Lab 18: Moment of Inertia and Frictional Torque
May Soe Moe
Lab Partners: Ben Chen, Steven Castro, Stephanie Flores
Dates: 17-May-2017, 22-May-2017
Objective: To determine the moment of the inertia of the system, to determine the angular deceleration, to determine the frictional torque, and to determine the time it takes to descend for a cart to get to one meter mark of the ramp
Introduction:
Our apparatus consists of a disk and two cylinders, which are all attached together. We will consider the system to be consisted of three cylinders. The moment of inertia of the system is the sum of the moment of inertia of three cylinders. Since we do not know the mass of the two cylinders from the sides, we will calculate the volume of the cylinders after measuring their radius and height, and the total mass of the whole system. After calculating the volume of the system and each of the cylinders, we will calculate the mass of each cylinder. Once we ind out the mass of the cylinders, we will find out the moment of inertia of each cylinder by using I=1/2MR^2. For part 2 of the lab, to figure out the angular deceleration, we will take a slow-motion video of the system rotating. We will use logger pro and to dot around the rim of the disk rotating, which will give us the angular velocity vs. time graph. We will find the angular deceleration by finding the slope of the angular velocity vs. time graph. Then we can find torque by using T=Iα. For part 3 of the lab, we will wrap a string around the middle disk and connect it with a 500-gram dynamics cart. Using the Newton's Second law to get a representative expression for acceleration of the cart. After that we will use the kinematics equation to figure out the time it takes to reach 1 meter mark of the ramp.
Experimental Procedure:
Part 1:
(1) Our apparatus looks as below:
(2) We took measurements of the diameters of the cylinders, the height of the cylinders. The total mass of the cylinders are stamped onto the big rotating disk.
Part 1 Data and Calculations:
Experimental Procedure:
Part 2:
(1) We put the ring stand in front of the apparatus and set up an iPhone to the ring stand.
(2) We align the iPhone's camera to the center of the system.
(3) We took slow-motion video of the disk rotating around its center. We made sure it was 240 frames per second.
(4) We opened our slow-motion video in Logger Pro and dot around the rim of the disk. The dots around the rim would produce the angular velocity vs. time graph.
(5) We used linear fit to find the angular deceleration, which is the slope of the angular velocity vs. time graph.
Part 2 Data:
When we did the dots around the rim of the disk, each dot was 30 frames per second, which is 8 times faster than the actual time, since we shot the video at 240 frames per second. Therefore, in the picture and graph above, our x-axis is actual time, and we divided the time we got for 30 frames per second by 8. Our angular deceleration for the disk came out to be -0.4395 rad/s^2, according to the graph.
Now we can calculate the frictional torque.
Part 2 Calculation:
The result from calculating frictional torque using the calculated moment of inertia from part 1 and the angular acceleration from part 2 came out to be -9.348x10^-3 kgm^2/s^2.
Experimental Procedure:
Part 3:
(1) We did the set up as below:
(2) After the set up, we measured the horizontal angle using the level from iPhone, which came out to be at 50 degree.
(3) After that we wrapped a string around the large disk, connecting to the cart.
(4) We started the rotation, and timed the time it took for a cart to reach 1 meter mark.
(5) We did this process three times. Our average time for the cart to reach 1 meter mark was 6.76 seconds.
Part 3 Calculation:
The calculated time based on our previous calculated results such as the frictional torque and moment of inertia of the system, came out to be 6.16 seconds, while the average timed time of the cart to reach 1 meter mark was 6.76 seconds. There is a 0.6 seconds difference. Therefore, I calculated the percentage error for our result.
The percent error for the time difference was 9.74%.
Conclusion:
For part 3 of the lab, where we compare the experimental time--the average time we got by using the timer for the cart to reach one meter mark-- and the theoretical time--the time we calculated by using the previous calculations from part 1 and 2 of the lab, which are the moment of inertia of a system and the frictional torque, we found that there was 0.6 seconds difference between the two. I calculated the percent error and it was 9.74%, which is less than 10% and we could say this is within acceptable range. Errors could be because the ramp moved every time the cart reached to the bottom, near 1 meter mark. Although we used several masses at the end of the ramp to make sure it stays still, it didn't work and we might not have readjust the angle to 50 degree as in the beginning after each trial. There could be some friction on the ramp that we did not consider in this lab and in our calculations. The measurement of the angle was done with the phone app, which might have some uncertainties in its measurements. Overall, the lab was successful that the error was within 9.74%.
