Lab Partners: Kevin Nguyen, Jose Rodriguez
May 26, 2017
Moment of Inertia and Frictional Torque
Below is the side view of the apparatus.
Purpose: To determine the moment of inertia of a spinning object and the frictional torque in the system and then test the friction torque by comparing the time it takes to descend a cart with the experimental value and theoretical value.
Introduction: In this experiment, we used the rotating part of the apparatus to determine its moment of inertia. We performed two parts for this experiment.
Below is the apparatus that we used to performed this lab. In the picture below, there are 3 rotating parts in the system: 2 small pulleys and 1 large pulley
Small pulley( cylindrical shape ):
-Diameter: 0.031 meters
-Height: 0.05 meters
Large pulley( cylindrical shape ):
-Diameter: 0.1997 meters
-Thickness: 0.016 meters
The mass of the whole system is 4.802 kg. The number in the picture below gives us the total mass of the system.
The mass of the whole system is 4.802 kg. The number in the picture below gives us the total mass of the system.
Below is the side view of the apparatus.
Note:
We can't exactly assume the entire system as one mass. So, we have to break it into 3 parts. We find the inertia of the individual pulleys and summed up the inertias in order to find the total inertia of the system.
First, I like to note that below are the volumes of the 3 pulleys.
V1/V3: the two cylinders on both sides
V2: The cylinder in between 1 and 3.
In order to find the individual inertias of each of the cylinders, we have to find the mass of each of them. Below is the formula to calculate for an individual mass. Our "M total" is 4.802 kg.
Below are the calculated results for the masses.
m1/m3: the cylinders on both sides.
m2: the cylinder in between 1 and 3.
Now with the masses, we were able to find the total inertia of the system.
Our next step is to find the frictional torque of the system. So, we spun the wheel to calculate the angular acceleration as it's slowing down within the 10 second time range. We jotted down points on the video to allow us to find the positions at multiple time frames, which will eventually give us a chart of a omega/time chart. As a result, we have an angular acceleration of -0.105 rad/s^2
Since we know that Torque= (Total inertia) x (Angular acceleration), we were able to find the frictional torque of the system.
Friction torque= (0.02 kgm^2) x (-0.105 rad/s^2)
Friction torque= -0.0021 N*m
Our second part of the lab was to attach a 547 gram dynamic cart to the apparatus. The cart will be rolling down an inclined track for a distance of 1 meter. The inclined track was angled at approximately 49 degrees.
My lab partners and I timed the cart as it rolls down 1 meter. We performed a total of three trials. As a result, we got:
Trial 1: 6.67 seconds
Trial 2: 6.58 seconds
Trial 3: 6.6 seconds
On average, the time was 6.62 seconds.
Below is the calculated work to compare the results of both the calculated time and the stopwatch time.
As a result, our calculated results was 6.74 seconds.
In comparison to the 6.62 seconds and the 6.74 seconds, the differences are off by 0.12 seconds off but relatively close. By calculating, we have a 1.78% error in the timing.
Conclusion:
-By comparing to the theoretical time 6.74 seconds, there is a 1.78% error, but we could say that they are really close to the true value.
-There are some uncertainties in this experiment:
-Uncertainty from the radii measured.
-Uncertainty from the angle measured.
-Uncertainty from timing the time the cart takes to roll down the distance of 1 meter.
- Overall, we could say that the method we use to find the frictional torque is accurate.
First, I like to note that below are the volumes of the 3 pulleys.
V1/V3: the two cylinders on both sides
V2: The cylinder in between 1 and 3.
In order to find the individual inertias of each of the cylinders, we have to find the mass of each of them. Below is the formula to calculate for an individual mass. Our "M total" is 4.802 kg.
Below are the calculated results for the masses.
m1/m3: the cylinders on both sides.
m2: the cylinder in between 1 and 3.
Now with the masses, we were able to find the total inertia of the system.
Moment of inertia of the cylinder:
Our next step is to find the frictional torque of the system. So, we spun the wheel to calculate the angular acceleration as it's slowing down within the 10 second time range. We jotted down points on the video to allow us to find the positions at multiple time frames, which will eventually give us a chart of a omega/time chart. As a result, we have an angular acceleration of -0.105 rad/s^2
Since we know that Torque= (Total inertia) x (Angular acceleration), we were able to find the frictional torque of the system.
Friction torque= (0.02 kgm^2) x (-0.105 rad/s^2)
Friction torque= -0.0021 N*m
Our second part of the lab was to attach a 547 gram dynamic cart to the apparatus. The cart will be rolling down an inclined track for a distance of 1 meter. The inclined track was angled at approximately 49 degrees.
My lab partners and I timed the cart as it rolls down 1 meter. We performed a total of three trials. As a result, we got:
Trial 1: 6.67 seconds
Trial 2: 6.58 seconds
Trial 3: 6.6 seconds
On average, the time was 6.62 seconds.
Below is the calculated work to compare the results of both the calculated time and the stopwatch time.
As a result, our calculated results was 6.74 seconds.
In comparison to the 6.62 seconds and the 6.74 seconds, the differences are off by 0.12 seconds off but relatively close. By calculating, we have a 1.78% error in the timing.
Conclusion:
-By comparing to the theoretical time 6.74 seconds, there is a 1.78% error, but we could say that they are really close to the true value.
-There are some uncertainties in this experiment:
-Uncertainty from the radii measured.
-Uncertainty from the angle measured.
-Uncertainty from timing the time the cart takes to roll down the distance of 1 meter.
- Overall, we could say that the method we use to find the frictional torque is accurate.
No comments:
Post a Comment