![Picture](/uploads/2/6/6/8/26684727/4754839.jpg?380)
Moment of Inertia Lab
Lab Partners: Michael Perkins, Kyle Troch, Ben Ronemus
Date Completed: April 4th
Lab Partners: Michael Perkins, Kyle Troch, Ben Ronemus
Date Completed: April 4th
Purpose
The purpose of the lab is to calculate the moment of inertia of a platform and a ring using torque and acceleration; to compare it to the measured inertia.
Theory
The moment of inertia defines how much torque would be needed to reach a sustained angular acceleration. Inertia can be found by multiplying the mass of an object and it's radius, but these equations occur for different objects with a different rotation axis. For example finding the inertia of a thin hoop with a rotation axis through the center can be found using MR^2. But to find the inertia of a thin hoop with a rotation axis through a central diameter it can be found using one half MR^2 plus one twelfth MW^2. For our purposes however we are going to try to find inertia after knowing the torque and acceleration. That would be found by dividing torque by the angular acceleration.
Experimental Technique
![Picture](/uploads/2/6/6/8/26684727/1109797.jpg?377)
As seen in the photo we have attached a plastic weight holder to a string that moves around the friction less pulley. The string is then attached to a rotation sensor that will start spinning when the weight is let go. The silver disk that is shown sits on top of the rotation sensor. We use that disk to find our first acceleration. Then we added the black ring on top of the disk to find our second acceleration. I tested it using .150 kilogram weight plus .005 kilograms for the plastic hanger.
Data and analysis
First I summed the forces and arranged it so we can solve for tension. Then I used the torque equation for tension and arranged that to solve for inertia. Once I had it solved I took what I found for tension and substituted it (first picture to second picture). Next, I plugged in the numbers to find the inertia of the disk only (top picture). Then I plugged in the numbers to find the inertia of the disk and ring (bottom picture). Lastly I subtracted the disk and ring inertia from the disk inertia to get the inertia of the ring. That gave me .0006 kgm^2.
Once I found the inertia of the two objects I found the percent difference of the between the measured and calculated. I got 183% difference for the disk and 18.6% for the ring.
Conclusion
The purpose of the lab was achieved because we were able to measure the inertia but I did not do it accurately. As one can tell my answers were very off from the actual inertia. I think I was inaccurate with my lab mainly do to my own incompetence. My equation was most likely wrong but even so there were a couple things that could have strew the information. If the whole system was not level I do not think it would have spun right. Also the string might not have been pulled in a perfect tangent and that could have caused more friction. Overall the lab could have been more effective if I did not mess up somewhere with the calculations.
Refrences
http://physics.bu.edu/~duffy/py105/Torque.html