May Soe Moe
Lab Partners: Ben Chen, Steven Castro, Stephanie Flores
Dates: 17-May-2017, 22-May-2017
Objective: To determine the moment of the inertia of the system, to determine the angular deceleration, to determine the frictional torque, and to determine the time it takes to descend for a cart to get to one meter mark of the ramp
Introduction:
Our apparatus consists of a disk and two cylinders, which are all attached together. We will consider the system to be consisted of three cylinders. The moment of inertia of the system is the sum of the moment of inertia of three cylinders. Since we do not know the mass of the two cylinders from the sides, we will calculate the volume of the cylinders after measuring their radius and height, and the total mass of the whole system. After calculating the volume of the system and each of the cylinders, we will calculate the mass of each cylinder. Once we ind out the mass of the cylinders, we will find out the moment of inertia of each cylinder by using I=1/2MR^2. For part 2 of the lab, to figure out the angular deceleration, we will take a slow-motion video of the system rotating. We will use logger pro and to dot around the rim of the disk rotating, which will give us the angular velocity vs. time graph. We will find the angular deceleration by finding the slope of the angular velocity vs. time graph. Then we can find torque by using T=Iα. For part 3 of the lab, we will wrap a string around the middle disk and connect it with a 500-gram dynamics cart. Using the Newton's Second law to get a representative expression for acceleration of the cart. After that we will use the kinematics equation to figure out the time it takes to reach 1 meter mark of the ramp.
Experimental Procedure:
Part 1:
(1) Our apparatus looks as below:
 |
| Front view of the apparatus |
 |
| The apparatus consists of one big disk, and two cylinders on the sides as in the picture. |
(2) We took measurements of the diameters of the cylinders, the height of the cylinders. The total mass of the cylinders are stamped onto the big rotating disk.
Part 1 Data and Calculations:
 |
| Measured data of the system |
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| Volume Calculation of the three cylinders to figure out the mass of each cylinders |
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| Calculation of Mass of each Cylinder to find the moment of inertia of the system |
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| Calculation of the Moment of Inertia of the System Consisting two cylinders and a disk |
Part 2:
(1) We put the ring stand in front of the apparatus and set up an iPhone to the ring stand.
(2) We align the iPhone's camera to the center of the system.
(3) We took slow-motion video of the disk rotating around its center. We made sure it was 240 frames per second.
(4) We opened our slow-motion video in Logger Pro and dot around the rim of the disk. The dots around the rim would produce the angular velocity vs. time graph.
(5) We used linear fit to find the angular deceleration, which is the slope of the angular velocity vs. time graph.
Part 2 Data:
 |
| The dots around the rim of the disk and how the dots produce graph |
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| The angular acceleration of the rotating disk around its center, which is -0.4395 rad/s^2-- slope of the graph. |
Now we can calculate the frictional torque.
Part 2 Calculation:
 |
| Frictional Torque Calculation using the Angular Deceleration we got from the graph |
Experimental Procedure:
Part 3:
(1) We did the set up as below:
 |
| Our apparatus set up for part 3of this lab |
 |
| The ramp is 50 Degree above horizontal |
(3) After that we wrapped a string around the large disk, connecting to the cart.
(4) We started the rotation, and timed the time it took for a cart to reach 1 meter mark.
(5) We did this process three times. Our average time for the cart to reach 1 meter mark was 6.76 seconds.
Part 3 Calculation:
 |
| Calculation for time it took for the cart to reach 1 meter mark |
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| Percentage error for the difference between experimental time and theoretical time |
Conclusion:
For part 3 of the lab, where we compare the experimental time--the average time we got by using the timer for the cart to reach one meter mark-- and the theoretical time--the time we calculated by using the previous calculations from part 1 and 2 of the lab, which are the moment of inertia of a system and the frictional torque, we found that there was 0.6 seconds difference between the two. I calculated the percent error and it was 9.74%, which is less than 10% and we could say this is within acceptable range. Errors could be because the ramp moved every time the cart reached to the bottom, near 1 meter mark. Although we used several masses at the end of the ramp to make sure it stays still, it didn't work and we might not have readjust the angle to 50 degree as in the beginning after each trial. There could be some friction on the ramp that we did not consider in this lab and in our calculations. The measurement of the angle was done with the phone app, which might have some uncertainties in its measurements. Overall, the lab was successful that the error was within 9.74%.
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