Purpose
The purpose of this lab is to find the moment of inertia of the rotating mass using angular acceleration, torque, the radius, and the hanging mass.
Theory
Moment of Inertia is the sum of the masses of each particle in the body multiplied by the square of the distance of that particle from the axis of rotation. It is used to find torque, and in reverse, torque and angular acceleration can be used to find moment of Inertia. Below are equations to find the moment of inertia for objects. Then beneath that is the equation for torque.
Experimental Technique
We set up a rotary motion sensor to a computer and on top of the rotary motion sensor we attached a disk or platform and found out the moment of inertia of that first. Then once it came to rest we set a ring on the top of the disk and found the moment of inertia for the two combined. Below are the equations I used to find how to solve for the moment of inertia, using the summation of forces using weight and tension.
Data & Analysis
Above are tables that inform you of the masses, radii, and moments of inertia of the disk and the ring we used. Below those tables is the final equation for the moment of inertia. We got .14kgm^2 as our final answer.
![Picture](/uploads/8/6/7/7/8677251/9408708.png?485)
This is a graph represents the angular velocity of the ring and the disk together.
![Picture](/uploads/8/6/7/7/8677251/3757820.png)
Percent difference is how far apart the answers we got using the two different methods of acquiring them. We came up with a 28% difference between the two methods.
Conclusion
The purpose of the lab was to find the moment of inertia using torque and angular acceleration. I did find moment of inertia, although it was not as accurate as I had hoped. Possible problems may have been in measurement, rounding, or even the equation itself. I suspect most of the error came for measuring and interpreting the graph off of data studio. However, the 28% difference is not extremely terrible, so it may have accomplished a bit of the purpose. It could have been better if I would have taken more accurate measurements or perhaps checked my math work.