Lab 17 Moment of inertia of a uniform triangle

Ana Leyva, Jonathan Goei
5/22/17

By doing this lab we are trying to find the moment of inertia of a uniform right triangle for two different orientations.

We did this experiment two ways we took a theoretical approach to the problem and an experimental approach. For the theoretical approach we used the parallel axis theorem to help us find the moment of inertia around the center of mass. However instead of getting the moment of inertia around the center of mass and then using that to find the moment of inertia around a parallel axis we did it the other way around. We first found the moment of inertia around the edge and then used that to find the moment of inertia around the center of mass. For our experimental approach we used the information from the second part of lab 16 to find the moment of inertia of the apparatus by itself and of the apparatus plus the triangle in two different orientations. We used the same apparatus from lab 16 and logger pro to help us find the average angular acceleration which we then plugged into the equation that was derived for us in lab 16 to help us solve for the moment of inertia. We then used these moments of inertia to help us find the the moment of inertia of the triangles by themselves.

To start of the experimental part of this experiment we first found the angular acceleration of the apparatus without mounting a triangle to it. We then used logger pro to help us calculate the angular acceleration of the apparatus system. We did this because by finding the angular acceleration of the system we can then find the moment of inertia of the system, After finding the values of the apparatus by itself we then mounted the triangle in two different orientations and calculated the moment of inertia for both of those. After gathering that data, we used the formula for the moment of inertia that we had been given in the previous experiment to calculate the moment of inertia of the the system and the triangle plus the system. Once we did that we were then able to subtract the moment of inertia of the apparatus plus the triangle minus the moment of inertia of the apparatus by itself. This gave us the moment of inertia of the triangle by itself.
For the theoretical approach of this problem we first found the center of mass of the triangle. We then found the moment of inertia of the triangle around an edge. We then used this information plus the parallel axis theorem to find the moment of inertia around the center of mass. In order to solve for this we had to first measure the triangle and find the mass of the triangle.

Measured Data

Angular acceleration calculations

Moment of Inertia Calculations

Moment of inertia of the triangles 

Theoretical Approach to find the Moment of Inertia around center of mass

Graphs that helped us calculate angular acceleration

With these previous graphs we were able to calculate the average acceleration of the apparatus and the apparatus plus the triangle placed in two different ways. 

Conclusion: Based on our theoretical and experimental results we did a good job in calculating the moment of inertia both ways. this is because both results were so close to each other. However although they are really close to each other they are not exactly the same this could be due to the frictional torque in the system. You can tell that there is a friction in our apparatus because the acceleration of the mass going down isn't the same as when the mass is going up. The difference in our experimental and theoretical value when the triangle the long side standing was of 0.00005 and when the long side of the triangle was horizontal the difference was of 0.00009 this difference is very small which helps us conclude that our theoretical and experimental values were really close to each other.