Lab 16: Moment of Inertia and Frictional Torque

Physics Lab #16 started on 5/11/15
Moment of Inertia and Frictional Torque
Annemarie Branks
Professor Wolf

Objective: Determine the moment of Inertia of the disks. If a falling mass is tied to the rotating disks, determine how long it would take for the mass to travel one meter at a certain angle.

Procedure:
     1.  Using a rotational apparatus like the one on the picture below, determine the apparatus's mass and dimensions. The apparatus had its total mass engraved on it, so we found the mass for each of the sections (using a volume to mass ratio) as well as their measurements using Vernier calipers. After doing so, we found the total Inertia of the system simply be adding the inertia of the individual sections. The accepted inertia for both a disk and a cylinder is 0.5MR^2.

Here are our measurements for this particular apparatus which gave us a net Inertia of 0.0209 kg*m^2.

     2.  Set up a camera an connect it to LoggerPro. Spin the apparatus and use video capture to mark its positional rotation. We added a piece of tape a drew a purple dot so we could better see and indicate where to make out marks. Form a theta (radians) versus time (seconds) graph. 

To generate the best of fit, we used a quadratic fit because of the equation θfinal = 0.5αx^2+ωx+θ

     3.  The A values, when averaged, will help give the angular acceleration of the system which in our case is -0.5644 rad/s^2. With this we can find frictional torque when considering the equation Torque=Inertia*angular acceleration. Our frictional torque is -0.01180 N*m..

     4.  The professor asked us to solve acceleration of the cart in a system like the one shown in the photo below where the ramp is at a 40 degree angle. 

     Using Newton's Second Law, first find the acceleration (which ended up being 0.0281 m/s^2) and then use kinematics to find the time it took to travel one meter. The calculations are shown below. The time it takes the cart to theoretically travel one meter at a 40 degree angle is 8.45 seconds.

     Now, simply replace the 40 degree angle for the actual angle and find the time it theoretically takes the cart to travel one meter. In our case the acceleration came out to be 0.0.409 m/s^2. This acceleration gave us a time of 6.99 seconds.

     5.  With the system set up at your actual angle, and the cart's string wrapped around the smaller cylinder, let go of the cart so that it will slide down 1 meter. Use a stopwatch to find the time it takes to travel that one meter and see if it matches up with your calculations.

     For our experiment, we conducted three trials.

Trial 1: 6.9 seconds

Trial 2: 6.8 seconds

Trial 3: 6.9 seconds

     These times are extremely close to the theoretical time, so we can say that we accurately found the system's moment of inertia and frictional torque.

Sources of Uncertainty/Error:

• Though the times for the trials are "desirable", there is still uncertainty in the stopwatch and the reaction time of the person using the stopwatch.
• There are uncertainties in the measurements and in the calipers being used
• There are uncertainties in the LoggerPro program
• There is a human uncertainty when plotting the points on LoggerPro. We plotted points at the tape mark which was not exactly at disk's edge.