Torque and Moments of Inertia (Disk)

Purpose: The purpose of the lab was to calculate the time at which a cart will reach the bottom of an inclined ramp by using the moment of inertia of the apparatus, which in this case was a solid uniform disk with a solid uniform cylinder in the center of the disk.

Procedure: Below is a picture of the disk and cylinder system. The moment of inertia was found by measuring the different parts of the systems like the radius of both the width as well as the diameter and mass.

Below is what the final set up would look like. By finding the moment of inertia of the system, a time can be found for when the cart reaches the bottom.

In order to get the time, the angular deceleration was needed so that the frictional torque of the system could be found. This was done by using Logger Pro with video capture and using a graph to find the angular deceleration of the system. Then we were given a problem where we had to find the time it took for a cart attached to the rotating system to reach the ground at a certain angle. The values were given to us and we solved it like regular problem. It served as a way to help us find the time of the system we had to physically set up.

Data: The data table below shows the information we got from Logger Pro when using video capture in order to find the deceleration of the system.

The graph below shows the angular velocity in the x and y direction which was used to acquire the angular deceleration of the system.

Using the equation Vt = sqrt(Vx^2 + Vy^2), the tangential velocity can be found and the graph below shows how the slope gives that tangential velocity.

Calculations: The calculations below are for how we solved the moment of inertia of the disk and cylinder system. The result was 1.92 x 10^-2 kg*m^2.

The calculations below show how the frictional torque, angular acceleration and the time it took the cart to drop 1 meter were acquired.

Summary: The lab was not a success because the time we calculated was off from what physically got. The ramp's angle in the calculated portion was 46 degrees and the time it took was 9.5 seconds. On the other hand, we physically set the ramp up to try and match that angle but we got about 12.5 seconds instead which is about 24% of error. We believe that the disk-cylinder system was tampered with or it was getting stuck somehow because after doing the trial multiple times the time kept increasing. Below is what the set up looked like at the end.