Lab #16: Angular Acceleration
Dahlia - Carlos
Dahlia - Carlos
02-Nov-2016
The purpose of the lab#14 is to to explore how angular acceleration changes when we use different hanging masses, rotating disks and combinations with different masses, and torque pulleys with different radii.
A. Part 1:
I. Set up:
The pictures below are showing how we set up the kit when doing this experiment.
From the side:
From the top:
There were a bottom steel disk, a top steel disk or top aluminum disk. they stayed next to the Pasco rotation sensor.
At the top of disks, there was a small pulley or large puller which was connected with a hanging mass.
For this experiment we used an apparatus that provides a constant air pressure that kept the disks and hanging mass pulley "floating/hovering" so that we had friction-less for this experiment.
The Pasco rotation sensor was connected with LabPro, so we could read value of angular position, angular velocity, and angular acceleration based on time.
II. Collect data:
1. Data of angular acceleration:
First, we turned on the constant air pressure and let the hanging mass started moving from the top of the string. And the disks also began rotating.
Next, we recording the movement. and this is what we had:
The first graph shows the relationship between angular position vs. time. And the second graph shows the relationship between angular velocity vs. time.
Because the purpose of this lab is to find the effects on acceleration of hanging mass, radius of pulley, and mass of rotating object, we paid attention to the graph angular velocity vs. time. (To find the angular acceleration, we just needed to find the slopes of the graph angular velocity vs. time)
Then, we had:
We did 6 trials of them, and this is what we had:
We used the caliber to measure diameters of top steel disk, bottom steel disk, top aluminium disk, small pulley and the large pulley. And we used a digital scale to measure the mass of top steel disk, bottom steel disk, top aluminium disk, small pulley, the large pulley, and the hanging mass supplied with the apparatus.
This is what we had:
From the trial #1, #2, and #3, We can conclude the effect of changing hanging mass.
Trial #1, hanging mass was 0.025 g, and the angular acceleration was 1.171 rad/s^2 (~1).
Trial #2, hanging mass was 0.050 g, and the angular acceleration was 2.298 rad/s^2 (~2).
Trial #3, hanging mass was 0.075 g, and the angular acceleration was 3.4245 rad/s^2(~3).
=> The angular acceleration was proportional with the hanging mass
From the trial #1 and #4, We can conclude the effect of changing the radius and which the hanging mass exerted a torque.
Trial #1, diameter of torque pulley was 0.0249 g, and the angular acceleration was 1.171 rad/s^2 (~1).
Trial #4, diameter of torque pulley was 0.0498 g, and the angular acceleration was 2.2235 rad/s^2 (~2).
=> The angular acceleration was proportional with the diameter of torque pulley.
Trial #4, rotation mass was 1356 g (~3*450), and the angular acceleration was 2.2235 rad/s^2 (~2).
Trial #5, rotation mass was 467 g (~1*450), and the angular acceleration was 6.2845 rad/s^2 (~6).
Trial #6, rotation mass was 1356+1348=2704 g (~6*450), and the angular acceleration was 1.124 rad/s^2 (~1).
By various changing in the hanging mass, radius of pulley, and rotation mass, we can conclude that the angular acceleration was proportional with the hanging mass, the radius of torque pulley, but the angular acceleration was inverse proportional with the rotation mass.
A. Part 1:
I. Set up:
The pictures below are showing how we set up the kit when doing this experiment.
From the side:
There were a bottom steel disk, a top steel disk or top aluminum disk. they stayed next to the Pasco rotation sensor.
At the top of disks, there was a small pulley or large puller which was connected with a hanging mass.
For this experiment we used an apparatus that provides a constant air pressure that kept the disks and hanging mass pulley "floating/hovering" so that we had friction-less for this experiment.
The Pasco rotation sensor was connected with LabPro, so we could read value of angular position, angular velocity, and angular acceleration based on time.
II. Collect data:
1. Data of angular acceleration:
First, we turned on the constant air pressure and let the hanging mass started moving from the top of the string. And the disks also began rotating.
