The purpose of this lab is to see how angular acceleration is changed when different known masses are pulling on a pulley, as well as how it changes as the diameter of the pulley varied.
Experiment
The set up for this experiment is an air table hooked up to a laptop with Logger pro which will read the angular displacement and velocity of the top disk. Then we hang various masses at the end a sting attached to a torque pulley and record the data, we do the same with a different sized torque pulley as well.
We then take the data collected from each trial and graph them, then from the graph we take use a linear fit to find the slope of the velocity going up and velocity going down. The slope of these lines represents the angular velocity of the hanging mass going up and going down. This was done with all the different trial and different scenarios.
We then took the accelerations and put them into a table along with weight of the masses we used, and the average acceleration calculated. From the table we see the trend that ass the weight of the masses increased so did the angular acceleration, also that as the size of the pulley increased so did that angular acceleration.
We used the acceleration to do two more comparisons for this lab, one in which we compared the angular acceleration to the tangential acceleration and then the theoretical inertia of the disk to the actual inertia of the disks. To compare the angular and tangential acceleration for our last trial we placed a motion sensor under the hanging mass so that logger pro can read it's velocity. We then do the same thing we did for the angular velocity graph for the tangential velocity, we take the slope on the velocity to get the acceleration. The way we compared he to is through the relationship between angular and tangential acceleration (a = αr).
We then take the data collected from each trial and graph them, then from the graph we take use a linear fit to find the slope of the velocity going up and velocity going down. The slope of these lines represents the angular velocity of the hanging mass going up and going down. This was done with all the different trial and different scenarios.
We then took the accelerations and put them into a table along with weight of the masses we used, and the average acceleration calculated. From the table we see the trend that ass the weight of the masses increased so did the angular acceleration, also that as the size of the pulley increased so did that angular acceleration.
We used the acceleration to do two more comparisons for this lab, one in which we compared the angular acceleration to the tangential acceleration and then the theoretical inertia of the disk to the actual inertia of the disks. To compare the angular and tangential acceleration for our last trial we placed a motion sensor under the hanging mass so that logger pro can read it's velocity. We then do the same thing we did for the angular velocity graph for the tangential velocity, we take the slope on the velocity to get the acceleration. The way we compared he to is through the relationship between angular and tangential acceleration (a = αr).
By using the acceleration comparison we can see that they are both really close showing that the difference between the two is indeed by a factor of the radius. There is a slight error in both the accelerations as it rises and descends and that is caused by some friction in between the disks, and that the motion detector had a harder time to read is since the mass was not close enough ad some points.
We then compared the theoretical and actual inertia of the disk based on the acceleration we found, and we did this by manipulating the equations mg-T=ma, Tr=Iα, and a=αr. After we manipulated the equation to get what we wanted to we found the theoretical and actual inertia of the disks. After comparing the two theoretical and actual inertia of the disk we can see that they are very close and that the error is due to the errors in the calipers and scales used to find the radius and mass for each disk.
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