09-Nov-2016: Lab 18 Problem-Moment of Inertia and FrictionalTorque

1. Title: Lab 18 Problem-Moment of Inertia and Frictional Torque
    Name: Sherry Ye
    Group Partners: Xavier
    Date: 09-Nov-2016

 2. Purpose
In this experiment, we determined the moment of inertia of an spinning object and the friction torque in the system. Calculated the acceleration of the object in order to find the time that a car was driving 1 meter.

3. Introduction
When the metal disk was rotating, there had friction force between disk and its central shaft. We would divided the metal disk into three parts to calculated it the moment of inertia, including two cylinders and one disk as shown. After, we found the moment of inertia of the object, use torque formula (torque*r=I*alpha) and liner motion formula( y=vt+1/2at^2) to find the time that the cart traveled in one meter.

4. Apparatus/Experimental Procedure
1) Apparatus
A metal disk with two cylinders on both side, a track, a car, a scale, and a string.
2) Experimental Procedure
Used scale to measured the metal disk. The measurement should be include the depth and diameter of the disk, the height and diameter of two cylinders. 

Set up the sensor to find the angular acceleration of the apparatus by Logger Pro.

Placed the track one side on the ground; another side on the lab table, that we would created the angle between the ground and the track. Used the string tired the car and the metal disk in order to let the car can travel one meter on the track.

5. Measured data and Calculation

Divided the metal disk into three parts: 2 cylinders and one disk. Once all the appropriate measurements have been taken, we could calculate the volume of each individual piece of the apparatus. Added them together to find the total volume of the apparatus. Used the relationship of the mass and volume, used the mass of cylinders divided the mass of the rotating part of the apparatus (is stamped onto the disk) were equal to the volume of the cylinder and the total volume. After, found the mass of the cylinder, we could find the mass of the disk. Finally, used the moment of inertia formula (I=1/2MR^2) to each piece moment of inertia and added together to get the whole system of the moment of inertia. 

After we determined the moment of inertia, we used the log pro to find the angular acceleration of the apparatus that we got the graph of time and rotational displacement.

We got the function about rotational displacement, then we took the derivative, we could get the equation about angular acceleration:

After we found the values of angular acceleration and the moment of inertia of the system. We draw the free body diagram in rotational motion in order to set up the equation about torque and force. Then, used the values to find the acceleration of the car, and the time that the car traveled one meter. After we got the value of the time, we placed the car on the track and let it go one meter to record the time its traveled. We ran the same trails three time and got the average of them. Compared both time, determined the different percent was less than 4%.

We ran the car three times and recorded each time was 7.35s, 7.32s, and 7.36s. The average of them was 7.34s, compared the to the calculated time 7.38s, the different percent of them was 0.68 %.

6. Conclusion
In this experiment, we combined the methods of using Newton's second law, torque and moment of inertia knowledge to find the acceleration and time. We used sensor to record the rotational displacement instead of using video method to find the angular acceleration because we thought the video method was more complicated than the sensor. Overall, we found the time very close the our experiment was perfect.