Next, we recording the movement. and this is what we had:
Because the purpose of this lab is to find the effects on acceleration of hanging mass, radius of pulley, and mass of rotating object, we paid attention to the graph angular velocity vs. time. (To find the angular acceleration, we just needed to find the slopes of the graph angular velocity vs. time)
Then, we had:
We used the caliber to measure diameters of top steel disk, bottom steel disk, top aluminium disk, small pulley and the large pulley. And we used a digital scale to measure the mass of top steel disk, bottom steel disk, top aluminium disk, small pulley, the large pulley, and the hanging mass supplied with the apparatus.
This is what we had:
From the trial #1, #2, and #3, We can conclude the effect of changing hanging mass.
Trial #1, hanging mass was 0.025 g, and the angular acceleration was 1.171 rad/s^2 (~1).
Trial #2, hanging mass was 0.050 g, and the angular acceleration was 2.298 rad/s^2 (~2).
Trial #3, hanging mass was 0.075 g, and the angular acceleration was 3.4245 rad/s^2(~3).
=> The angular acceleration was proportional with the hanging mass
From the trial #1 and #4, We can conclude the effect of changing the radius and which the hanging mass exerted a torque.
Trial #1, diameter of torque pulley was 0.0249 g, and the angular acceleration was 1.171 rad/s^2 (~1).
Trial #4, diameter of torque pulley was 0.0498 g, and the angular acceleration was 2.2235 rad/s^2 (~2).
=> The angular acceleration was proportional with the diameter of torque pulley.
Trial #4, rotation mass was 1356 g (~3*450), and the angular acceleration was 2.2235 rad/s^2 (~2).
Trial #5, rotation mass was 467 g (~1*450), and the angular acceleration was 6.2845 rad/s^2 (~6).
Trial #6, rotation mass was 1356+1348=2704 g (~6*450), and the angular acceleration was 1.124 rad/s^2 (~1).
By various changing in the hanging mass, radius of pulley, and rotation mass, we can conclude that the angular acceleration was proportional with the hanging mass, the radius of torque pulley, but the angular acceleration was inverse proportional with the rotation mass.
B. Part 2:
We can use our data collected and measurements to calculate moment of inertia for the system. We used Newton's second law to find the tension, T, in the hanging mass. We also used the equation for torque and plugged in tension to this equation (also changing linear acceleration to angular acceleration):
This equation was the way to calculate the inertia based on the angular acceleration we got from part 1. So, I entered data of part 1 into a sheet of excel, and then I calculated the experimental inertia. Moreover, because the disks were solid and rotated around center, so the theoretical inertia was 1/2MR^2. I calculated the theoretical inertial in the same excel sheet as well.
To be more clear, I listed 2 ways to calculate the inertia:
Then, I calculated the percent error of them
Conclusion: The result came out was pretty good. the highest percent error was -3.35% and the lowest was 0.85%. The error occurred because of several reasons: first, because we assumed that the torque of friction was the same in all directions and independent of angular velocity, but in reality, it was not.Second, we assumed the disks were solid and apply I=1/2MR^2, but actually, it had a little hole at the center. And finally, when we recorded the angular acceleration from log pro, there were many up-down graph of it, so there was an uncertainty when taking value of angular acceleration. However, other than that, the result was really good and now, we can realize the amazing of physic to the real life.
We can use our data collected and measurements to calculate moment of inertia for the system. We used Newton's second law to find the tension, T, in the hanging mass. We also used the equation for torque and plugged in tension to this equation (also changing linear acceleration to angular acceleration):
Then we had:
This equation was the way to calculate the inertia based on the angular acceleration we got from part 1. So, I entered data of part 1 into a sheet of excel, and then I calculated the experimental inertia. Moreover, because the disks were solid and rotated around center, so the theoretical inertia was 1/2MR^2. I calculated the theoretical inertial in the same excel sheet as well.
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