparatus:
The apparatus on this experiment consisted of two rotating discs which rotate about an axis placed at their center of mass, yet the rotation of this discs is generated by a torque which depends on the tension that the hanging mass provides and the pulley on which the string is wrapped around. This particular apparatus is connected to and air valve to reduce the friction between the discs. the lab pro in this experiment is used to collect important data will the discs are in motion, and the laptop is used to analyze the data collected by the lab pro.
Experimental Procedure: The first thing done in the experiment was to take the different measurements of the apparatus that was going to be used, the measurements taken were the dimensions of the apparatus; therefore the measurements taken were the diameter and mass of the discs in the apparatus, the diameter of the pulleys that were going to be used as well as the masses of the pulleys,the mass of hanging mass was also measured. Once this measurements were taken and recorded we proceeded and connected the lab pro to apparatus and modified it so it would count 200 hundred marks per rotation (the discs on the apparatus have different marks as shown in the picture of the apparatus, important detail in order to obtain the correct result for the moment of inertia). Once this was done the experiment was conducted using different variations, which are going to give a different angular acceleration to the rotating bodies. For every variation we obtained a graph of the angular velocity of the rotating discs, and from this graph we took the slope of the graph, when it was increasing and when it was decreasing, by doing this we obtained the angular acceleration up and the angular acceleration down of the rotating bodies. from these accelerations the average acceleration was determine. After doing the same procedure for the different variations the experimental part for the first experiment is done.
The graphs obtained should look similar to this graph, this is a demonstration graph to show how the graph should look. In this graph is shown where the derivative(linear fit) was taken in order to determine the angular accelerations.
Data Collected
Table of the measured data ( dimensions of the apparatus).
Table of variations with collected data : Data collected after running the experiment with the specified variation.
From the data collected doing the different variations it is clear that when the mass increases the angular acceleration increases as well due that the tension in the string increased, which at the same time increased the the torque, for example for the first trial the average angular acceleration came up to be 1.138, for the second trial 2.374 for the third trial 3.401, which lets one infer that increasing the hanging mass increases the angular acceleration, another pattern found from the data collected is that if the radius of the pulley increases so the angular acceleration due that the torque in in this case depends on the tension in the string and the radius of the pulley the bigger the pulley the bigger the torque, yet when the mass of the rotating discs increase the angular acceleration decreases it can be noticeable in the trial where the aluminum discs was used the angular acceleration is almost as 6 times bigger than when the steel disc was used, which lets one infer that the inertia of the discs depends on a great deal on the material of the disc.
From the data collected and the interpretation of the data we determined the moment of inertia if the apparatus using an equation that was derived in class by the professor.
having these equation and using the data collected the moment of inertia of the apparatus was determined and calculated.
The sources of error in this particular lab were minimum, the measurements of the dimensions of the discs and other pieces of the apparatus were made with electronic calibers, to reduce the error, the other data collected was collected by the lab pro and analyzed using logger pro, which lets one assume that the results are not affected drastically by the error in the experiment and the propagated uncertainty.
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