Purpose: The purpose of this lab is to determine the moment of inertia of a right triangular thin plate around its center of mass, for two perpendicular orientations of the triangle.
Theory:
Finding the moment of axis for a triangle is much easier around the axis at the edge than the center of mass, so finding the moment of inertia of a triangle around its center mass needs the parallel axis theorem.
By using the disk rotation system, we can measure the angular acceleration of the system and use that to find the moment of inertia of the system. The moment of inertia of the triangle would be the difference in the moment of inertia of the system and with a triangle attached.
Data:
Calculations:
Calculation for the theoretical moment of inertia around the center of mass of the two triangles
Calculation for the experimental moment of inertia around the center of mass
Analysis:
This is the derivation of how the moment of inertia for the center of mass is found theoretically.
Conclusions:
The results were all within 10%, which is a decent result. Where the most error may have occurred is the measurement of angular acceleration, as the apparatus was not entirely frictionless. Even though it is already accounted for in the calculation, it is still someplace error could have occurred. Another would be the fact that the triangular plates still has some mass to it, even though we considered it to be negligible.
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