Procedure: Because this triangle has an irregular shape we do not have an inertia formula that we can just plug values into. We will have to create our own by setting up an integral where we selected a vertical slice of the shape as our dm and integrated from the tall edge to the point. However, by doing this we found the inertia as if we were rotating about the outter edge. Thankfully we can now use the parallel axis theorem to find the moment of inertia and solve for the inertia about its central axis!
Now for the eperimental calculations we set up an air table with rotating disks and a hanging mass like in our previous angular acceleration/ inertia lab. The difference is that now we already know what the moment of inertia for the disk should be, so when we set up a system with the additional tiangle mounted on top we can subtract the inetria provided by the disk to find the inertia of the triangle.
We set up logger pro to collect and graph data on the angular velocity of the rotating system. We had logger pro analyze linear fits for the velocity vs time graphs and we averaged the values to find out angular acceleration.
Now that we have collected all the values we need to solve for the system and triangle inertia, we set up tangential and angular equations and manipulated them to solve fot the total inertia of the system. As stated before we calculated the inertia of the triangle by subtracting the inertia of the disk from the inertia for the entire system.
Once finding Our theoretical value for the triangle's inertia we compared it to the theoretical value and came up with very small percent errors. These errors could be due to the air pressure not being set perfectly or minor frictions throughout the system.
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