Nov-9-2016: Lab 18 - Moment of Inertia and Frictional Torque

LAB 18 - Moment of Inertia and Frictional Torque

Tony Wu, Michell Kuang, Richard

November 9, 2016

Lab Goal: To understand and test the relationship between moment of inertia of a rotating disk and the frictional torque acting on the apparatus.

Theory/Introduction: We are given the mass of the rotating part of the apparatus at the start of the lab.  However, we need to calculate the mass of large rotating disk. The given mass includes the mass of the disk as well as the metal cylindrical arms.  Using calipers, we measured the dimensions of the disk and the metal arms.  We solved for the mass of the metal disk by using the following ratio:

Mass_of_disk / Total_Mass = Volume_of_Disk / Total Volume

Mass_of_disk = (Volume_of_Disk * Total_Mass) / Total_Volume

Now that we have the mass of the rotating disk, we can calculate its moment of inertia, 1/2 * MR^2. In this lab, we will attach a cart with a string to the rotating metal arm.  Since the apparatus has a certain inertia and frictional torque, we can predict the amount of time it takes for the cart to roll down the ramp.

Below is a free-body diagram of the forces acting in our system.  

Apparatus:

The ramp and string are both placed at a 40 degree angle.  We placed tape down to mark where 1 meter is.

Experimental Procedure: After making appropriate measurements of the rotating disk, we calculate its inertia.  We win the apparatus and use video capture to determine its angular deceleration as it slows down.  Using the video, we calculate the friction torque acting on the apparatus.

 

We calculate the net force on the cart and thus are able to predict the amount of time it takes for the cart to travel 1 meter down the ramp.  We estimate that it would take 10.12 seconds to roll down.  We ran three trials and took the average.

Data and Calculations:

Below are the calculations for estimating the amount of time it take the cart to roll down 1 meter.

 

Conclusions: We were very close to our estimated time, within 2.697% error.  Our average experimental time was 10.393 seconds, compared to our estimated time of 10.12 seconds.  It makes sense that the experimental time is a little longer than the estimated time because there are assumptions made about the setup.  The first error could simply be human error, not accurately stopping our stopwatches.  When we calculated the estimated time, we used 0.5 kg in our calculations instead of the actual mass of the cart, 0.4986 kg.  The cart also has inertia in the wheels that we did not consider.