For this experiment, we will be using the same apparatus that we used in the angular acceleration experiment done, about two labs ago. First, we calculated the theoretical moment of inertia for a triangle using calculus.
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| Deriving the moment of inertia for a triangle about its center. |
To find the moment of inertia about its center, we first had to find the moment of inertia about the end of the triangle. The parallel axis theorem was then used to move the axis of rotation to the middle of the triangle. Once the moment of inertia was found at the center of mass, the experiment was done on the air ring to obtain values that can be compared to the theoretcial value.
The triangle was then mounted on the spinning air disk and the same process used to find the angular acceleration was used. However, this time, moment of inertia of the disk was found. These moments were recorded on the board seen above and compared to the theoretical value also found above. The experiment was done twice with the long side up and the long side down to show that the moment of inertia at the center of mass should not be different. This was also proven as the moment of inertia was very close to each other.
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| The same method as the angular acceleration lab was used but this time, to calculate the experimental moment of inertia |
The moment of inertia when compared to the theoretical was very off due to it being a magnitude off. This may be due to the way the measurements were taken as the expression for the theoretical was correct.
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