Lab 18 - A Lab Problem- Moment of Inertia and Frictional Torque

Purpose: To predict the time for a cart on a downward-angled track to descend 1meter at a 40 degree incline, that is tied by a light string to a large metal disk that will spin as the cart descends. We will do this by first calculating frictional torque for the heavy metal disk.

Apparatus: A large, heavy metal cylinder on a lathe-like stand with known mass, and unknown moment of inertia. A cart-track is angled down off the edge of the lab table at a 40 degree angle with the horizontal. A cart is tied to a light string, which is then wound around the smaller diameter of the large disk, which will exert a torque on the disk as the cart descends down the ramp a distance of 1meter.

Procedure: We first started by calculating the frictional torque of the large disk by placing a piece of tape on the large disk, somewhere around the outer diameter and marking it with a dot. Then we recorded a video while it spun, and slowed down with friction in its own axis. We then used logger pro to pinpoint the location of the dot as it went around in a circle. We then plotted linear velocity vs. time to get a linear acceleration (deceleration). After we figured out a linear acceleration, it was easy to find α by simply dividing the linear acceleration by the radius from the axis of rotation to the dot.

Below is a picture of the whiteboard where we recorded all of the dimensional information for the wheel as we measured it. The total mass was stamped on the wheel, which was 4.862kg. After we summed up all of the volume for the different sections of the wheel, we used ratios of volume/total volume = mass of section/total mass to figure out how much each piece of the wheel weighed. This is because the wheel was a large disk, with a smaller diameter cylinder protruding out the sides through the axis of rotation, so each piece has a different moment of inertia.

 After calculating how much mass is distributed to the cylinders and to the disk, it was pretty straight-forward to calculate the moment of inertia of each piece. Then, the moments were summed up in order to know the moment of inertia for the wheel as a single piece.

 Frictional torque  = Iα
α = derived from the video earlier on logger pro.

This is a picture of the apparatus all put together in the end. Most of the time was spent calculating the frictional torque for the metal disk in order to accurately calculate the predicted time of descent.

Trial 1: 10.22 sec
Trial 2: 10.85 sec
Trial 3: 10.07 sec

Average: 10.36 sec

 Theoretical: 10.43 sec

Percent Error: 0.70%

 Below are my calculations for the theoretical time of descent.

Conclusion: In this lab I learned that any object that is spinning has some kind of frictional torque. This is because if there wasn't, the object would just keep spinning forever and that is impossible. I learned that I can express the amount of friction inside a spinning system as a torque value. This is important because this makes it fairly easy to calculate how friction inside a rotating assembly will affect the motion of other things in the system. I was a little weird to see that our average value for the time it took the cart to travel 1m was smaller than the theoretical. This could be due to many reasons, one being human error. There is much room for error when timing the cart to descend 1 meter because certain things such as reaction time for the stopping and starting of the stopwatch can vary from person to person, and even trial to trial. Another reason is that we calculated the frictional torque and ran the trials on two separate days. On the second day we noticed that the wheel had started to squeak, which probably indicated that for one reason or another (maybe more moisture in the room), there may have been slightly different values for the frictional torque. It was pretty cool to be able to relate linear kinematics with rotational kinematics and rotational friction. 

My lab partners were Mia and Jarrod.