December 4,2014. Moment of Inertia of a uniform triangle about its center of mass

Purpose: To be able to calculate the moment of inertia of a uniform triangle about its center of mass.

Apparatus: We used a Triangle, disk, hanging mass, a sensor, and a piece of string.

What we did:  First we took the measurements of the triangle.

 Next we got the apparatus. We tied a string onto the apparatus  with a hanging mass on the other end. Then we got the string and put it over a pulley. Next we opened up the hose clamp so that the bottom disk could rotated independently from the top disk. After doing this we opened up logger pro and opened up our sensors. We used the Rorary motion sensor and used the setting to count 200 marks per rotation.  Finally we collected our data. The slope of these graphs were the angular acceleration/ deceleration. In order to get our alpha we used ( alpha of hanging mass rising + alpha of the hanging mass dropping and we divided it by two. This gave us an average alpha to use in our calculations. 

Part two: We mounted the triangle in a vertical position and used the same technique to find alpha for the apparatus to find the alpha of the apparatus with the triangle.

Next we mounted the triangle horizontally and used the same technique to find alpha for the system while the triangle is horizontal.

Finally we used all the alphas to calculate the moment of inertial of each situation based on the hanging mass and the angular acceleration (alpha) In order to get the inertia of the triangles alone we had to find the inertia of the system with the triangle and subtract the inertia of the system with out the triangle.

Below are all of our calculations

INERTIA

Conclusion: Using all these different formulas we were able to get the actual inertia of the triangle in both positions. My lab partners Isaac and Mathew had a major role in this Lab. They guided  and showed me how to get all of these calculations.