Lab 16 Angular Acceleration

Partners: Matthew Ibarra, Billy Justin
Date of Lab: 2 November 2016 

Lab 16 Angular Acceleration

Mission Statement:To determine the angular acceleration and moment of inertia of an object that can rotate when a known torque is applied. 

Theory and Experimental Procedure for Part 1 of Lab 16: In this lab, we set up the following apparatus, shown below:

- As we can see, the apparatus involved several stacked disks (the bottom disk is kept from ricocheting by a drop pin) which would rotate independently when spun due to a cushion of air between them, with the top disk (either steel or aluminum, depending on the trial) floating upon this cushion of air when the blower was activated.

-In order for the top disk to rotate, we installed a hanging mass, shown above, such that the hanging mass would exert a force, translated through the pulley, onto the floating top disk, hence producing a torque, which in turn would rotate the disk. Diagrams of this interaction are shown below.

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-As can be discerned from the diagram immediately above, the entire point of this setup is to determine the various angular accelerations of the top disk. To do this, we utilized a rotational sensor which, when synchronized with LoggerPro, could yield graphs of angular position velocity, and acceleration verses time. Due to systemic deficiencies, we discarded the angular acceleration graph outright and were forced to manually calculate said accelerations. With everything good to go, we activated the air and released the hanging mass so that the mass would move up and down while the top disk would rotate clockwise and counterclockwise. As aforementioned, we were to use the omega verses time graphs obtained via the sensor to obtain the associated alpha values.
-In total, we conducted six different trials, each beginning with different experimental conditions designed to document the effects said conditions would produce. Below is the empty table specifying those conditions.

Below is now our completed table specifying those conditions along with documenting our collected and calculated data.

Conclusions for Part 1 of Lab 16

Now equipped with the necessary information,we were able to draw numerically specific conclusions about the effect on the acceleration of the system by increasing the hanging mass, radius of the torque pulley, and/or the rotating mass, all shown below.

Theory and Experimental Procedure for Part 2 of Lab 16::
Next, we needed to determine the relevant experimental and theoretical moments of inertia. First, we utilized the experimental formula derived for us in the instructions to calculate the experimental moments of inertia, shown below. Also, armed with the knowledge of the standard formula for the moment of inertia of a disk, we found the respective moments for top steel, top + bottom steel, and aluminum plates, shown at the bottom of the page shown below.

As can be seen from the above calculations, the correspondence between our experimental and theoretical values proved to be exact to three significant figures. Hence we verified the validity of the standard formula. Given the accuracy of our results, sources of error were likely negligible save for the hanging mass possibly swaying side to side rather than be kept straight as it rose and fell.