The purpose of this lab is to find the moment of inertia of a triangle using calculus and comparing the theoretical results to the actual.
Apparatus:
We mounted the triangle on a holder and disk, attached the air tube to a supply of air, and attached a pulley
between the disk and triangle with a string wrapped around the pulley. On the other end of the string is a hanging mass of 25 g. With the system released, the hanging mass should pull on the pulley and the disk should be spinning on on a cushion of air, for frictionless rotation. The triangle spins at a certain angular acceleration.
Explanation:
My partners for this lab was Kenji Karuhaka, Ivan Contreras, and Henry Shih. We derived an equation for the moment of inertia, show below.
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| The equation of inertia |
The graph above shows how we obtained the angular acceleration using Logger Pro. According to Logger Pro, our acceleration was around 1.8173 rad/s2. We came up with an expression to evaluate the actual moment of inertia of the spinning triangle. The calculation below shows the actual and the theoretical moment of inertia. The theoretical inertia was 5.609*10-4, and the actual moment of inertia was 3.35*10-3, which gives us a significantly large percent error of almost 500%.
Conclusion:
We first derived an equation for the theoretical moment of inertia of a right triangle spinning at the center mass. Then we expressed the actual moment of inertia using Newton's 2nd law. In the end, our percent error was massively large. The large percent error was due to the fact that we didn't take the inertia of the disk into account when calculating for moment of inertia. With the mass of the disk added into the equation, moment of inertia should be larger, and would giving us a significantly smaller percent error.
You need to subtract the moment of inertia of the apparatus from the moment without the triangle. The difference in I's is the moment of inertia of the triangle.
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